MEMORANDUM REPORT

SEPTEMBER, 1975

FCD BACKWATER PROFILE COMPUTATION

B YSUN-FU SHIH

RESOURCE PLANNING DEPARTMENTCENTRAL AND SOUTHERN FLONIDA

FLOOD CONTROL DISTRICT

MEMORANDUM REPORT

September, 1975

FCD BACKWATER PROFILE COMPUTATION

by

Sun-Fu Shih

Resource Planning Department Central and Southern Florida Flood Control District

West Palm Beach, Florida 33402

1

FCD BACKWATER PROFILES COMPUTATIONPage

List of Tables iii

List of Figures iii

INTRODUCTION 1

OBJECTIVES 1

DESCRIPTION OF THE METHODS 2

BASIC THEORY 2

HYDRAULIC ELEMENTS OF FLOW CROSS SECTION 2

Category A. Mean Constant Roughness Coefficient 3

Conclusion 1. 7

Conclusion 2. 8

Category B. Varied Roughness Coefficient 8

Case 1. 10

Case 2. 11

GRADUALLY VARIED FLOW EQUATION 12

COMPUTER PROGRAM DESCRIPTIONS 14

E070 - CHANNEL CROSS SECTION PERFORMANCE 14

Input of Program , 14

Output of Program 15

E081 - BACKWATER COMPUTATION WITH EQUAL MESH SIZE ASSIGNMENT 15

Input of Program 15

Output of Program 17

E071 - BACKWATER COMPUTATION WITHOUT CONSIDERING THE MESH SIZE 18

EXAMPLES OF APPLICATION 18

EXAMPLE 1: SIMPLE GEOMETRIC CHANNEL 18

EXAMPLE 2: WATER SURFACE PROFILE COMPUTATION IN C-123 CANAL 19

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Page

EXAMPLE 3: WATER SURFACE PROFILE COMPUTATION IN C-24 CANAL 20

EXAMPLE A: DESIGN CHANNEL WITH DIFFERENT ROUGHNESS COEFFICIENT MATERIALS 21

DISCUSSION AND SUMMARY

REFERENCES

APPENDIX

1. USERS MANUAL FOR E070

2. USERS MANUAL FOR E081

3. USERS MANUAL FOR E07I

4. E070 - COMPUTER PROGRAM

5. E081 - COMPUTER PROGRAM

6. E07I - COMPUTER PROGRAM

ANNEX A: EXAMPLE OF E070 OUTPUT

ANNEX B: EXAMPLE OF E081 OUTPUT

ANNEX C: EXAMPLE OF E071 OUTPUT

- in -

LIST OF TABLES

Table 1. Comparison of the results of the elevation of water surface computed based on the single section representation (SR) and multiple section representation (MR).

Page

25

Table 2. Comparison of the results of the conveyance computed by single section representation (SR) and multiple section representation (MR).

LIST OF FIGURES

Figure 1. Natural channel section with constant Manning's n.

Figure 2. Design channel cross section.

Figure 3. Example of overbank flow.

Figure 4. Comparing water surface profiles of C-24, St. Lucie County, Florida.

25

26

26

26

27

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INTRODUCTION

The results of backwater profile computation have been extensively used

in the fields of design, planning, management and quality control of water

resources problems. Methods of integration of the equation of gradually

varied open channel flow have been presented by several investigators.

However, a rigid technique used to determine the hydraulic radius is not

reliable because at the present time the vertical partition of the subchannel

associated with a given wetted perimeter is not a proper procedure in some

areas. An improper procedure used to partition the subchannel cross section

can cause a significant difference of backwater computation. A proper technique

used to compute the backwater profile should be studied further because an area

such as the District is flat in slope and very sensitive in stage difference.

