REGULATION OF STREAM FLOW FOR MILITARY PURPOSES

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• Release Decision: RIPPUB
• Original Classification: K
• Document Page Count: 52
• Document Creation Date: December 27, 2016
• Document Release Date: October 25, 2013
• Sequence Number: 3
• Publication Date: June 1, 1957
• Content Type: REPORT

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REGULATION OF STREAM FLOW
FOR MILITARY PURPOSES
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11
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11
MILITARY HYDROLOGY BULLETIN 11
JUNE 1957
A
CORPS OF ENGINEERS
RESEARCH AND DEVELOPMENT REPORT
PREPARED UNDER DIRECTION OF
CHIEF OF ENGINEERS
BY
MILITARY HYDROLOGY R & D BRANCH
U. S. ARMY ENGINEER DISTRICT, WASHINGTON
STAT
STAT
202469
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Military Hydrology R&D Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 pp. illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
Unclassified Report
UNCLASSIFIED
1. Military Hydrology
2. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
Military Hydrology R&D Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 pp. illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
Unclassified Report
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
UNCLASSIFIED
I. Military Hydrology
2. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
Military Hydrology R&D Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 pp. illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin presents methods of computation of
operation ot dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
UNCLASSIFIED
1. Military Hydrology
2. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
Military Hydrology R&D Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 pp. illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
UNCLASSIFIED
1. Military Hydrology
2. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
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1
1
S.
Military Hydrology R&D Branch, U.S. Army Engineer
UNCLASSIFIED
Military Hydrology R&D Branch, U.S. Army Engineer
UNCLASSIFIED
District, Washington, D. C.
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
L. Military Hydrology
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
1.
Military Hydrology
June 1957, 31 pp. illus. 20 tables & plates
2. Dam Outlet Releases
June 1957, 31 pp. illus. 20 tables & plates
2.
Dam Outlet Releases
(Military Hydrology Bulletin 11)
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
I. U. S. Army Engineer DA R&D Project 8-97-10-003
I.
U. S. Army Engineer
District, Washington
District, Washington
Military Hydrology
Military Hydrology
Unclassified Report
Bulletin 11
Unclassified Report
Bulletin 11
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
Military Hydrology R&D Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 PP- illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
UNCLASSIFIED
1. Military Hydrology
2. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
Military Hydrology RED Branch, U.S. Army Engineer
District, Washington, D. C.
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
June 1957, 31 pp. illus. 20 tables & plates
(Military Hydrology Bulletin 11)
DA R&D Project 8-97-10-003
Unclassified Report
This bulletin presents methods of computation of
operation of dam outlets to produce controlled
variation in river depth, width, and velocity at
downstream points, including methods of evalu-
ating the proper magnitude, duration, and timing
of reservoir releases and the downstream hydraulic
effects.
UNCLASSIFIED
1. Military Hydrology
2.. Dam Outlet Releases
I. U.S. Army Engineer
District, Washington
Military Hydrology
Bulletin 11
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-*MILITARY HYDROLOGY BULLETIN 11
REGULATION OF STREAM FLOW FOR MILITARY PURPOSES
PREPARED IN CONNECTION WITH
RESEARCH AND DEVELOPMENT PROJECT NO. 8-97-10-003
FOR
ENGINEER RESEARCH & DEVELOPMENT DIVISION
OFFICE, CHIEF OF ENGINEERS
BY
MILITARY HYDROLOGY R&D BRANCH
U.S. ARMY ENGINEER DISTRICT, WASHINGTON
CCaPS,OF ENGINEERS
JUNE 1957
PRINTED Br ARMY MAP SERVICE, maps OF ENUI1TERSy 3-58
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PREFACE
This bulletin is the eleventh of a series dealing with the
various aspects of hydrology involved in military operations
and with the hydrologic techniques and methods of analysis
which are considered most suitable for Army use. A number of
these techniques were developed in the course of Research and
Development Project No. 8-97-10-003, assigned to the Army
Engineer District, Washington, on 14 March 1951 by the Office,
Chief of Engineers. Printing of the Bulletin was authorized
by the Office, Chief of Engineers, on 9 May 1957.
Mr. A. L. Cochran of the Office, Chief of Engineers, formu-
lated the objectives and scope of this Bulletin. Mr. B. G.
Baker developed the original procedures and Mr. W. B. Craig
prepared the final method and text under the supervision of
Mr. R. L. Irwin and Mr. F. B. garkalow, Military:Hydrology
R&D Branch, Washington District.
iii
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PREFACE
SUMMARY
Paragraph
CONTENTS
CHAPTER I: INTRODUCTION
1 Purpose 1
2 Scope 1
3 Discussion of Problem 1
4 Arrangement 2
5 Related References 2
CHAPTER II: PRINCIPLES AND BASIC THEORY
6 Pertinent Factors 3
7 Reservoir Effective Storage 3
8 Reservoir Regulated Outflow 4
9 Physical Characteristics 5
10 Hydraulic Elements 5
11 Average Wave Velocity 6
12 Determination of AK 6
13 Determination of ZK 7
14 Determination of At 7
CHAPTER III: FLOOD ROUTING BY THE SEMI-GRAPHICAL METHOD
15 Semi-Graphical Method 9
16 Basis of Derivation of Semi-Graphical Method 9
17 Peak Modification Curves 9
18 Weighted Discharge 10
19 Hydrograph Ordinates 11
20 Downstream Hydrograph Peak (P0) 13
21 Release Hydrograph Peak (Pi) 13
22 Procedure for Solution 13
23 Average Hydraulic Characteristics of Reach 13
24 Duration of Initial Block Hydrograph (Li) 14
25 Time of Downstream Peak 14
26 Time of Beginning of Rise of Downstream Hydrograph 14
27 Downstream Hydrograph Shape 14
28 Verification of Results 15
29 Discussion of Adopted Flood Routing Method 15
30 Cyclical Disbharges 15
31 Efficiency Ratio 16
32 Duration of Cycle 17
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iaragraph
CONTENTS (CONT)
CHAPTER IV: GATE-OPERATION SCHEDULE
Page
33 Problem 19
34 Initial Data 19
35 Schedule of Reservoir Water Surface 19
36 Gate Opening and Discharge 20
37 Principles of Selecting the Gate Opening 20
38 Gate-Operation Schedule 21
39 Adjustment of Outflow Hydrograph Peak 21
40 Cyclical Releases 22
CHAPTER V: EXAMPLES
41 Outline of Examples
42 Problem I
43 Problem II
44 Problem III
REFERENCES
LIST OF PLATES
vi
447 23
23
26
27
29
31
SUMMARY
Military crossings of major rivers in the face of the enemy
represent engineering achievements of a high order, even when
normal river conditions prevail. When natural river flows and
stages are augmented by carefully-timed flood-wave releases of
predetermined magnitude from upstream reservoirs, the dif-
ficulties encountered in the crossing operation may well become
almost insurmountable. This manual describes the hydraulic
factors involved in the release of a flood wave through the
outlet structures of a dam to produce sudden changes in depth,
width, and current velocity at the downstream crossing site.
It then presents formulas and short-cut methods of evaluating
these effects, with examples. Lastly, the manual includes a
discussion of cyclical flood waves, produced by a series of
reservoir releases.
vii
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CHAPTER I
INTRODUCTION
Par. 1
1. Purpose. The purpose of this bulletin is to discuss the sudden
changes in discharges, depths, velocities, and widths of streams created
by manipulating the regulating outlets of a dam; and to provide methods
for obtaining rapid estimates of such effects, which are suitable for
hydraulic studies pertaining to military operations.
2. Scope. The bulletin presents an analysis of the factors involved
in estimating reservoir releases to effect desired hydraulic conditions
at selected points downstream. While the analysis presented herein is
oriented toward establishing the timing and manner of operation at dam
outlets to produce a desired hydrograph at a selected point downstream,
essentially the same procedures can also be used where it is necessary
to estimate the downstream results from given outlet operations. The
bulletin outlines the data required to establish the outflow hydrograph
at a dam outlet or outlets, and the factors which modify the outflow
hydrograph as it travels downstream. A semigraphical method of routing
the reservoir outflow hydrograph from the dam to the downstream point is
presented. The construction of solution diagrams is facilitated by
utilizing a coefficient expressing the relationship between discharge
and storage. The methods for deriving a gate operation schedule to
produce a block-type reservoir outflow hydrograph meeting the downstream
requirements are outlined. A procedure is developed to determine the
effect of cyclical flood waves, consisting of a series of block releases
alternated by periods of low flow. Examples are then given to illustrate
the application of the derived equations and diagrams to specific problems.
3. Discussion of Problem. a. Many high dams impounding large volumes
of water have been constructed throughout the world's potential theaters
of operation, and have important military capabilities for artificial
flooding. The term "artificial flooding" is used in this manual to denote
an artificially-created increase in stage over the existing natural-flow
conditions in a stream or area. It is generally accomplished by increasing
the streamflow by regulation or breaching of dams, or by creating drainage
obstacles. The manipulation of the regulating outlets of a dam to produce
sudden changes in stream discharge, thereby affecting the depth, width, and
velocity throughout the stream channel, is one example of the techniques
of artificial flooding.
b. A given hydraulic system, consisting of one or more reservoirs
in a river basin, may have certain capabilities for offensive or defensive
operations that are of major importance to a field commander. Artificial
flooding operations have proven to be a definite obstacle in the assault
of a river line, as encountered by our forces during the Rapido and Ruhr
Rivet crossing operations in World War II. Experience has shown that it
is extremely difficult to assault a fortified river line if there are
major fluctuations in the stream stages, surface widths, or velocities.
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Par. 3 b
Under such conditions assault boats are carried far downstream in the
high-velocity current and tactical control may be lost. The second
phase of the crossing operation, raft and bridge construction, is
even more critical, since its completion is required for the build-
up of the heavy weapons necessary in securing the bridgehead against
an enemy counterattack. Cyclical floodwaves, created by block reser-
voir releases above the bridgehead spaced at appropriate intervals
during this phase of the crossing, would make almost impossible the
construction of rafts and bridges and the build-up of fire support.
Without an adequate and rapid build-up of the fire-support echelon
of the attacking forces, a river-crossing operation is normally doomed
to failure. From the above considerations it is apparent that the
field commander should be informed of the capabilities of hydraulic
structures in his vicinity to disrupt or aid his military operations,
and that he should be furnished data as accurate and as far in advance
as possible on the depths, widths, and velocities of artificial flood
waves resulting from the use of these structures as weapons of war-
fare.
4. Arrangement. The remaining chapters of the bulletin are
arranged to provide a logical development of the techniques of so-
lution of artificial flood wave problems. Chapter II presents the
basic hydraulic principles and theory directly involved in the so-
lution. Chapter III describes a sami-graphical method, convenient
for military use, of determining the extent of modification of the
reservoir outflow hydrograph as it travels downstream to the target
point. Chapter IV outlines methods of determining gate operation
schedules of reservoir releases. Lastly, Chapter V presents
examples of solution of specific flood-wave problems, using the
methods described in the preceding chapters. Plates providing graphic
illustrations and detailed explanation of the text, are presented at
the end of the bulletin.
5. Related References. A bibliography of related references
appears in the rear of the manual following the text. The following
bulletins, also prepared by the Military Hydrology R&D Branch, are
of special significance as they are frequently referred to in this
bulletin:
Military Hydrology Bulletin 10, "Artificial' Flood Waves".
Military Hydrology Bulletin 12, "Handbook of Hydraulics".
Dept. of the Army Technical Bulletin, TB 5-550-3 "Flood
Prediction Techniques".