Over 1,550 miles of canals and levees have been constructed for flood protection

and water supply. The average slope of those canals are between 0.3 and 0.4

foot per mile and the mean velocity is about one to two feet per second. It

is obvious that a few inches of the flow stage difference can cause a serious

impact of canal structures on an operating system. A technique to determine

the flow stage of the canal systems in South Florida becomes a very important

feature. Therefore, the technique used to compute the backwater profile should

be applied carefully in the South Florida area.

OBJECTIVES

The objectives of this report are:

(1) to introduce a basic theory used to perform the backwater profile

computation;

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(2) to mathematically prove that the conveyance of the channel section

calculated by multiple section representations is never less than

that by a single section representation;

(3) to introduce the flow equation and numerical technique used to

integrate the gradually varied flow;

(4) to develop the computer programs for cross section computation

and backwater profile calculation;

(5) to exemplify numerically that different techniques used to perform

the subcross sectional area associated with the wetted perimeter

gives different conveyance of the channel section;

(6) to present a water surface calculation which is affected signi­

ficantly by the different techniques used to partition the channel

cross section; and

(7) to demonstrate the applications of computer programs.

DESCRIPTION OF THE METHODS

1. BASIC THEORY.

The calculative procedure is based on the Bernoullis theorem for total

energy at each cross section and Manning'sformula for the friction head loss

between cross sections. In the program, average friction slope for a r«ach

between two cross sections is determined in terms of the average of the

conveyances at the two ends of the reach.

2. HYDRAULIC ELEMENTS OF FLOW CROSS SECTION

In an open channel, the flow which is transferred across a section equals

the product of the cross sectional area and mean velocity component at right

angles to the section. The equations commonly used for uniform flow in open

channel are the Chezy formula and the Manning formula. Both equations show

- 3 -

that the mean velocity of flow is directly proportional to the hydraulic radius

and slope of channel. In general, the slope of channel is assumed to be a

predeterministic value because the elevation between two reaches is near

constant. However, the determination of the hydraulic radius is a varying

procedure because the technique used to partition the subcross section asso­

ciated with a given wetted perimeter is not unique because the hydraulic

radius is not a constant value and the result of conveyance is also varied.

As mentioned in the introduction, most canals in South Florida are assumed

to be a one dimensional flow system because of the flat slopes of the canal,

low velocities and the long narrowness of the canal, etc. Based on the

existing canal systems in the District, the canals can be classified into

two categories: First, a canal with mean constant roughness coefficients;

second, a canal with varied roughness coefficient. The concept and summary

of the hydraulic representation of flow cross sections have been studied by

Shih and Hamrick (1975). The detailed analysis of the two categories are

introduced in the following sections.

Category A. Mean Constant Roughness Coefficient

A channel with irregular cross sections such as occurs in a natural channel

may be markedly different from a simple geometric channel such as a design channel

However, it is usually possible to divide such irregular shapes into some

geometric shapes for easy calculation. For instance, Figure 1 shows that this

irregular channel can be divided into three elementary forms, that is, two

triangles and one trapezoid shape. According to the equation of continuity,

total discharge in the entire channel is equal to the sum of discharges of

subchannels, I, II and III, i.e.,

Q = Ql + Q2 + Q3 (1)

4

in which Q, Q-j» Q2, anc* Q3 are discharges in the entire channel, subchannels

I, II, and III, respectively. Equation 1 can be rewritten as:

AV = A-]Vi + A2V2 + A3V3 (2)

in which A is the cross sectional area and also eauals A-|+A2+A3; where A],

A2, A3 and V-|, V2, V3 are cross section areas and mean velocity of subsection

channels I, II, and III, respectively. After applying Manning's formula into

equation 2 and eliminating the common factors such as 1.486 roughness coefficient

n, and slope of channel in both sides of the equation givesAt(A/P}2/3 + A2(A/P)2/3 + A3(A/P)2/3 = A1(A1/P1)2/3 + A2(A2/P2)2/3 + A3(A3/P3)2/3 (3)

where P = P-j + P2 + Py, in which P-| , P2, and P3 are wetted perimeters of

subchannels I, II, and III, respectively. The -qual condition in both sides

of equation 3 exists only if the following equivalent term of both sides are

equal , i.e. ,

A/P - A-f/P-, = A2/P2 = A3/P3 (4)