2
Par. 6
CHAPTER II
PRINCIPLES AND BASIC THEORY
6. Pertinent Factors. The determination of possible streamflow
variation as a result of operating dam outlets requires a knowledge
of several pertinent factors. These include the physical and hy-
draulic characteristics of the reservoir, the dam and appurtenant
works, and the reaches of the stream from the dam to the stream lo-
cation where artificially regulated patterns of discharge and stage
are to be determined. In the case where a certain magnitude of
stage and frequency of variation cycle is desired at a given stream
location, there is required, in addition to the aforementioned data,
the amount of water available for regulation, and the character-
istics of the outlet structures including the rate of opening and
closing the outlets. The shape of the outflow hydrograph during its
passage downstream is a function of the physical and hydraulic
characteristics of the stream which include the slope of the stream,
configuration and dimensions of the stream boundaries, meander
pattern, changes in cross section, vegetative .cover, sediment-character-
istics (sediment size, sand bars, etc.), length of water course and
other factors. Depth and velocities of flow at selected locations
depend upon the discharge and upon the shape and dimensions of the
cross section at that location. Having determined the discharge
through routing procedures and knowing the cross-sectional character-
istics, depths of flow and velocities at problem locations may be
readily determined. The way in which the techniques of streamflow
regulation are affected by the physical and hydraulic characteristics
of the stream channel are described in the following paragraphs.
7. Reservoir Effective Storage. a. Streamf low regulation, to
be effective as a military weapon, requires an adequate supply of water
for a specific period of time. The effective reservoir storage is
defined as the water stored above the spillway crest or above the gate
seats of the outlet conduits. In any river hydraulic system, the
effective storage is the most important single factor in determining
the capability of the system for artificial flooding. Normally over
one-half the storage of a reservoir is impounded in the upper quarter
of its depth. This portion of the storage, impounded at a high head,
creates high discharge rates through the outlet structures and thus
constitutes a favorable condition for artificial flooding. Heavy
rainfalls may occur over the drainage basin during certain periods of
the year, and the resulting inflows would augment the capabilities of
the reservoir for artificial flooding.
b. The effective storage of a reservoir at a given pool
elevation is obtained by subtracting from the total storage at that
elevation the storage at the elevation of the lowest outlet struc-
ture. These values are taken from the elevation-capacity curve, which
is usually obtained by the following method:
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Par. 7 b
(1) Planimeter the area within each contour of elevation
on a topographic map of the reservoir site, and by subtraction compute
the areas within adjacent contours;
(2) Multiply the area within adjacent contours by their
difference in elevation, and accumulate these products;
(3) Plot the accumulated products against the correspond-
ing upper-contour elevations.
c. A method of estimating the reservoir capacity curve is
given in "Engineering Construction - Flood Control" by the Engineer
School, Ft. Belvoir, Va., and in MH Bulletin 10, "Artificial Flood
Waves", by the U. S. Army Engineer District, Washington. In this method,
the storage curve is computed by a simple exponential equation in
which the exponent is selected from a table based on a general classifi-
cation of the terrain characteristics of the reservoir site.
8. Reservoir Regulated Outflow. The regulated outflow from a
dam, as considered in this bulletin, consists of either a single
block hydrograph or a series of cyclical block hydrographs released
through the outlet structures. The peak discharge, duration, and
timing of these hydrographs must be selected in such a way as to
satisfy critical downstream requirements pertaining to depth,
velocity, etc. This selection must take into consideration the
modification of the outflow hydrograph by channel conditions as it
proceeds downstream. An equally important consideration in making
this selection, however, is the discharge capacity of the outlet
structures in relation to the amount of effective reservoir storage.
A block release hydrograph with a high peak and of short duration
may accomplish with greater economy of water volume the same result
at the target location as a release hydrograph with a lower peak and
of longer duration. Of course, the capacity of the reservoir outlets
must be sufficient to release a discharge that will give the required
flood hydrograph at the problem location. When the gates on the struc-
ture can be rapidly opened, the resulting flood wave may advance as a
bore, causing a rapid change in stage and thus producing damage not
obtainable by high velocities alone. The maximum discharge that can
be released at any given reservoir elevation is determined from the
combined discharge rating curve of all the outlet structures, computed
by methods described in MH Bulletin 12 "Handbook of Hydraulics", from
the physical description of the spillway and outlet works. When the
various components of the problem (including the target objectives,
downstream hydrograph modification, storage available, and outlet
discharge capacity) have been determined, the peak discharge,
duration, and timing of the block outflow hydrograph may be suitably
selected.
4
Par. 9
9. Physical Characteristics. a. From the moment the block hydro-
graph leaves the outlet structures of the dam, it is subject to con-
tinual modification in the stream channel. The physical character-
istics which produce this modification, and which must be evaluated
before the eventual hydrograph at the target location may be de-
termined, are the following:
(1) The length of the stream from the dam to the down-
stream target location.
(2) The variation in the cross-sectional area and shape
of the channel and overbank for each reach.
(3) The variation of the water-surface width with change
in stage and discharge.
overbank.
(4) The bottom profile of the stream.
(5)
The roughness coefficients of the channel and
(6) The storage capacities of the channel and overbank.
(7)
The locations and physical characteristics of
channel bends, constrictions, and rapids.
b. For the purposes of this bulletin, additional inflow
between the dam and the selected point downstream was not con-
sidered. However, tributary inflow could be added to the base flow
with no major difficulty. Rises resulting from natural causes such
as precipitation could also be added to base flow.
10. Hydraulic Elements. a. The procedure whereby the hydrograph
at the lower end of a reach is determined from the known or assumed
inflow hydrograph at the upper end of the reach is known as flood
routing. The method of flood routing used in this manual is based on
the "Muskingum Method" of storage routing, and involves the deter-
mination of certain hydraulic elements from the physical character-
istics listed above. These elements include discharge and velocity
rating curves at a sufficient number of cross sections to represent
the entire reach, and other hydraulic data.
b. The most direct method of determining the hydraulic
elements pertaining to a given cross section is to conduct a series
of discharge measurements covering the expected range of flows, using
stream-gaging procedures described in standard hydraulic handbooks
and in MH Bulletin 3. When circumstances do not permit making dis-
charge measurements, a stage-discharge curve may be computed by the
use of Manning's equation, as described in MH Bulletin 12, "Handbook
of Hydraulics", or in standard textbooks on open-channel hydraulics.
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Par. 10 b
The data collected in the discharge measurements may also be utilized
in evaluating other hydraulic elements.
11. Average Wave Velocity. The flood routing method used in this
bulletin is a modification of the Muskingum Method of flood routing
and involves the determination of the average wave velocity "U" for
each routing reach. In a given reach, the value of the average wave
velocity "U" corresponding to a given discharge is obtained by
averaging the wave velocities for that discharge at representative
cross sections in the reach. The wave velocity at a single cross
section is determined by plotting discharge as ordinate against the
corresponding cross-sectional area as abscissa, and drawing a smooth
curve through the plotted points. The slope of this discharge-area
curve at any point is then the wave velocity for that discharge. If
a typical cross section for the reach can be selected, the wave
velocity for each discharge at that cross section may be considered
the average wave velocity at that discharge for the entire reach.
12. Determination ofA K. a. Both the standard Muskingum Method
of flood routing and the Semi-Graphical modification used in this
bulletin require the determination of a storage factor "K" for each
reach through which the flood hydrograph is to be routed. In this
bulletin, the storage factor for a single reach is designated "AK".
If, as is usually the case, the length of channel from the dam to
the target point must be divided into a series of subreaches in
order to satisfy the requirements for routing by the Muskingum
Method, the storage factor for a subreach is designated "AK", and
that for the entire series of subreaches is designated "2K".
b. The value of "AK" for a given single reach or subreach
may be computed in a number of ways, depending on the types of basic
data available. "AK" is defined as the change in storage per unit
change in discharge, and has the dimension of time. The following
methods of computing "AK" are frequently used:
(1) A loop storage curve, derived from observed flood
hydrographs at the upper and lower ends of the reach, is determined
by plotting accumulated storages at the end of successive time inter-
vals against the corresponding outflows, with storage as ordinate and
outflow as abscissa, and drawing a mean line through those points.
The value of "AK" for the incremental time period is equal to the
slope of this line.
(2) AK is the travel time of the center of mass, or
other characteristic point, of the hydrograph through the subreach.
(3) AK is the quotient obtained by dividing the length
of the subreach by the average wave velocity "U", described in the
previous paragraph.
6
Par. 12 b (4)
(4) AK is the slope of the curve representing the volume
within the reach under the computed profiles for steady flows versus the
corresponding discharges.
(5) Studies described in MH Bulletin 10 indicate that AK
varies not only with reach length but also with discharge in the reach,
and provide a method whereby the "ideal reach length" for routing a
given discharge, and the corresponding value of AK, may be determined
from the physical characteristics of the reach. The value of AK cor-
responding to a given discharge in a subreach of ideal length is given
by the equation
where:
Q=
U =
bw =
So =
AK _ 0.000365 cl
U2 bw so
the discharge in cfs
the average wave velocity at discharge Q in ft/sec
the water-surface width in ft at discharge Q
the average bottom slope of the reach
The coefficient in this equation corresponds to an "X"-value of zero
in the Muskingum Method of flood routing.
13. Determination of ZK. The value of ZK, the storage factor for
the entire series of subreaches, may be obtained by the methods shown
above, or by summating the values of AK for the various subreaches.
0
14. Determination of At. Flood routing is ordinarily accomplished
by a numerical procedure involving selection of discharge hydrograph
ordinates at fixed time intervals "At". The following considerations
are involved in the selection of At:
(1) Discharge ordinates taken at intervals of At units
must adequately define the hydrograph.
(2) The water-surface profile in the subreach during
the interval At should be rplatively straight.
(3) The travel time of the flood wave through the
subreach must be equal to or greater than At.
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*0"
t_
Par. 15
CHAPTER III
FLOOD ROUTING BY THE SEMI-GRAPHICAL METHOD
15. Semi-Graphical Method. a. Many different methods and pro-
cedures of flood routing have been described in engineering literature.
In general, the methods that attempt a strict mathematical treatment
of the many complex factors affecting flood-wave movement are not prac-
tical for routing floods through long reaches of natural river channels.
The flood routing methods normally used in practice either ignore many
complex factors, or make simplifying assumptions that reduce comput-
ation difficulttes to an acceptable level. The two basic methods of
flood routing commonly used in practice are:
(1) Storage methods, in which energy factors are largely
neglected and only the effects of storage in the reach and local inflows
are considered.
(2) Average inflow lag methods, in which a time-displace-
ment method of averaging the inflows is used to determine the shape of
the flood wave at the lower end of the reach.
b. The "Muskingum Method" of storage routing is used in this
bulletin to derive a less laborious semi-graphical method of routing
artificial flood releases. The method represents an adaptation of the
procedures presented in MH Bulletin 10, "Artificial Flood Waves". The
procedures used in deriving the basic curves and computational techniques
and in applying the results are described in the following paragraphs.
16. Basis of Derivation of Semi-Graphical Method. A rectangular
block hydrograph representing a reservoir release was successively
routed through a series of subreaches by the Muskingum Method, with
AK equal to At in each subreach and with a Muskingum X-value of zero.
The peak discharge of the initial block hydrograph was set at 100 units
of flow, and its duration 100 units of time. Several sets of routings
were performed, using values of AK equal to 1, 2, 5, 10, 20, and 40
units of time. It was assumed that all subreaches have equal values of
AK. Thus the value of ZIC is obtained by multiplying AK by the total
number of subreaches through which the hydrograph was routed. Values
of ZK ranging as high as 520 were attained by the routing procedure.
Selected representative hydrographs resulting from these routings are
shown on Plates No. 1-a and 1-b. The downstream hydrograph ordinates
are expressed in percent of the initial hydrograph peak, and the time
abscissa are shown as percentages of the duration of the initial hy-
drograph. These routings constitute the basis upon which the curves
and procedures described in the following paragraphs were derived.
17. Peak Modification Curves. As a flood hydrograph moves down a
river channel the peak discharge is reduced. A study of the routings
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Par. 17
described above showed that the reduction of the downstream peak is a
function of the product AK. ZK. For convenience, AK and ZK were ex-
pressed as ratios of the duration of the initial hydrograph Li, and
denoted as AKr and ZKr, respectively. Values of the downstream hydro-
graph peaks, computed as shown above for various values of AKr and ZKr,
were expressed as percentages of the initial hydrograph peak and
plotted against corresponding values of the product?AKr1Kr, and
smooth curves were drawn through these points. These curves are desig-
nated "Peak Modification Curves" and are shown on Plate No. 2. The
peak modification curve determines the peak discharge of the downstream
hydrograph as a functiom of AKr?ZKr. It will be noted from the curve
that the peak of the downstream hydrograph does not fall below the peak
of the initial block hydrograph until a AKr?ZKr value of about 0.022 is
reached.
18. Weighted Discharge. a. The use of the semi-graphical method
of flood routing through a series of subreaches involves the deter-
mination of the routing flow for the entire reach. An inspection of
the peak modification curve on Plate No. 2 shows that the peak does.
not decrease uniformly as the hydrograph moves downstream, so that an
average of the peaks of the reservoir outflow hydrograph and a down-
stream hydrograph is not a true mean of the peak through the reach.
Neither is a peak discharge computed by averaging the intermediate
routing peaks a true index of the proper routing flow through the
reach as the shape of the hydrograph also has an influence in se-
lection of the routing flow.
b. A "Weighted Discharge Curve", shown on Plate No. 3, was
developed that gives a proper routing flow for use in routing a
flood hydrograph from dam release through a series of uniform sub-
reaches in one computation. The procedure used in the development
of the curve is described as follows: Hydrographs at downstream
points with peak discharges of 100, 95, 90, 75, 50 and 24.6 percent
of the initial peak reservoir release were arbitrarily selected from
those obtained in the basic routings, and the value of AKrS?.r cor-
responding to each of these peaks was determined from the peak modi-
fication curve. Six sets of computations, one for each of the above
peaks, were then made to determine the weighted mean flow for the
successive downstream hydrographs through a series of subreaches cor-
responding to a given value of AKrXr at the lower end. Each set of
computations was determined in the same manner as that for the 50 -
percent peak, which is described in the following steps:
(1) AKr2Kr has the value 0.566 for the downstream peak
corresponding to 50-percent of the initial peak, as determined from
Plate No. 2.
(2) Successive hydrographs below the dam were selected
from the previously-routed hydrographs that had AK,ZKr values increasing
from zero to 0.566 by varying increments.
10
Par. 18b(3)
(3) The average discharge of each hydrograph during
the period from the beginning of rise to the point on the recession
side where the discharge equals 50 percent of the initial peak re-
lease was determined.
(4) The mean discharge of each successive hydrograph,
as computed in step (3), was weighted by the incremental value of
AKr2kr in the subreach above it.
(5) The weighted discharge for 50-percent peak modi-
fication was computed by accumulating the weighted discharges of
step (4), and dividing the total by 0.566, the value of AKrZkr
determined in step (1).
(6) The value of the weighted discharge (34 percent)
was plotted against the value of AKrZKr and formed one point on
the "Weighted Discharge Curve".
c. The five other sets of computations were obtained and
plotted in the same manner, and a smooth curve, as shown on
Plate No. 3, drawn through these points.
19. Hydrograph Ordinates. a. The hydrographs of Plate No. 1
were cross plotted to form a series of curves used in determining
the ordinates of the downstream hydrograph. The series of curves
shown on Plate No. 4 are expressed as time from beginning of rise
(in percent of the duration of the initial hydrograph) as ordinate
and the product AKrZKr as abscissa; the parameter represents the
hydrograph ordinates (in percent of the downstream peak) for both
the rising and recession legs of the hydrograph.
b. The hydrographs of Plate No. 1 show a fillet shape at the
beginning of rise which would probably not actually occur with a
block-type release. To give an abruptly rising hydrograph at the
beginning of rise, it was arbitrarily assumed that the time of the
beginning of rise of the downstream hydrograph was the time of
occurrence of the 5-percent ordinate. The percentage values of the
parameter curves shown on Plate No. 4 were arbitrarily selected
and are adequate to define the shape of the downstream hydrograph
in most cases.
c. Table 1 shows the method of computing one point on each
parameter curve. The example hydrograph selected was forAK = 5
andZK = 250 with a peak discharge of 84.8 percent of the initial
block hydrograph peak (See Plate No. la).
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Par. 19 c
TABLE I
Par. 20
20. Downstream Hydrograph Peak (Po). A, The required peak
discharge (P0) ot the downstream hydrograph depends on the tactical
situation and the purpose for which it is to be used in the flood-
Hydrograph Ordinates Time from
Time from
ing operation. The required peak is established by the conditions
Percent of
downstream peak
Percent of release at dam
initial peak
beginning of rise
that are desired to be produced - such as increased river velocity,
depth, or width. The relation of these to the required peak (Po)
Col. 1
Col. 2 Col. 3
Col. 4
depend upon the physical and hydraulic characteristics of the cross
Rise
5
4.2
193
0
25
21.2
223
30
50
42.4
243
50
75
63.6
263
70
90
76.3
277
84
100 = Peak
84.8
300
107
Recession
76.3
322
129
90
75
63.6
337
144
50
42.4
356
163
25
21.2
379
186
5
4.2
415
222
Explanation
(1) The products of the percentages of Col. 1 and the
peak discharge in percent of the initial block hydrograph (84.8)
were entered in Col. 2.
(2) The time of travel from the dam in percent of the
duration of the initial hydrograph was determined from the hydrograph
on Plate la for each ordinate of Col. 2, and entered in Col. 3.
(3) The time from beginning of rise was computed as the
difference of the times of Col. 3 and the 5 percent ordinate (193),
and entered in Col. 4.
(4) The time from beginning of rise of Col. 4 was
plotted on Plate 4 as ordinate for the value of the product
AKrZiCr = 0.125. Each value of the time from beginning of rise
formed one point on the parameter curves corresponding to the value
of percent of the downstream peak in Col. 1. Ordinates for other
hydrographs were computed and plotted in the same manner as described
above and smooth curves drawn between each set of points and shown on
Plate No. 4.
section at the problem location.
b. The average velocity curve of the channel and the area,
surface width, and discharge curves of the total cross section are
determined at the downstream problem location by the methods de-
scribed in Military Hydrology Bulletin 12 "Handbook of Hydraulics".
For any desired velocity, stage, or surface width the corresponding
discharge can then be determined. This discharge is then the re-
quired downstream hydrograph peak (P0).
21. Release Hydrograph Peak (Pi). The procedure considered in
this bulletin is based on the assumption that a choice of dam oper-
ation exists and that it is possible within wide limits to release
any desired discharge for any selected length of time in order to
create desired conditions at the target site. Under these assump-
tions, an initial hydrograph is selected and then routed downstream
to ascertain if the desired Po occurs at the selected downstream
point. If the initial hydrograph is fixed by conditions, the
procedure illustrated in this bulletin could nevertheless be used.
The peak discharge of the initial block hydrograph released at the
dam is arbitrarily assumed as somewhat greater than the required
downstream hydrograph peak (P0). Its value is selected after con-
sidering the discharge capacity of the outlet structures and the
effective storage in the reservoir. The various factors affecting
the selection of the release hydrograph peak are discussed in
Paragraphs 7 and 8.
22. Procedure for Solution. The procedure for routing a block
hydrograph down an open channel by the semigraphical method of
flood routing is based on the application of the dimensionless
graphs shown on Plates 2 to 4, inclusive. Knowing the required
downstream hydrograph peak (P0) and assuming the initial hydrograph
peak (Pi), the procedure for determining the duration of the
initial release hydrograph (Li), the downstream hydrograph ordinates
and the times from beginning of release is described in the following
paragraphs.
23. Average Hydraulic Characteristics of Reach. The average wave
velocity, PK, andZK are determined for each reach as explained in
Paragraphs 11, 12 and 13. The average values oft, K andZK for each
reach are plotted against the corresponding discharge and smooth
curves drawn between the points. The average values ofQ K andZK
13
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Par. 23
are read from the curves and the product AKEK computed and plotted.
The three average hydraulic characteristic curves (AK, ZK, and AK2K)
plotted for each reach are used in determining the duration of the
initial block hydrograph.
24. Duration of Initial Block Hydrograph (Li). The value of the
downstream peak discharge (Po) in percent of the peak discharge of
the initial block hydrograph (Pi) is computed from the known data.
AKr2Kr is then determined from Plate 2 corresponding to this value.
The routing flow is then determined from Plate 3 for the above value
of AKrZKr. The product AlaK is determined from the average hydraulic
characteristic curves (derived in paragraph 23) for the value of the
routing flow. From this, the duration of the initial block hydrograph
is computed as:
Li = (AKZKIAKr2Kr)?-5
Maintaining release from the dam at the initial peak (Pi) for this
duration (Li) will produce the desired downstream peak discharge
(P0), after which the downstream hydrograph will recede back to normal.
25. Time of Downstream Peak. The time of the peak discharge (P0)
of the downstream hydrograph as measured from the time of beginning of
release of the initial block hydrograph at the dam is computed as:
ZK + (Li/2)
The values of ZK and Li used are those determined in preceding para-
graphs 23, 24 respectively.
26. Time of Beginning of Rise of Downstream Hydrograph. As pre-
viously explained in paragraph 19, the point of beginning of rise of a
downstream hydrograph has been arbitrarily assumed as the time of
occurrence of the 5-percent ordinate. By entering Plate 4 with the
same value of AKr2kr used in paragraph 24, the time interval (in per-
cent of Li) between the 5-percent and 100 percent parameter curves can
be determined. This (converted into actual units of time by multi-
plying by the value of Li) and subtracted from the time of peak as
determined in paragraph 25, will then establish the time of beginning
of rise of the downstream hydrograph.
27. Downstream Hydrograph Shape. The shape of the downstream
hydrograph can be determined from Plate 4, by entering with the same
value of liKrar used in paragraphs 24 and 26, and reading the times
of occurrence from the beginning of rise (in percent of Li) for each
parameter discharge percentage curve. These can be converted into
actual time and discharge units by multiplying by Li and Po, respec-
tively. By adding these time units to the time of beginning of rise
as determined in paragraph 26, the time of each ordinate of the down-
14
-
Par. 27
stream hydrograph as measured from the beginning of release at the
dam can be determined. Reference may be made to Plate lib for an
example of these computations together with more detailed explan-
ation.
28. Verification of Results. The hydrographs computed by the
semigraphical method were checked by the storage-indication method
of flood routing. This method, although more laborious than the
semigraphical method, is particularly suitable as a check, since
it provides for the use of a variable storage factor while main-
taining an equal volume under the inflow and outflow hydrographs.
The details of the method of computing the storage indication
routing are given in Bulletin TB-5-550-3, "Flood Prediction
Techniques for Military Purposes", or in standard text books on
hydrology. The storage-indication routings checked the semi-
graphical method of routing within 5 percent of the peak dis-
charges of the downstream hydrographs. The hydrographs exhibited
a good degree of consistency in shape and time from beginning of
release at the dam.
29. Discussion of Adopted Flood Routing Method. a. The
adopted semigraphical method of flood routing is based on curves
obtained by routing a dimensionless block hydrograph using a uni-
form "K" value corresponding to a uniform wave velocity. The
degree of accuracy to be attained by the semigraphical method
depends on how closely the following conditions are satisfied:
(1) The reach is fairly uniform in cross section
and slope, and capable of representation by an average cross
section.
(2) The average wave velocity does not vary greatly
through the range of discharge.
b. The limits of permissible variation from these con-
ditions which will still give satisfactory results have not been
established at this time. Further studies would have to be made
to determine the effects of valley cross sections exhibiting large
variations in average wave velocities through a reach.
30. Cyclic Discharges. Repeated streamflow variation may be
possible under some cases where a sufficient volume of water is
available for regulation and where the enemy lacks the power to
prevent further streamflow variation after the first cycle.
While it may be possible to cause any desired downstream discharge
by releasing an equal discharge at the dam, the length of time and
thus the volume of water required may be greater than desirable.