However, in practical application, P-j, P2, P3 are assumed predeter­

mined values, and A-j, A2 and A3 are performed by dividing the channel along

vertical coordinates which are associated with the given wetted perimeters P-j,

P2 and P3. The total area, A] + A2 + A3 obtained by any partitioning techni­

que, is a constant value; but the result of using the vertical partitioning

technique may not satisfy the condition as given in equation 4. If equation

4 is not considered, the results of the right hand side of equation 3 is

never less than the left hand side.

Proof:

Based on the convex function theorem {Rockefeller, 1970), if function

f is a postively homogeneous proper convex function, then

+ ... + Amxra) ± .^f^) + ... + xmf(xm) (5)

- 5 -

whenever X] >0, ..., xm > 0.

The equation 3 can be rewritten as

5/9 5/2 O/J5 5/2 5/2(A5/2)2/3 , ,2/3 + (A2 ,2/3 + (£ ,2/3 (6,

P p-| H2 P3

The elements of equation 6 such as A, Ap A2, A3, P, P], P2, and P3 are

all positive values, so each term of equation 6 is a positive function. The

wetted perimeters P, Pp P2 and are some predetermined values, but A, Ap

A2, and A3 are functions of flow depth D, Dp D2, and D3 and multiple channel

width B, Bp B2, and B3, respectively. For example, cross section A can

be expressed as

A = CDB, (7)

where C is some constant. Let D=pD and B=pB, in which p is any positive

number. Substituting equation 7 and new parameters pD and pB into the left-

hand side of equation 6 gives

((CpDpB)5/2)2/3 = p10/3 (iCDB)^£)2/3 = p10/3 {A^2/3 (8)

p p p

Based on Euler's Theorem on Homogeneous functions (Spiegel, 1963), a

function f(Xp X2, ...» Xm) is called homogeneous of degree n if, for all

values of the parameter p and some constant n, we have the identity

f(pXp pX2, p Xju ) = p nf {Xi, X2, . • •, Xjy|). (9)

So the function of (A5^2/?)2^3 is a homogeneous function, similarily,

the functions of (A^/P-,)^3, (A2^2/P2)2?f3, and (Ag^/P-j) can be

proved as homogeneous functions.

The results of first and second derivatives with respect to D and B

in the left hand side of equation 6 can be expressed as

A5/29(p----- )2/3 5 r5/2 2/3 2/3 5/3~| (j- ) D B (10)

30

6

,A5/2,2/3

jB

TD2

,2,^2 2/3

r c5/2 2/3 5/3 2/3- (- ) D B3 P

in C5/2 2-/3 5(~ ) (b5/d) 1/3(12)

10 r^2 2/3 5 ^3(£ , 73 (D /B)

;i n

( 1 3 j

The right-hand side of equations 10, 11, 12 and 13 are all greater than

zero, so the function (A^/p)2/3 is a proper convex function. The functions

of (2/p )2/< 3, (A^2/?^^ anci (A^/P^)"^ can be proved in a similar way

as proper convex functions. Therefore, each term of equation 6 is a positively

homogeneous proper convex function.

According to the convex function theorem described,

then

,5/2 5/2 5/2(■.,/+ ,/2 A’Pl 2ps ’3p,

5/2 5/2 5/2a. (fl )2/3 + A?(^ )2/3 + ',,(53 )2/3pp1 1 2p2 3Vp3

(14)

Let the left-hand side equal to

5/2

(a17T

5/2A2 ,

Pl ''2P2

5/2A3

3p2)2/3 - 01

5/2 5/2x2 a2

5/2<3A3 }2/3

(15)>■4 P

This equal condition will exist under the condition of equivalent

both sides are equal, i.e.5/2 5/2

. Ai = Mllpl X4P

5/2 5/2A2 A2a2

An----- = --------P2 MP

terms If

(16)

(17)

- 7 -

(18)

5/2 5/2a3 = x3^3

3p-j ^4P

Eliminating the

three equations

conmon parameters of equations, 16, 17 and 18 and summing these

together gives

A4 = 1/3 (19)

Based on the convex function theorem, the numerator of the right-hand side of

equation 15 yields

X-j + XgAg/ + X3A3 >_ (x-jAq + ^2^2 + ^3^3)

combining equations 14, 15, 19 and 20 together gives

5/2 5/2 5/2 5/2,(*1*1 * *2A2 * *3*3) 2/3 . A, 2/3 Ap , 2/3 , , ,A3' 2/3 . .(---------T73“p------------------) i *1 (py ) + *2 <jsp 3<P3 (2 '

(20)

As the convex function theorem indicated, a-|,A2,A3 > 0, so let a-j = Ag =

a^ = 1/3, equation 21 yields

5/3 5/3 5/3A5/3 A] A2 A3 ^ip2/3 +^7J+p2/3

(22)

Multiplying a common factor of 1.

back into equation 22 gives

5/3E486 < E486 *1

n p2/3; - n ^p2/3

486/n which was eliminated in equation 3,

a|/3 a|/3(23)

The terms of equation 23 are known as the conveyance of the channel section.

For convenience, the left-hand side of equation 15 is called a single section

representation (SR) and the right-hand side is termed a multiple section

representation (MR). As equation 23 shows, the following two conclusions

can be drawn:

Conclusion 1. If an equal mean velocity is assumed and the subchannels are

not partitioned based on the conditions given by equation 4, then the conveyance

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of the channel section obtained by the MR method is never less than that by the

SR method.

Conclusion 2. If the stages and discharges of a one-dimensional flow canal

are recorded, then the elevation of the backwater profile calculated by the

SR method is lower than that of the MR method, because the SR method develops

less conveyance for the given channel section.

Category B. Varied Roughness Coefficient

Chow (1959) mentioned that the cross section of a channel may be composed

of several distinct subsection with each subsection different in roughness

from the others. For example, an alluvial channel subject to seasonal floods

generally consists of a main channel and two side channels as shown in Figure

3. Henderson (1969) indicated that the distinct regions of flow shown in

Figure 3 have different velocities. Kinori (1970) described that experience,

both in the field and in the laboratory, and indicated that it is meaningless

to calculate such a cross section in the usual way; that is, to treat it as

a whole. The mean velocity in the main channel is greater than the mean

velocities in the side channels because the side channels are usually found

to be rougher than the main channel. After applying the Manning formula to

equation 2 and eliminating the common factors such as 1.486 and slope of

channel,

in which n is an equivalent roughness coefficient, np ng, and n3 are

roughness coefficients of subsection channels I, II, III, A=A1+A2+A3 and

P=Pl+Pg+p3. The equal condition in both sides of equation 24 exists only

if the following equivalent terms of both sides are equal, i.e.

A A1

nP “ niP1P1 "2P2

1__ = A2 = ^3 (25)

- 9 -

If the conditions of equation 25 are not considered, then equation 24

can be rewritten as

V? „5/2 n5/21 (A /^2/3< lA >2/3, lA ,2/3 1_( n ^P ' _ ni P1 n2 P2 + n3V

,5/2 A 2/3 (26)

'1 rl ' "2 r2 "3 r3

A similar technique as introduced in the section of constant roughness

coefficient is used to prove each term of equation 26 as a postively

homogeneous proper convex function. Based on the convex function theorem

as mentioned in equation 5, the right-hand side of equation 24 can be

expressed as

(xi

5/2Ai

plnl37? + x,

5/2A2

'p2n: 3/2

5/2 5/2 5/2x , A3 \2/3 , /A1 \2/3 , , ,A2 >2/3

P,n1"1P2"A

.5/2

+ 2/3

P3n;72

(27)