By increasing the discharge at the dam (Pi) the desired downstream
peak (P0) can be caused with a much smaller volume of water. The
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4Tfx
al
Par. 30
duration of the flood wave however, will also be smaller. Where it
is desirable to maintain the discharge above a selected minimum at
all times at the downstream point, the selection of the most effi-
cient release may become involved. In the following paragraphs,
there has been developed a procedure for determining the timing of
cyclical releases to produce waves at the downstream location with
desired peak and trough discharges.
31. Efficiency Ratio. a. The "Efficiency Ratio" is a working
tool used in computing the duration of each cycle, or the time
interval from the start of one block hydrograph to the start of
the next. It is based on the following considerations: Suppose
that a given peak discharge (P0) is desired at a certain point
downstream from the dam, Po may be achieved at the downstream
point by releasing an equal discharge at the dam for a period of
sufficient length, say Lh hours. Po may be achieved at the down-
stream point by releasing a higher discharge (Pi) for a shorter
period (Li). The latter release will produce a hydrograph at the
downstream point rising to Po and then receding. Assume that the
hydrograph at the downstream point recedes to a flow of Pt at Lt
hours after the time of beginning of rise at that point. Then,
if flows lower than Pt, called the trough discharge, are not to be
permitted, it follows that a new cycle must begin at the dam Lt
hours after the start of the first cycle. The efficiency ratio,
used in computing the timing of successive cycles, is equivalent
to the fraction:
where
Lt =
Po =
Li =
Pi =
b.
Lt Po = Efficiency Ratio
L. p.1 1
time at downstream point from beginning of rise to trough
downstream peak discharge
length of dam release
peak discharge at dam
The "Efficiency Ratio Curves" presented on Plate No. 5
show the efficiency ratio as ordinate and the peak discharge (P0)
of the downstream hydrograph, (in percent of the initial hydrograph
peak Pi) as abscissa. The parameter curves represent trough dis-
charges (Pt) corresponding to 5, 10, 15, 20, and 25 percent of the
downstream peak. Six sets of computations were made to determine
the curves of Plate No. 5 - - one for each downstream peak dis-
charge of 100, 95, 90, 80, 70, and 50 percent of the initial peak.
As a preliminary step, supplementary working curves of the "dis-
charge hydrograph ordinates" for the recession ordinates equal to
10, 15, and 20 percent of the downstream peak, similar to those
shown on Plate No. 4 and discussed in paragraph 19 were computed
and drawn. Each set of computations was then determined in the
same manner as that for the 90-percent peak discharge, which is
described in the following steps:
16
^
Par. 31 b
(1) The value of ARnERr of 0.092 was determined from the
peak modification curve (Plate 2) for a downstream peak of 90 percent
of the initial peak.
(2) The time from beginning of rise of the downstream
hydrograph for values of recession ordinates of 25, 20, 15, 10, and
5 percent of the downstream peak were determined from the discharge
hydrograph ordinate curves corresponding to a AKrZKr value of 0.092.
(3) The values obtained in Step 2 were multiplied by
the factor 0.90, the ratio of the downstream hydrograph peak to the
initial peak, to compute the efficiency ratio for each recession
ordinate.
(4) The five efficiency ratios of Step 3 were plotted
against a downstream peak discharge of 90 percent of the initial
hydrograph peak. Each ratio has as a parameter the corresponding
value of recession ordinate, or trough discharge in percent of
downstream hydrograph peak.
c. The steps described above were repeated for downstream
peak discharges of 100, 95, 80, 70, and 50 percent of the initial
peak, and smooth curves as shown on Plate No. 5 were drawn through
the sets of points thus computed.
32. Duration of Cycle. The "Efficiency Ratio Curves" of Plate
No. 5 are used in determining the timing of cyclic block releases
to produce a downstream hydrograph of desired peak and trough dis-
charges. The duration of a block release at rate equal to the
downstream peak is obtained by multiplying the initial block hy-
drograph duration (Li) by the ratio of peaks (Pi/P0). The product
of this value and the efficiency ratio (as determined from Plate
No. 5 for the desired trough discharge) is then the time interval
between beginning of successive cyclic releases. Reference may be
made to Table II of Plate ha for an example of this computation.
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Par. 33
CHAPTER IV
GATE-OPERATION SCHEDULE
33. Problem. After the initial block hydrograph is determined by
the methods described in Chapter III, the problem remains of deter-
mining a gate-operation schedule to release the hydrograph. The re-
lease hydrograph, instead of being a true rectangular block hydro-
graph with a constant discharge, in actual operations will be a saw-
tooth hydrograph with the discharge varying with time. Rs the
reservoir water surface drops with release of water through the gate
opening, the discharge will also drop, unless the gate opening is
increased. If the average discharge for each gate setting is to be
the required peak discharge of the initial block hydrograph, the ini-
tial discharge of each gate setting must be above and the final dis-
charge below that required discharge. It is obvious that the more
gate settings, the more nearly will the release hydrograph approxi-
mate a true block hydrograph. If the gates are continuously changed
during the release it is theoretically possible to release a constant
discharge. For military purposes it is not necessary to have such a
close approximation. The initial data required to solve the operation
problem and the method of computing a reservoir water surface and
gate-operating schedule are described in the following paragraphs.
34. Initial Data. The initial data required to compute a
gate-operation schedule include the following:
(1) The volume of water to be released (computed as the
product of the required peak discharge (Pi) and the time duration
(Li) ,of the block hydrograph as described in Chapter III.
(2) The elevation-capacity curve of the reservoir (com-
puted by the methods described in paragraph 7.)
(3) The discharge rating curves for the outlet structures
of the dam with partial and full gate openings. The method of deter-
mining the rating curves is described, in Military Hydrology Bulletin 12
"Handbook of Hydraulics".
(4) The initial reservoir elevation or reservoir storage
(usually given OT asaumed in the basic data of the problem).
35. Schedule of Reservoir Water Surface. A schedule is first com-
puted of the elevation of the reservoir water surface after the block
release. The schedule is computed by tabulating the difference between
the initial reservoir storage and the volume of water released. The
reservoir water-surface elevation at the end of the release is then
determined from the elevation-capacity curve. The drop in the reser-
voir water surface is computed and tabulated in the schedule.
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36. Gate Opening and Discharge. a. The opening necessary to
release the required peak discharge for each gate setting is based
upon the discharge rating curve. The discharge is determined for a
head equal to the water surface elevation at the midpoint elevation
of the drop in water surface. If the drop in the reservoir water
surface is large, the gate schedule should include several gate
settings for that release.
b. The method of determining the required number of gate
settings for each release is described as follows: Determine the
discharge at the beginning and end of the gate setting from the dis-
charge rating curve. If the difference in discharge is large or if
the discharge rating curve is not a straight line over the range of
discharges, the gate operation schedule should be divided into
several gate settings. The duration of the initial block hydrograph
is arbitrarily divided into smaller increments of time, and the
volume of release computed for each time increment at the required
initial peak discharge rate. The water surface elevation at the
end of each time increment is determined from the elevation-capacity
curves. The change in discharge from the beginning to the end of
each time increment is determined from the discharge rating curve.
If the change in discharge is still large, the hydrograph duration
is broken up into shorter time increments, and the above procedure
repeated.
37. Princi les of Selectin the Gate 0 ening. The actual gate
setting for a particular water-surface elevation is not specific,
but is an arbitrary opening selected from several choices. The
principles which should govern the ultimate choice are as follows:
(1) Regulating valves, normally found in dams for irriga-
tion projects, give the closest regulation for the various types of
outlet structures.
(2) Partially-opened gates on a spillway crest give better
control over the discharge than partially-opened high pressure gates
in the outlet conduits.
(3) The head on a partially-opened spillway gate should
have a ratio of head-to-gate opening greater than 2 to give a
reliable dispharge rating.
(4) Generally, gates should be fully opened if possible
to give the required discharges, leaving cnly one gate partially
opened to give the final regulation required in the gate operation
schedule.
(5) The stilling basin of an overfall or chute spillway
may require a relatively even distribution of flow over the spill-
way to prevent excessive scour at the foundation of the dam. If
such is the case, several or all spillway gates should be operated
to give an even distribution of flow at partial gate opening rather
than a single gate fully opened to give the required discharge.
(6) The time required to open the gates may be a control-
ling factor. The gate-operating machinery of a dam may not be
workable because of the lack of power or enemy damage. In such
cases, the gates should be operated by hand or by hoists that are
powered by organizational equipment. Operation of as few gates as
20
Par. 37 (6)
possible to give the required discharges in this case may then be
the controlling factor of the gate-operation schedule.
38. Gate-Operation Schedule. The gate-operation schedule is.
determined from the basic data and rating curves, reservoir water
surface schedule, and gate-opening principles as described in the
preceding paragraphs. The operation schedule is determined as
follows:
(1) From the reservoir water surface schedule and
discharge rating curves the required number of gate settings is
determined, as described in Par. 36.
(2) The volume of water remaining in the reservoir
after each gate setting is computed and the reservoir water-
surface elevation determined from the elevation-capacity curve.
(3) From the tabulation of reservoir elevations,
compute the elevation of the midpoint of the drop in the reser-
voir water surface for each gate setting.
(4) Enter the discharge rating curves of each outlet
structure at the elevation of the midpoint of the drop in the
reservoir water surface for the first gate setting. Determine
the discharge for each type gate at various gate openings for this
elevation.
(5) From the discharge of each gate and the number
of gates involved, select the gate schedule that will give the
required discharge, using the principles of operation stated in
Par. 37. This determines the gate setting for the first incre-
ment of the initial hydrograph release.
(6) If the initial hydrograph release is divided
into several time increments, the gate setting must be changed at
the end of each time increment. To determine the gate opening
for each setting the same procedure is carried out as described
above. The gates are closed at the end of the last time incre-
ment. The method of computing an operation schedule is described
in more detail in Chapter V for problem I.
39. Mjustment of Outflow Hatz.ILTAph Peak. As the reservoir
water surface lowers, a point is usually reached in which the out-
let structures will not release the required initial peak discharge
of the block hydrograph. At this time the block hydrograph is
adjusted by reducing the required peak discharge and increasing the
duration of release. The procedure to accomplish this is to select
a substantially lower peak discharge for the release hydrograph,
and recompute the required duration to obtain the same downstream
effects at the problem location. The method of cemputation is the
same as described in Par. 21 to 27. When the new initial hydro-
graph peak discharge and duration have been determined, the
computation of the gate-operation schedule is continued in the
same manner as described in Par. 38.
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Par. 40
40. Cyclical Releases. When cyclical releases from the reser-
voir are involved, the time between beginning of releases of each
cyclical block discharge must be determined as described i'
Paragraph 22 in addition to the other initial data as outlined in
Paragraph 34. The procedures outlined in this chapter are repeated
for each successive release hydrograph to complete the gate-
operation schedule for the series of cyclical releases.
22
C
Par. 41
CHAPTER V
EXAMPLES
41. Outline of Examples. Three example problems are presented
in this section and are shown on Plates Nos. 6 to 20, inclusive.
The problems are representative of the basic data and conditions
that probably would exist under field conditions. The first two
examples assume a uniform river channel with a varying bottom slope,
and the third has a varying channel cross section as well as a
changing bottom slope. The examples illustrate the methods of
determining the required initial release block hydrograph that would
cause flooding in a downstream reach, and the reverse procedure of
determining the downstream flooding from a given initial release
hydrograph.
42. Problem I. a. SITUATION. A large reservoir located on a
tributary stream within the army combat zone appears to be capable
of augmenting the defense of the river line to our immediate front.
It is desired to evaluate the effects of artificial flooding by
cyclical regulation to prevent an enemy assault crossing of the
river.
b. GIVEN DATA. Construction drawings and other intel-
ligence data furnished the following information:
(1) Dam
Type of construction
(2) Spillway
2 spillway gates
(3)
Spillway crest profile
Design Head
Coefficient of discharge
at design head
Outlet Conduits
10 outlet conduits
Length
Entrance condition
Gates & location
Gate seat elevation
Manning's '11"
Tailwater effects on
discharge
(4) Reservoir
Elevation-storage capacity curve shown on Plate No. 7
Concrete gravity
Tainter gates
50' long 40' high
See Plate No. 6
40'
3.96
Sq. 6' x 6' concrete
120 ft.
Bell mouth without
trash racks
Vertical-lift slide &
guard gate 100 & 90 ft.
from conduit entrance,
respectively
1000 ft. msl
0.013
Negligible
23
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Par. 42b(5)
(5) Physical Characteristics of the River. The channel
cross section is trapezoidal in shape, with a 40 ft. bottom width
and 1 to 1 side slopes to a depth of 10 ft. The overbank side slopes
are 1 on 10. The channel roughness coefficient is assumed to be
0.040 and the overbank roughness 0.080. The bottom slope varies in
accordance with the equation:
Sm = 750/(150 + x)
Where: Sm = bottom slope in feet per mile
x = the distance in miles below the dam.
c. REQUIRED. The hydrographs and gate-operation schedule
causing maximum surface velocities of 11 ft/sec and minimum trough
discharges of 1700 cfs at a point 40 miles below the dam.
d. SOLUTION.
(1) Rating Curves of Outlet Structures. The discharge
rating curves for a partially-opened tainter gate and single-outlet
conduit gate (computed by the methods described on Plates 614, 805,
905, 908 of Military Hydrology Bulletin 12, "Handbook of Hydraulics")
are shown on Plate No. 6.
(2) Hydraulic Elements of a Cross Section. The hy-
draulic elements of the 40-mile river reach are based upon the physi-
cal data of the river. The hydraulic elements of area, water surface
width, average channel velocity, and conveyance are computed for the
average cross section of each reach. The channel and overbank cross
sections are assumed to be uniform for the entire river reach; there-
fore the hydraulic elements are computed for a single cross section,
as shown on Plate No. 8a.
(3) Velocity and Discharge at Mile 40. The channel
discharge at mile 40 is computed as the product of the channel con-
veyance and the square root of the bottom slope at mile 40. The
average channel velocity is computed as the channel discharge divided
by the channel area. The total discharge of the channel and overbank
at mile 40 is computed as the product of the total conveyance and the
square root of the bottom slope at mile 40. The average channel
velocity and total discharge at mile 40 are computed and plotted on
Plates No. 8a and 8b, respectively.
(4) Weighted Average Bottom Slope. The bottom slope
of the channel changes for each mile of river reach in accordance
with the equation given in the basic data. To determine the average
hydraulic characteristics of the 40-mile reach of river it is neces-
sary to compute a weighted bottom slope. The point bottom slope is
computed every four miles from the dam through mile 40. The average
slope is computed for each of the four-mile subreaches and is multi-
plied the length of the subreach. The above products are accumulated
and divided by the sum of the subreaches to give the weighted bottom
slope for any reach between the dam and a downstream point, as shown
on Plate No. 9.
24
J.
Par. 42d(5)
(5) Discharge Rating Curve for the 40-Mile Reach. The
average discharge rating curve for the 40-mile river reach is com-
puted as the product of the conveyance for the total cross section
and the square root of the weighted average bottom slope for the
40-mile reach_ The computation is shown in Col. 14 of Table I,
Plate No. 8a, and the resulting curve plotted on Plate No. 8b.
(6) Average Hydraulic Characteristics for the 40-mile
Reach. The average wave velocity, AK, and ZI( are determined from
the hydraulic elements and the discharge rating curves of Plate 8b.
For convenience, area and surface width curves may be plotted against
discharge, as shown on Plate 8c. The values of AK are computed by
Escoffier's equation as given in par. 12b (5). The computation of
the average wave velocity, AK, EK, and AKZK is shown in Tables Nos. I
and II of Plate 10a and these values are plotted on Plate 10b.
(7) Determination of the Downstream Peak Discharge (P0).
From the requirements of the problem it is desired to create a channel
surface velocity of about 11 ft/sec at mile 40. Data from Military
Hydrology Bulletin 2, "River Characteristics and Flow Analysis for
Military Purposes", indicates that the channel surface velocity in a
stream is about 1.5 times the average channel velocity. Therefore,
an average channel velocity of about 7.5 ft/sec would be equivalent
to a surface velocity of 11 ft/sec at mile 40. From Plate 8b with an
average channel velocity of 7.5 ft/sec, the peak discharge at mile 40
is determined to be 14,000 cfs.
(8) Peak Discharge of Initial Block Hydrograph
The peak discharge of the release hydrograph at the dam is arbitrarily
assumed. Its value is selected after considering the discharge
capacity of the outlet structures and the effective storage in the
reservoir as described in paragraphs 7 and 8. For this problem the
peak discharge (Pi) is selected to be 28,000 cfs.
(9) Duration of Initial Block Hydrograph (Li). The
duration of the initial block hydrograph (Li) for a peak discharge
of 28,000 cfs is computed in Table I, Plate lla. The general method
of determining the initial hydrograph duration is as follows: A
routing flow is first computed for an initial peak of 28,000 cfs
from the peak modification and weighted discharge curves. The value
of the product A K2k. is then determined from the average hydraulic
characteristic curves for the weighted discharge. From this, the
initial hydrograph duration is computed as the square root of the
ratioAKEK/AKr?Kr. The time from beginning of release to the time
of closure for each cyclical flood hydrograph is thus computed to
be 4.55 hours.
(10) Duration of Cycle. The time from the beginning
of release of the first cycle to the time of beginning of release
for the second cycle is computed to be 16.4 hours, as explained in
Table II, Plate lla.
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25
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Par. 42d(11)
(11) Downstream Hydrograph. The discharge ordinates
and the time from the beginning of release from the dam are computed
and explained in Table III, Plate 11b. The resulting hydrographs
for the first two cycles are plotted on Plate 11c.
(12) Gate Operation Schedule. The gate operation
schedule for ten cyclical release hydrographs is determined from the
elevation-capacity curve (Plate No. 7), the discharge rating curves
(Plate No. 6), and the hydraulic characteristic curves (Plate 10b).
The reservoir water surface schedule is computed and explained in
Table I, Plate 12a. Each release cycle is divided into two time
increments of 2.55 hours and 2.0 hours. The time sequence of each
gate setting and the gate schedule are computed and explained in
Table II, Plate 12b.
43. Problem II.
Problem I, Par. 42a.
b. GIVEN DATA. The physical and hydrological data are the
same as Example Problem I, Per. 42b.
c. REQUIRED. The downstream hydrograph at mile 21.07 when a
block hydrograph is released with a peak discharge of 28,000 cfs and
duration of 4.55 hours at the dam. The trough discharge between
cyclical hydrographs at mile 21.07 is to be about 1700 cfs.
d. SOLUTION. (1) Average Hydraulic Characteristics of the
Reach. The average wave velocity,AK andZK are determined in the
same manner as described on Plate 10 or Example Problem I, but with
a weighted bottom slope of 8.86 x 10- as read from Plate 9. The
average hydraulic characteristics for the 21.07 mile reach are shown
on Plate 13.
(2) Determination of @the Downstream Peak Discharge. A
weighted discharge (Pw) is assumed andAKra(r is determined from
Plate 3 for the assumed value of Pw in terms of Pw % Pi. The
value of AM is determines from Plate No. 13 for the assumed value
of Pw. A check value of AKrEKr, is computed by dividing the value of
&UK by the square of the hydrograph duration (4). If the values
ofAKy7Kr check, the assumed value of the weighted discharge (Pw)
was correct; conversely, if the values of AK,Z(... do not check out,
another trial is made with the new AK,-. The weighted flow in
percent of the initial hydrograph peak is determined from Plate No. 3
for the new value of AK_ZKr and Pw computed from the initial peak
discharge. The same procedure is followed as in the first trial in
computing the check AKra(r. The process is continued until the two
values of AKrZKr check. After the weighted discharge has been deter-
mined as described above, the downstream peak discharge is computed
from Plate No. 2 for the AKr a(r determined from the final trial com-
putation. The ordinates of the downstream hydrograph and the time of
release from the dam is computed by the method described on Plate 11b.
The downstream hydrograph for the first cycle at mile 21.07 is com-
puted and explained on Plate 14a and plotted on Plate 14b.
a.
SITUATION. Assumed identical to Example
Par. 44
44. Problem III. a. SITUATION. The situation is the same
as in Example Problem I, Par. 42a.
b. GIVEN DATA. The information given on construction
drawings and other intelligence data is the same as Example Problem I,
Par. 42b, except that the river cross section and bottom slope have
been changed as shown in the following table.
Reach
River Mile Bottom
Below Reservoir Width Side Slope
Feet
PHYSICAL AND HYDRAULIC DATA OF RIVER
Channel Cross Section Stream Slope
Feet
Per So
Mile
Base
Flow
c.f.s.
0-10
40
1 on 1
10
0.00189
0
10-25
60
1 on 1-1/2
4
0.000757
0
?
25-45
80
1 on 2
2-1/2
0.000473
1,000
c. REQUIRED. The initial block hydrograph to cause a
maximum surface velocity of 11 ft/sec at a point 45 miles below the
dam with a minimum trough discharge of 1700 cfs.
d. SOLUTION. The discharge rating curves for the
spillway gates and outlet conduits, and the reservoir storage curve
are the same as Example Problem I, and are shown on Plates No. 6 and 7,
respectively.
(1) Average Hydraulic Characteristics. The
hydraulic elements of area water surface width, conveyance, and dis-
charge are computed in the same manner as Example I for the three
reaches (Mile 0-10, 10-25 and 25-45) and are shown on Plates No. 15
to 17. Values of AK, ZK,,and the product AKZK are computed for each
reach and plotted on Plates No. 18 and 19. The total values of EK
and AKZK are determined for the 45 miles of river and also plotted
on Plates No. 18 and 19. The above hydraulic characteristics were
computed in the same manner as described on Plate 10a.
(2) Determination of the Downstream Peak Discharge
at Mile 45. The channel discharge at mile 45 and the average channel
velocity are computed as described in Example I. For an average
channel velocity of about 7.5 ft/sec (equivalent to a surface velocity
of 11 ft/sec), the discharge of the total cross section is determined
to be 32,500 cfs.
(3) Determination of the Initial Block Hydrograph.
The duration of the initial block hydrograph for an assumed peak dis-
charge of 60,000 cfs is computed on Plate No. 20a in the same manner
as given for Example Problem I.
(4) Determination of the Downstream Hydrograph.
The discharge ordinates for a single release hydrograph and their
time from beginning of release are computed and explained on Plate
No. 20a. The hydrographs for a single cycle is plotted on Plate
No. 20b. Successive cyclical hydrographs can be computed in the same
manner as for Example I as described on Plate 11b.
27
26
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REFERENCES
Military Hydrology Bulletins
1. MHB 1: Applications of Hydrology in Military Planning and Operations
2. MHB 2: River Characteristics and Flow Analyses for Military Purposes
3. MHB 3: Stream-Gaging Methods and Equipment for Military Purposes
4. MHB 4: Transmission of Hydrologic Data for Military Purposes
5. MHB 5: Card-Indexing and Filing of Information Pertinent to
Military Hydrology
6. MHB 6: Directory to European Sources of Information on Military
Hydrology
7. MHB 7: Glossary of Terms Pertinent to Military Hydrology
8. MHB 8: Selected References on Military Hydrology
9. MHB 9: Flow Through a Breached Dam
10. MHB 10: Artificial Flood Waves
11. MHB 11: Regulation of Stream Flow for Military Purposes
12. MHB 12: Handbook of Hydraulics
Department of the Army Technical Bulletins.
13. TB 5-550-1: Flood Prediction Services
14. TB 5-550-2: Compilation of Intelligence on Military Hydrology
15. TB 5-550-3: Flood Prediction Techniques
Other Publications.
16. Rouse, H. (Editor). Engineering Hydraulics, New York:
John Wiley and Sons, 1950.
17. Part CXIV, Hydrology and Hydraulic Analysis, Chapter 8,
"Routing of Floods Through River Channels". Engineering
Manual for Civil Works, Office, Chief of Engineers, Corps of
Engineers, Dept, of the Army, Sept. 1953.