Let the left-hand side of equation 27 equal

5/2 5/2 5/2 a5/2 5/2 5/2, , *3 ,2/3- , A J2A2 + *3A3 ,2/3

„ V2 A* ■ ’--------- 7 p-3/Z- ----------- >P2n2 P3n3' A“ p "

i A1 A2+ x2- (28)

plnl Pono' Pon'j' A4

The equal condition in equation 28 will exist under the conditions of equivalent

termsof both sides are equal, i.e.,

1x4Pn3/2 (29)p,nf2

1 = 1P2ni/2 x4 Pn3/2 (30)

1 1p3n3/2 ' >4 A (31)

10

After summing equations 29, 30, 31 together

1 /l"l/2+ p2n2/2+ p3n3/2,

Pn3/2

(32)

Reling on the convex function theorem, the numerator of the right-hand side

of equation 19 can be related as

5/2 5/2 5/2 5/2X^A-j + a2A2 + \3A3 1 (>■•} A] + a2A2 + x3A3^

Combining equations 27, 28, 32, and 33 together;

5/2 5/2(x,A, + X2A2 + a3A3) ,/3 a, 2/3 A,

(----------------------------- ---------— } + M

(33;

,2/3

i(P „3/2, P n3/2+ P n3/2) pl"?/:3'Plnl + *2 2 3n3 '

P„n3/f. ^2n2

—j/TP3n3 c 34

As the convex function theorem indicated, parameters Xp x2 and X3 can

be equal to 1/3, so equation 34 is rewritten as

5/3,5/3

3/2//3', 3/2 3/2 D(Pj n] + P2n2 + P3n3 ) nlpl

2/y

5/3 5/3a2 a2

27T +n2P2

02/3n3P3

;35)

X4 = i <‘

A

The left and right side of equation 35 are termed as homogeneous techniques

with roughness coefficient (HTR) and composite technique with roughness

coefficient (CTR), respectively.

The following two cases can be used to discuss the physical concept

of equation 35;

Case 1. Each subsection of channel with different coefficients of

roughness has the same mean velocity which was assumed by Horton (1933).

This assumption may be existing in some design channel with different

construction material for side walls and channel bottom. According to this

assumption, Chow (1959) indicated the following relationship

??.,4

- 11-

3/2 2/3 3/2(Pn ) ’ = (P^/ + P„n

3/2 2"2

, 3/2.2/33n3 > (36)

where n is an equivalent coefficient of roughness- Substituting equation 36

into equation 35 gives

A5/3 5/3

*1>5/3

nlPl27T

4/3

n2p2/3(26)

As equation 25 indicated, both sides of equation 26 will be equal under the

conditions introduced in equation 25. From equations 25 and 36, the

following functions can be drawn:

n „ 3/2A - ' ’

Pl"l/2+ P2n2/2+ P3n3/2

3/2p2An2

A2 = „ 3/2 “ 3/2 n 3/'2" P^n-j + P2n2 + P3n3

(37)

(38)

A3 =

n ■ 3/2 p3An3

P n3/2 plnl + P2n2

(39)

If a channel is assumed such that each part of a subchannel has the same mean

velocity and the Ap A2, and A^ are not chosen by the conditions introduced

in equations 37, 38, and 39, then a higher mean velocity will be obtained

by the CTR method according to equation 26. A later example will show the

numerical difference between HTR and CTR methods.

Case 2. An alluvial channel with different roughness coefficients in

the main channel and side channels has a distinct different mean velocity in

each subchannel. In this type of channel, a CTR method is more reliable

because the assumption of the same mean velocity in the entire channel is

not practical. However, it should be realized that the technique of selecting

12

boundaries between side channels and main channel will affect the results of

computation. But, in practical application, a vertical boundary between

the main channel and side channel is assumed because of the following two

reasons: First, the number of main channel and side channel boundaries are

limited to a few numbers of subsections such as shown in Figure 3 as only

two boundary lines; second, the possible deviation of area due to the vertical

boundary assumption is also very small as compared with each subchannel area.