18. "Flood Control," Engineering Construction Text X-156.
The Engineer School, Fort Belvoir, Virginia, 1946.
19. Linsley, Kohler & Paulhus. Applied Hydrology. New York: McGraw-Hill,
1949.
29
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.t7-z
LIST OF PLATES
la Downstream Hydrographs
lb Downstream Hydrographs
2 Peak Modification
3 Weighted Discharge
4 Downstream Hydrograph Ordinates
5 Efficiency Ratio, Cyclical Operation
6 Example Problem I, Discharge Rating
7 Example Problem I, Reservoir Storage
8a Determination of the Area, Surface Width, Conveyance,
Average Channel Velocity and Discharge Curve at
Mile (40) Forty
8b Example Problem I, Hydraulic Elements at Mile 40
8c Example Problem I, Average Discharge-Area and Surface
Width Curves, 40-Mile Reach
9 Example Problem I, Weighted Average Bottom Slope
10a Determination of the Average Hydraulic Characteristics
of Mile Forty Reach
10b Example Problem I, Average Hydraulic Characteristics,
40 Mile Reach
lla Determination of Cyclical Hydrographs at Mile Forty,
Tables I & II
lib Determination of Cyclical Hydrographs at Mile Forty,
Table III
llc Example Problem I, Hydrographs at Mile 40
12a Determination of the Gate Operation Schedule, Table I
12b Determination of the Gate Operation Schedule, Table II
13 Example Problem II, Average Hydraulic Characteristics,
21.07 Mile Reach
14a Determination of Downstream Hydrograph at Mile 21.07
14b Example Problem II, Hydrograph at Mile 21.07
15 Example Problem III, Average Hydraulic Elements, Mile 0-10
16 Example Problem III, Average Hydraulic Elements, Mile 10-25
17 Example Problem III, Average Hydraulic Elements, Mile 25-45
18 Example Problem III, AK & ZK, 45 Mile Reach
19 Example Problem III, AKEK, 45 Mile Reach
20a Determination of Cyclical Hydrograph at Mile Forty Five
20b Example Problem III, Hydrograph at Mile 45
31
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DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS
100
80
60
40
20
?
K.220
AKEK=220
(AKr)(EKr)=. 022
(A
A K=2
K.320
AKIK=640
r)(EKr) =064
A K=2
E K=460
A K Z K=9a0
(AK )(1Kr)=.092
(SEE SCALE BELOW)
AK=5
E K=250
LKZK=1250
(AK r) (Z K).125
AK=5
EK=320
A KZ K=1800
Kr) (E Kr)x.1 6
AK=5
EK= 380
KZK= 1900
(AK r) Kr). 19
AK= 5
E K=480
EK= 2400
(Aly (ZKr)=. 24
600 640
160 200 240 280 320 360 400 440
TIME IN PERCENT OF INITIAL HYDROGRAPH DURATION
DOWNSTREAM
HYDROGRA PHS
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
480 520 560 Prepared by Wge Date A us 1 . 9 4:5-
Drawn by iR E'S
MHB II .
PLATE NO. la
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DEPARTMENT OF THE?ARMY
CORPS OF ENGINEERS
60
40
20
0
AK?I0
IKAL:K?I?
IK-360 AK 10
EK-460
200 240 280 320 360 400 440 480 520
TIME IN PERCENT OF INITIAL HYDROGRAPH DURATION
a_
>-cx
2 rr
tiJ
cx ?-
_J
LL
Ui
cx IL
Ui
crUi
50
40
30
20
10
0
560
600
640
680
720
400 480 560 640 720 800 880 960 1040 1120 1200
TIME IN PERCENT OF INITIAL HYDROGRAPH DURATION
DOWNSTREAM
HYDROGRAPHS
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by vYA C Date Rug /.9.1:5-
Drawn by tES
MH I
PLATE NO. lb
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p
INITIA
HYDROGR
-
(AKr) aKr) 00
0 0.04 0.08
^
20 40 60 80 100
TIME IN PERCENT
0.12 0.16 0.20
^
1.6 1.8 2.0
^
as
--:
^
I
'NOTES:
&Kr = The ratio of the Muskingum K of
each subreach to the duration of
the initial hydrograph in hours.
EKr = The ratio of the Muskingum l< of
the entire routing length of
stream to the duration of the
initial hydrograph in hours.
Pet1HB II
PEAK
MODIFICATION
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Preparedrown byAz
by inr Date du/ AQCS
D
PLATE NO.2
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(41Kr) ( Kr)
900 004 0.08 0112 016 0.20
80
? 70
ROUTING FLOW IN% OF INITIAL PEAK
60
50
40
30
200 04 0.8 1.2 1.6 2,0
(4011
9.0
8.84
8.6.
84
MHB II
0 10 20 30 40
RIVER MILE BELOW DAM
EXAMPLE PROBLEM
WEIGHTED AVERAGE
BOTTOM SLOPE
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by LiVeC Date Ata I oss'
Drawn by .REs- PLATE NO.9
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DETERMINATION OF THE AVERAGE HYDRAULIC CHARACTERISTICS
OF MILE FORTY REACH
TABLE I
SUMMARY OF COMPUTATIONS OF A lc Amo Ex
Q.
1000
cfs
A
feet2
u =Aga A
feet/sec
u2
bw
feet
A K =
0.435g
Z K =
211,200
3600 U
hours
2 uw
u
hours
Col. 1
Col. 2
Col. 3
Col. 4
Co1.5
Col. 6
col. 7
1.0
300
3.33
11.1
53
0.74
17.6
2.0
500
5.00
25.0
60
0.58
11.7
3.0
690
5.26
27.6
107
0.144
11.1
4.0
930
4.17
17.4
140
0.71
14.1
6.0
1380
4.44
19.7
196
0.68
13.2
8.0
1840
4.35
18.9
238
0.77
13.5
10.0
2310
4.26
18.1
275
0.87
13.8
12.0
2780
4.26
18.1
308
0.94
13.8
16.0
3690
4.40
19.3
362
1.00
13.3
20.0
4520
4.82
23.2
405
0.92
12.2
24.0
5370
4.71
22.1
445
1.06
12.4
28.0
6190
4.88
23.8
484
1.06
12.0
TABLE II
AVERAGE HYDRAULIC CHARACTERISTICS
OF FORTY MILE REACH
Q
1000 cfs
Av.AK
from
curve
Av.21K
from
curve
AK. EK
hours2
Col.1
Co1.2
Col.3
Col. 4
6.0
0.74
13.4
9.9
8.0
0.82
13.4
11.0
10.0
0.88
13.4
11.8
12.0
0.93
13.4
12.45
14.0
0.96
13.3
12.75
16.0
0.97
13.2
12.8
18.0
0.98
12.85
12.6
20.0
0.99
12.6
12.47
22.0
0.99
12.4
12.27
24.0
1.00
12.2
12.2
26.0
1.00
12.2
12.2
28.0
1.00
12.1
12.1
TABLE I
EXPLANATION OF COMPUTATIONS
Col.
(1) Discharges are selected to cover the range of flows expected in the problem
and entered in Column 1.
(2) The total channel and overbank areas in Column 2 are determined for the dis-
charges of Column 1. The cross sectional area is determined from the hydraulic
element curves for an average bottom slope of 8.4 x 10-4 on Plate 8b or directly
from Plate 8c.
(3)
The average wave velocity in Column 3 is computed as the ratio of the increment
in discharge to the increment in cross sectional area for each discharge.
(4) The average wave velocities of Column 3 are squared and entered in Column 4.
(5)
(6)
( 7)
The water-surface widths at each discharge of Column 1 are determined from
Plate 8c and entered in Column 5.
The value of AK is computed by means of the Escoffier Equation, described in
Paragraph 12,and entered in Column 6.
The EK is computed in Column 7 for each discharge as the ratio of the forty mile
reach length in feet to the average wave velocity in feet/sec.. The ratio is
divided by 3600 to convert EK from seconds to hours.
Note The values of AK and 2:K in Columns 6 & 7 respectively are plotted against the
corresponding values of the discharge in Column 1 and a smooth curve drawn
through the points, as shown on Plate 10b.
TABLE II
EXPLANATION OF COMPUTATIONS
Col.
(1) Representative discharges.
(2) For each discharge listed in Column 1, the average value of AK is determined
from curve on Plate 10b and entered in Column 2.
(3)
Note
For each discharge listed in Column 1, the average value of EK is determined
from curve on Plate 10b and entered in Column 3.
The products of the values AK and ZE are determined and entered in
Column 4.
The values of AK IK of Column 4 are plotted against the corresponding
discharges of Column 1 and a smooth curve drawn between the points as
shown on Plate 10b.
MHB 11
PLATE NO. 10 a
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24
20
0
o I
z ?
M.1113 II
?
8 10 12 14
KK IN HOURS2
AK Eili< IN HOURS
EXAMPLE PROBLEM I
AVERAGE HYDRAULIC
CHARACTERISTICS
40 MILE REACH
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by INA c Date At. I os-s-
Drawn by A)E-q PLATE NO.10b
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DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS
DETERMINATION OF CYCLICAL HYDROGRAPHS
AT MILE FORTY
TABLE I
DURATION OF INITIAL BLOCK HYDROGRAPH Line
Line
Item
Unit
1
Po
14,000 cfs
2
Pi
28,000 cfs
3
Po % Pi
50%
4
AKr 2Kr
0.566
5
Pw % Pi
33.8%
6
PW
9,460 cfs
7
2K
13.4 hours
8
AK 2K
11.65 hours2
9
(Li)2
20.6 hours2
10
Li
4.55 hours
TABLE II
DURATION OF ONE CYCLE
.
Line
.----
Item
Unit
1
Duration of Po
for equivalent
volume hydrograph
9.1 hours
2
Pt % Po
12.1%
3
Efficiency ratio
1.80
4
Duration of
one cycle
16.4 hours
EXPLANATION OF COMPUTATIONS
TABLE I
(1) The downstream peak discharge (P0) is determined from the discharge curve at mile forty, (Plate 8b)
for an average channel velocity of 7.5 feet / second.
(2) The initial block hydrograph peak is assumed after considering the factors described in Paragraphs
7 and 8.
(3) The downstream peak is determined as a percent of the initial peak (14,000/28,000) 100.
(4) The ratio LlKrZKr is determined from the "Peak Modification Curve" (Plate 2) for Po = 50% Pi
(5) The routing flow Pw in percent of the initial peak is determined from the Weighted Discharge
Curve (Plate 3) for a ZiKr2Kr = 0.566 (Line 4).
(6) The routing flow (P) is computed as the product of 33.8% and 28,000 cfs (Lines 5 & 2).
(7) The value of .EK is determiied from Plate 1Gb for a routing flow of 9,460 cfs (Line 6).
(8) The value ofLIKEK is also determined from Plate 10h for a Pw of 9,460 cfs.
(9) The square of the initial hydrograph duration is computed as the ratio ofAKEK on Line 8 to
the value of LiKrZKr on Line 4, 11.65/0.566 = 20.6 hours2.
(10) The square root of Line 9 is the initial hydrograph duration in hours.
EXPLANATION OF COMPUTATIONS
Line TABLE II
(1) The duration of an equivalent block release having a peak discharge equal to the downstream
hydrograph peak is computed as LiP1/P0 = 4.55 x 28,000/14,000 = 9.1 hours. These values
are taken from Lines 10, 2, and 1, respectively, Table I.
(2) The trough discharge (Pt in basic data) is computed in percent of Po. (1700/14,000)*10? 124%.
(3) The efficiency ratio is determined from Plate 5 for the trough discharge 12.1% Po (Line 3) and
the downstream peak discharge of 50% Pi (Line 3, Table I).
(4) The duration of one cycle is computed as the product of the efficiency ratio (Line 10 and the
duration of the equivalent block hydrograph (Line 0, 1.80 x 9.1 = 16.4 hours.
MHB 11
PLATE NO. 1(0
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DETERMINATION OF CYCLICAL HYDROGRAPHS
AT MILE FORTY
TABLE III
DOWNSTREAM CYCLICAL HYDROGRAPHS
FIRST CYCLE
SECOND CYCLE
4
HYDROGRAPH TROUGH
percent of
Time
rime
Discharge
Time from
Time from
Time
Discharge
Discharge
i
Discharge
Line
downstream
Peak (P0)
% Li
beginning
of rise
beginning of
release at dam
beginning of
release at dam
1st cycle
2nd cycle
total
hours
cfs
hours
hours
hours
cfs
cfs
cfs
Col. 1
Col. 2
Col. 3
Col. 4
Col. 5
Col. 6
Col. 7
Col. 8
Col. 9
Col. 10
1
0
0
0
0
7.4
23.8
23.8
1800
0
1800
2
25
57
2.6
3500
10.0
26.4
25.0
900
1500
2400
3
50
94
4.3
7000
11.7
28.1
26.0
300
3000
3300
4
75
126
5.7
10500
13.1
29.5
27.0
0
4800
4800
5
90
150
6.8
12600
14.2
30.6
6
100
183
8.3
14000
15.7
32.1
7
90
224
10.2
12600
17.6
34.0
8
75
246
11.2
10500
18.6
35.0
9
50
282
12.8
7000
20.2
36.6
10
25
323
14.7
3500
22.1
38.5
11
5
391
17.8
700
25.2
41.6
-
EXPLANATION OF COMPUTATIONS
Col
(1)
(2)
FIRST HYDROGRAPH
The values of the parameters on Plate 4 (Hydrograph Ordinates in Percent
of the Downstream Peak) are entered in Column 1.
The time from beginning of rise of the downstream hydrograph (expressed
in percent of the initial hydrograph duration) is determined from
Plate 4 for each ordinate of Column 1. The time of each ordinate is
taken for the value of LIK/ALICr of 0.566 (determined on Line 4, Table I
Col
(6)
SECOND HYDROGRAPH
The time in hours from the beginning of release at the dam for the first
cycle to each downstream hydrograph ordinate of the second cycle is
listed in Column 6. The duration of one cycle (16.4 hours from Line 5,
Table II) is added to the values of Column 5. The values of Column 4 &
Column 6 are plotted on Plate 11c and. determined the second cyclical
hydrograph.
Plate 11a) and entered in Column 2.
HYDROGRAPH TROUGH
(3)
The time from the beginning of rise of Column 3 is computed as the product
of the values of Li and Column 2. The duration of the initial hydrograph
(7)
Time abscissas are selected to define the hydrograph trough and entered in
Column 7.
(Li) is taken from Line 10, Table I, Plate 11a, to be 4.55 hours.
(8)
The discharges on the recession leg of the first hydrograph are determined
(4)
The downstream hydrograph ordinates are computed as the product of Column 1
and the required downstream peak discharge of 14,000 cfs and entered in
from Plate 11c at the times of Column 7 and entered in Column 8.
(5)
Column 4.
The time from beginning of release at the dam to the time of peak of the
(9)
The discharges on the rising leg of the second hydrograph are read at the
times of Column 7 and entered in Column 9.
downstream hydrograph is computed as the sum of 1K and Li/2 which equals
15.7 hrs.. E IC and Li are taken from Lines 7 & 10 respectively in Table I,
Plate ha.
(10)
The hydrograph trough discharge is equal to the sum of Columns 8 & 9 and
entered in Column 10. The trough hydrograph is plotted on Plate 11c
at the times of Column 7 and the discharges of Column 10.
Note:
The time of beginning of rise of the downstream hydrograph is computed as
the difference of Line 6, Col. 5 and the time of peak on Line 6, Col. 3,
Table III. The time of beginning of rise equals 7.4 hours.
Column 5 lists time from beginning of release to each downstream hydro-
graph ordinate and is computed as the sum of Line 1, Col. 5 and Co].. 3.
The first cyclical hydrograph is plotted on Plate llc from Col. 4 and
Col. 5.
MHB II
PLATE NO. lib
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24
20
16
?
0
0 ?
z 12
DISCHARGE
MHB II
8
4
i ?
0
0 10 20 30 40 50
TIME IN HOURS
EXAMPLE PROBLEM I
HYDROGRAPHS
AT MILE 40
MILITARY HYDROLOGY R BD BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by W8- C? Date /AL avt Drawn by by 4.) A Al ? PLATE NO.1Ic
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DETERMINATION OF THE GATE OPERATIOA SCHEDULE
TABLE I
RESERVOIR WATER SURFACE SCHEDJLE
Cycle No.
Reservoir
Inflow
ac.ft.
Reservoir
storafr,e
End of cycle
ac.ft.
Reservoir
elevation
End of cycle
ft.ms1
----,
Water
surface
drop per
cycle
ft.
Col. 1
Col. 2
Col. 3
col. 4
col. 5
Initial
0.0
200,000
1120.0
0.0
1
0.0
189,450
1118.0
2.0
2
0.0
178,900
1116.0
2.0
3
0.0
168,350
1114.0
2.0
4
0.0
157,800
1112.0
2.0
5
0.0
47,250
1110.0
2.0
6
0.0
136,700
1107.4
2.6
7
0.0
126,150
1104.5
2.9
8
0.0
115.600
1101.2
3.3
9
0.0
105,050
1097.8
3.4
10
0.0
94,500
1094.0
3.8
EXPLANATION OF COMPUTATIONS
Cot
(1) The initial reservoir conditions and the hydrograph cycle
number are listed in Column 1.
(2) The inflow into the reservoir during the release period is
listed in Column 2.
(3)
(4)
(5)
HB II
The reservoir storage at the end of each cyclical release
is listed in Column 3. The volume of water released in each
hydrograph (10,550 acre feet taken from Line 1, Table II,
Plate 11a) is subtracted from the reservoir storage re-
maining after the previous release and the inflow of
Column 2 is added.
The reservoir elevation at the end of each release cycle is
determined from the reservoir storage curve (Plate 7) for
each storage of Column 3 and entered in Column 4.
The difference in water surface elevation for each release
cycle is computed as the difference in elevations of
Column 4 and tm-tered in Column 5.
PLATE NO. 12 a
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DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS
DETERMINATION OF THE GATE OPERATION SCHEDULE
TABLE II
GATE OPERATING SCHEDULE
Line
Hydrograph
Time
Volume of
Reservoir
Res. N.S.
Time
Gate Operating Schedule
Alternate Setting
Cycle No.
Increment
Release
Storage
Elevation
"H" hours
End of Per.
End of Per.
hours
ac.ft.
ac.ft.
ft.ms1
Hrs. - Min&
Col. 1
Col. 2
Co].. 3
Col. if
Col. 5
Col. 6
Col. 7
Col. 8
1
1
0.00
200,000
1120.0
0 - 0
2 tainter gates at 10' opening
2
2.55
5900
194,100
1119.0
2 - 33
2 tainter gates at 10' & 1 conduit at 1.7' opening
3
2.00
4650
189,450.
1118.0
4 - 33
Close spillway and conduit gates.
4
Z
0.00
16 - 24
2 tainter gates at 10.5' opening
5
2.55
5900
183,550
1117.0
18 - 57
2 tainter gates at 10.5' & 1 conduit at 1.7' opening
6
2.00
11.650
178,900
1116.0
20 - 57
Close spillway and conduit gates.
7
3
0.00
32 - 48
2 tainter gates at 11' opening
8
2.55
5900
173,000
1115.0
35 - 21
2 tainter gates at 11' & 1 conduit at 1.1' opening
9
2.00
4650
168,350
1114.0
37 - 21
Close spillway and conduit gates.
10
4
0.00
49 - 12
2 tainter gates at 11' & 1 conduit at 2.2' opening
11
2.55
5900
162,450
1113.0
51 - 45
2 tainter gates at 11' & 2 conduits open
12
2.00
4650
157,800
1112.0
53 - 45
Close spillway and conduit gates.
13
5
0.00
65 - 36
2 tainter gates at 12' opening (Near limit of gate opening for head on rate)
14
2.55
5900
151,900
1111.0
68 - 09
2 tainter gates at 12' & 1 conduit at 1.1' opening
15
2.00
4650
147,250
1110.0
70 - 09
Close spillway and conduit gates.
16
6
0.00
82 - 00
2 tainter gates at 12.5' opening
1 tainter gate fully open for entire 4.55 hourperiod
17
2.55
5900
141,350
1108.4
84- 33
2 tainter gates at 12.5' & 1 conduit at 2.7' opening
(Av. Q slightly high).Stilling actiGn may be bad.
18
2.00
4.650
136,700
1107.4
86 - 33
Close spillway and conduit gates.
19
7
0.00
98 - 24
2 tainter gates at 13.5' opening
1 tainter gate fully open for entire 4.55 hour period
20
2.55
5900
130,800
1106.0
100 - 57
2 tainter gates at 14' opening
Stilling action may be bad.
21
2.00
4650
126,150
1104.5
102 - 57
Close spillway gates.
22
8
0.00
114 - 48
1 tainter gate 7.0' opening & 1 tainter gate full open
23
2.55
5900
120,250
1102.8
117 - 21
1 tainter gate 7.5' opening & 1 tainter gate full open
24
2.00
4650
115,600
1101.a
119 - 21
Close spillway gates.
25
9
0.00
131 - 12
1 tainter 10' opening, 1 tainter & 1 conduit full open, 1 conduit 0.7' open
26
2.55
5900
109,700
1099.0
133 - 45
2 tainter gates full open
27
2.00
4650
105,050
1097.8
135 - 45
Close spillway gates.
28
10
0.00
147 - 36
2 tainter gates & 1 conduit full open, 1 conduit 0.7' open
29
2.55
5900
99,150
1096.0
150 - 09
2 tainter gates & 3 conduits full open. 1 conduit 0.7' open
30
2.00 _
4650
94,500
1094.0
152 - 09
Close spillway and conduit gates.
p
EXPLAILTIONS OF COMPUTATIONS
.1112
(1)
From an inspection of the amount of drop in the reservoir water (5) The reservoir water surface elevation is determined from the (8) The gate operating schedule is determined from the discharge
surface for each release cycle as given in Column 5, Table I, storage curve (Plate 7) for each volume given in Column 4, rating curves at a head equal to the midpoint elevation of the
and the slope of the discharge rating curves on Plate 6 the dur- and entered in Column 5. reservoir for each gate setting (Column 5). At time zero (line
ation of each release cycle is divided into 2 time increments of 1, Column 6) the reservoir water surface is at elevation 1120.0
2.55 hours and 2.00 hours respectively. (6) The time from the beginning of release of the first cyclical ft. mel (Line 1, Column 5). At the end of the time increment
hydrograph to the beginning of release of eachsucceeding hydro- for the gate setting (2.55 hrs.) the water surface lowers one
(2)
The volume of water released in each 2.55 hour and 2.00 hour in- graph is determined by adding the time increment of one cycle foot to elevation 1119.0 ft. mel. The average elevation for the
crement period is determined as the product of the time increment (16.4 hrs from Line 5, Table II, Plate 11-1) to the preceding gate setting is therefore 1119.5 ft. mel. A gate setting is
in hours, the peak discharge in cfs. and the constant 0.0826. hydrograph initial time. The lines giving the hydrograph selected from Plate 6 that will release 28,000 cfs at an average
cycle numbers in Column 1 also list the time of beginning of elevation of 1119.5 ft. mel. The gate setting selected is arbi-
(3)
The hydrograph cycle number, the time increment from beginning of release of each hydrograph in Column 6. trary as there are a large number of combinations of gate openings
release for each hydrograph, and the volume of water released dur- that will release the required discharge. From the considerations
ing each increment are entered in Columns 1, 2 & 3 respectively. (7) The time of the intermediate gate settings is computed as the given in Section IV, "Gate Operating Schedule" the gate opening is
sum of the time increments of Column 2 (2 hrs - 33 min. & selected to be 10' for the 2 tainter gates.