So the deviation caused by a different technique to partition the boundary

between the main channel and side channel is assumed a negligible value in

alluvial channel.

3. GRADUALLY VARIED FLOW EQUATION.

Chow (1959) indicated that the differential equation of gradually varied

flow is

dz . ~ ST- (40)

cix , aQ2T1 - gjr-

in which y is the depth of flow; x is the distance along the channel bed;

Sq is the slope of the stream bed; is the energy gradient; a is the

energy coefficient; and Q is the discharge; T is the top width of the channel

section; g is the acceleration due to gravity; and A is the cross-sectional

area of the channel. When the fianning formula is used the energy slope is

Sf =2.22 R

4/3 (41)

Substituting V = Q/A and R = A/P into equations 41 and 40 yields

n2QV/3

_ S0 2.22 f42}

OlQ2T

gA31

- 13 -

in which V is the velocity of flow; n is Manning's roughness coefficient;

R is the hydraulic radius; and P is the wetted perimeter. The parameters

A, P, n and T are functions of the depth of flow y and channel geometry.

So equation 42 is nonlinear. This nonlinear equation can be solved by

numerical procedure which is based on the iteration technique (Hildebrand,

1956; Prasad, 1970). However, as indicated in the previous section of

hydraulic elements of open channel flow, the technique used to partition

the channel cross section was neglected. Therefore, some modifications

were made in this study. The value of a was introduced in detail value

by Chow (1959) as follows:

CHANNELSValue of a

Minimum Average Maximum

Regular channels, flumes, spillways 1.10 1.15 1.20

Natural streams and torrents 1.15 1.30 1.50

Rivers under ice cover 1.20 1.50 2.00

River valleys, overflooded 1.50 1.75 2.00

As can be seen from the above table, the values of a ranged from 1 to 2.

Based on the author's previous study in the Kissirmee River area, the value

of a equaling 1 is quite satisfactory in most cases.

14

COMPUTER PROGRAM DESCRIPTIONS

Three computer programs are involved in the backwater profile computation•

First, the parameters of wetted perimeter and the top width In each reach

computed based on different stages. Second, the backwater profile is commuted

by using an equal size of AX assignment. Third, the backwater profile is

integrated by using an unequal size of aX.

1. E070 - CHANNEL CROSS SECTION PERFORMANCE

The channel cross section performance was developed in a computer program

called E070.

Input of Program:

(a) Canal Name (CN card): Each run of the program should be identified

with a name such as the name of the canal, structure or location,

dates, etc.

(b) Elevation Limit and End of Slope (EL card): The maximum elevation

limit to which the end slopes of the canal are extended. It should

be noted that the elevation limit needs to be higher than the possible

stage of computation. Two options are involved in this card. Option

1 is the slopes of both sides of the canal which are extended to the

end point of the section. The main purpose of this option is to

keep discharge in both floodplain and main channel. Option 2 is toe

slopes of both sides of the canal which are extended to the high

points in each side of the canal. The purpose of option 2 is to

keep the flow in the main design channel. The assignment of horizontal

extension of slope for each foot of elevation to the elevation limit

is also required.

15

(c) Manning's "n" classification (CL card): Since Manning's "n"

coefficient depends on such factors as type and amount of

vegetation, seasonal variation of vegetation growing, channel

configuration and stage, several options are available to vary

"n". Five different coefficients are classified in this program:

(d) Channel Station (ST card): The input of station is based on

feet because the distance between two stations is subtracted

from two stations' input. Where it is desired to change the

flow beginning at a certain cross section, such as confluence,

with another tributary or a significant variation of the cross

section configuration portion, a new station should be indicated.