(4)
The reservoir storage at the end of each increment is computed as 2 hrs) and the preceding time increment.
the difference in reservoir storage at the end of the previous (9) The other gate settings of the operating schedule are
time increment and the volume released in each increment. The determined in the sell* manner as in Item (8) above.
reservoir storage at the end of each increment period is entered
in Column 4.
M H B II
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?
-Yr2013/10/25: - -01043Ron9fInnnAnnn
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
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Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
TABLE I
DOWNSTREAM PEAK DISCHARGE
Line
Item
Unit
1
Pi
28,000 cfs
2
L.1
4.55 bra
FIRST TRIAL
3
Assume Pw
12,000 cfs
4
P % P
w.i
42.9%
5
AK EK
r r
0.292
6
AK EK
5.86 hrs2
7
(L )2
i
20.7
SECOND TRIAL
8AK
r EKr
0.283
9
Pw % Pi
43.3%
10
Pw
12,100 cfs
11
AK E K
5.87 hrs2
12
AK EK
r
0.284
13
Po % Pi
65.6
14
Po
18,400 cfs
_ 15
EK
6.96 hrs.
LaiLlt
(1)-(2) Given data
(3) As a first ;orial assume a waighted Pw discharge of 12,000 cfs.
(4) The weighted, flow is computed as the percent of the initial peak discharge. (12,000/28,000)100.
(5) The product AKrZK is determined from Plate 3 for a PW % Pi of 42.9%.
(6) The values of LIK IK in hours2 is determined from Plate 13 for a weighted Pw discharge of 12,000 cfs.
(7) The value of the duration of the initial block hydrograph (Li from Line 2) is squared and entered on
this line.
(8) A check value of LKr EKr is computed as the ratio of L1K EK (Line 6) and Li2 (Line 7). The
assumed weighted peak discharge (Line 3) is not correct as the value of AKr EKr of Lines 5 & 8
are not equal.
The weighted flow in percent of the initial peak is determined from Plate 3 at a AKrEKr of
0.283 (Line 8).
(10) The weighted peak discharge is computed as the product of Line 9 and the peak discharge (28,000 cfs).
(11) The value of LIK ZIC is determined from Plate 13 for a weighted flow of 12,100 cfs.
(12) The check value of AKr 2:Kr is computed from Lines 7 & 11 as for Line 8 and checks that value
closely.
DETERMINATION OF DOWNSTREAM HYDROGRAPH
AT MILE 21.07
EXPLANATION OF COMPUTATIONS
TAB1E I
(9)
(13) The downstream peak discharge (P0) in percent of Pi is determined from Plate 2 for a value of
AKr. ):Kr of 0.284.
(14) The downstream peak discharge at mile 21.07 is computed as the product of the initial peak dis-
charge (28,000 cfs from Line 1) and the downstream peak discharge in percent of the initial
peak discharge (65.6% from Line 13).
(15) The value of EK is determined from Plate 13 for a value of 12,100 cfs of the weighted Pw discharge.
TABIE II
DURATION OF ONE CYCIE
Line
1
Item
Unit
1
Duration of Po
for equivalent vol
of hydrograph
6.90 hours
2
Pt % Po
9.24%
3
Efficiency ratio
1.83
4
Duration of one
cycle
12.6 hours
EXPLANATION OF COMPUTATIONS
TABLE II
Line
(1 -14) Compute the duration of one cycle in the same manner as
described on Plate ha.
TABLE III
DOWNSTREAM HYDROGRAPH
.
Line
Percent of
downstream
peak Po
' Time
% Li
Time from
beginning
of rise
hours
,
Discharge
cfs
Time from
beginning
of release
at dam
hours
Col. 1
Col. 2
Col. 3
Co).. 4
col. 5
1
o
o
0.0
0
2.8 ?
2
25
43
2.0
4,600
4.8
3
50
71
3.2
9,200
6.0
4
75
95
4.3
13,800
7.1
5
90
114
5.2
16,600
8.0
6
loo
140
6.4
18,400
9.2
7
90
169
7.7
16,600
10.5
8
75
188
8.6
13,800
11.4
9
50
213
9.7
9,200
12.5
lo
25
244
11.1
4,600
13.9
11
5
295
13.4
920
16.2
_
EXPLANATION OF COMPUTATIONS
TABLE III
Line
(1) The downstream hydrograph is computed in the same manner
as described on Plate 11b.
MHB 11
PLATE NO. 14 a
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pprovea tor Release ? 5 - r
/2 . CIA-RDP81-01043R0072,nnnRnnnq_q
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
I
%
8 12
TIME IN HOURS
7-4
EXAMPLE PROBLEM
HYDROGRAPH
AT- MILE 21.07
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by Wg C.: Date tifdy /955
Drawn by R6 C PLATE NO. 14b
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25 ? CIA-RDP81-01043R002300060003-3
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
DEPARTMENT?OF THE -ARMY
52 48
44
40
36
32 28 24
DISCHARGE IN 1000 cfs
20
16
12
CORPS OF ENGINEERS
8
4
CHANNEL
b = 40'
channel side slope =1:1
overbank side slope = I:10
channel "n" = 0.040
overbank "n" = 0.080
So =18.9 x 10"
20
40
MHO II
60 80 100 120 140
CONVEYANCE IN UNITS)x 10-4
AREA IN 100 ft2
SURFACE WIDTH IN 10 ft
Declassified in Part - Sanitized Copy Approved for Release
160
180 200
50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
EXAMPLE PROBLEM
AVERAGE
HYDRAULIC ELEMENTS
MILE 0-10
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by WA c Date Acts -c-c"
Drawn by s
PLATE NO. 15
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
DEPARTMENT OF THE ARMY
CORPS OF ENGINEERS
8 4 0
40 36 32 28 24
DISCHARGE IN 1000 cfs
32
28
2 20
16

CONVEYANCE IN UNITS x l0
AREA IN 100 ft2
SURFACE WIDTH IN 10 ft
140
20 40 60 80 100 120
channel side slope =1:1.5 220
overbank side slope=1:10
channel "n" = 0.040
overbank " n" =0.080
So = 7.58 x10-4
160 180 200
240 260
EXAMPLE PROBLEM=
AVERAGE
HYDRAULIC ELEMENTS
MILE 10 - 25
MILITARY HYDROLOGY R a D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by IN8c Date Ac'Y
Drawn by R47-5
MHB IL
PLATE NO. 16
Declassified in Part - Sanitized Copy Approved for Release @ 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
DEPARTMENT OF THE ARMY
52 48 44 40 36 32 28 24
DISCHARGE IN 10 00 cfs
20
16 12
CORPS OF ENGINEER.S
4 0
8
b = 80'
channel side slope= 1:2
overbank side slope =1,10
channel "n" = 0.040
overbank "n" 0.080
So = 4.74 x 10-4
20
40
60 80 100 120 140 160
CONVEYANCE IN UNITS x 10-4
AREA IN 100 ft2
SURFACE WIDTH IN 10 ft
180
200
220
240 260 280
EXAMPLE PROBLEMIEL
AVERAGE
HYDRAULIC ELEMENTS
MILE 25-45 _
MILITARY HYDROLOGY R & D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by WS C. Date 49 /96-c
Drawn by Rc
MHB II
PLATE NO.17
Declassified in Part - Sanitized Copy Approved for Release
50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
DEPARTMENT OF THE ARMY
0
0
0
DISCHARGE
60
50
0
-J
20
10
2
AK IN HOURS
60
50
0
o 40
DISCHARGE
30
0
0
-J
1,4
20
4
?
10
6 8
EK IN HOURS
10
12 14
?
EXAMPLE PROBLEM Ex
1K& EK
45 MILE REACH
MILITARY HYDROLOGY R & D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by 1/1/6'C DateAtig
Drawn .by JES
MHB II
Declassified in Part - Sanitized Copy Approved for Release
50-Yr 2013/10/25 : CIA-RDP81-01043R002300060003-3
PLATE NO. 18
r-
1,
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DEPARTMENT OF THE ARMY
0
0
0
DISCHARGE
6
5
4
3
2
CORPS OF ENGINEERS
0
?
1
o
_ w
_J
i
to
01
I
0
UI
cr.
I
in
CV
la
-.1
NC
4
?J
yr
i
1-..
0
/-
?1
i
)
1
)
)
D
_ 18 20 2'
0
2
4
6
1lJ
AK EK IN HOURSe
EXAMPLE PROBLEM rEr
AK EK
45 MILE REACH
MILITARY HYDROLOGY R & D BRANCH
WASHINGTON DISTRICT CORPS OF ENGINEERS
Prepared by Infoc Date AII5t
Drawn by az?-5
MHB
Declassified in Part - Sanitized Copy Approved for Release
?
50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
PLATE NO. 19
Declassified in Part - Sanitized Co .y Ap roved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
TABLE I
DURATION OF INITIAL BLOCK HYDROGRAPH
I.
Line
Item
Unit
1
Base flow
1,000 cfs
2
Po total
32,500 cfs
3
130 net
31.500 cfs
4
Pi
60,000 cfs
5
Net Po ,2 Pi
52.5%
6
AlCr ZKr
0.500
7
Pw % Pi
35.5%
8
PW
21,300 cfs
9
EK
12.95 hours
10
AK EK
18.78 hours2
11
(L1)2
37.6 hours2
12
Li
6.14 hours
-
EXPLANATION OF COMPUTATIONS
TABLE I
Line
(1) From the basic data of the problem a base flow of
100 cfs occurs in the reach from Mile 25 - 45.
(2) The total discharge for the cross section at mile 45
to give a surface velocity of 11 feet/second
(Computed in the same manner as Problem I, Plate ha.
(3)
The net discharge at mile 45 computed as the total
discharge minus the base flow.
(4)-(12) Detailed explanation the same as Lines 2-10,
Table I, Plate ha.
DETERMINATION OF CYCLICAL HYDROGRAPH
AT MILE FORTY FIVE
TABLE II
DURATION OF ONE CYCLE
Line
-
Item
Unit
1
Duration of Po
for equivalent
volume hydrograph
11.7 hours
2
Pt % Po
5.23%
3
Efficiency ratio
1.94
4
Duration
22.7 hours
EXPLANATION OF COMPUTATIONS
TABLE II
Computed in the same manner as described in Lines
1-4, Table II, Plate ha.
TABIE III
DOWNSTREAM CYCLICALROGRAPH
Line
Percent
of peak
Time
percent
Li
_
Time
First Cycle
downstream hydrograph
hours
Discharge
cfs
Total
cfs
Time
hours
Col. I.
Co].. 2
col. 3
Col. 4
Col. 5
col. 6 ,
1
o
0.0
0.0
o
1,000
5.32
2
25
54.0
3.31
7,875
8,875-
8.63
3
50
89.8
5.50
15,750
16,750
10.82
4
75
120
7.36
23,600
24,600
12.68
5
go
143
8.78
28,450
29,450
14.10
6
loo
175
10.7
31,500
32,500
16.02
7
90
213
13.0
28,450
29,450
18.3
8
75
233
14.3
23,600
24,600
19.6
9
50
270
16.6
15,750
16,750
21.9
lo
25
310
19.0
7,875
8,875
24.3
11
5
370
22.7
1,575
2,575
28.0
.
.
.
EXPLANATION OF COMPUTATIONS
TABLE III
Col.
(1)-(4),(6) Columns 1, 2, 3, 4 and 6 are computed in the same manner as explained
on Plate lib with the peak discharge of Line 6, Column 4 equal to
the net peak of 31,500 cfs.
(5)
The total downstream hydrograph is computed as the sum of Column 4
and the base flow (1000 cfs) and entered in Column 5. The values
of the total discharge (Column 5) are plotted against the time
(Column 6) and are shown on Plate 20b.
MHI3 II
Declassified in Part - Sanitized Co .y Ap?ro ed for Rel
? 50-Y
-01 043 00230006(mm
. PLATE NO. 20a
Declassified in Part - Sanitized Copy Approved for Release ? 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3
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Declassified in Part - Sanitized Copy Approved for Release 50-Yr 2013/10/25: CIA-RDP81-01043R002300060003-3