(e) Range and Elevation: The cross sections may be oriented looking

either upstream or downstream since the program considers the

left side to be the lowest range number and the right side the

highest. The inputs of range and elevation are in feet.

Output of Program:

The inputs of canal name, elevation limit, channel station, range

of each coefficient classification, and range associated elevation

are all printed out. Rearrangement of range and elevations with

the end of slope adjustment, top width and wetted perimeter of

five coefficient classifications are also printed out.

2. E081 - BACKWATER COMPUTATION WITH EQUAL MESH SIZE ASSIGNMENT.

The backwater functions have been integrated by several investigations.

Chow (1955) presented a method of integration in which a set of tables

of the varied flow function is required. Keifer and Chu (1955) showed

a method of numerical integration for circular conduits. Pickward

(1963) demonstrated a numerical integration based on a finite series of

1 b -

polylogarithms and polynomials, u.r/',', Prasad (1973) ’ntcoduced ■

numerical solution based on a sira.-lc- i anidly converging; i ter; i •'

However, no single method has beer; found to be suitable in bout-. .

because of the flat slopes of the canals and low velocity of tne r

Therefore, a modification of iterative method as indicated in ta,,,

hydraulic elements of cross sections is used in this computer prop

Due to several errors involved in the numerical solution, Shin ;1j

a detailed description of six possible errors which can make the r

solution meaningless. Therefore, the technique used in tins mice

of backwater function should be applied carefully. For example. ■:

a better approximation of the backwater function is desirable in i

a small mesh size, the cumulative effect of error in rounding off

increased. Therefore, decreasing the mesh size will not always ir

the accuracy of the finite difference calculations. Koundoff err;

a random character, which makes it difficult to deal with. In t;

the ranges of mesh size between 25' to 100' are suggested. The j-

note that if a smaller mesh size is used a longer computer horn;

Therefore, the decision of mesh size not only depends .non the aa,

and computer time but also the size should be smaller than h/H t

distance between two stations. Foi c,ample, ii the distance bt,Te­

stations is only 50' then the mesh i.’r should be smaller tnan da

Input of Program:

Alfa = energy coefficient, dimensionless constant,

UPDWN - Either upstream run or downstream run: dimensionless con'

SIT = Mesh size for iterating method, in units of feet.

NS = Number of stages. The maximum value is 20.

NFC - Number of friction coeffirien•a to change in run isaluhim

friction coefficients- I'he ms ■ imum riuuiifor' is ah

i 1 tha ,!■/;

, a i ng

17

NST1 = Position or location of station in run to start profile calculation

NST2 = Position or location of station in run to end profile calculation.

SI(IS) - Initial stages to be used in runs. IS is ranged from 1 to NS.

SQ(IQ) - Station value (in feet) at which discharge is to be changed.

IQ is ranged from 1 to NQ.

Q(IQ) = New discharge at the correspond!ng SQ(IQ) station.

SF(IC) = Station value (feet) at which roughness coefficients for each

classification are to be changed. IC is ranged from 1 to NFC.

XFC(IC,J) = New roughness coefficients at the SF(IC) station. J is

ranged from 1 to 5.

The output of the E070 program has also become an input of this E081

program.

Output of Program;

The input data such as canal name, discharge, initial stage, roughness

coefficient and station are all printed out. The computed results are

listed as follows:

Water Stage: the stage of water in unit 6f feet.

Depth: The water depth in unit of feet.

Top Width: The width of water surface in unit of feet.

Area: Cross section area of water flowing in unit of square feet.

Conveyance: Conveyance of the canal section is defined in equation

23 of the SR method.

Accumulated Surface Area: Accumulated average top width multiplied by

distance in unit of acres.

Accumulated Volume: Accumulated the average area multiplied by

distance in acre-ft.

Section Intercept at Left: Where the range is starting to flow,the

c

18

water in unitsof feet.

Section Intercept at Right: Where the range is ending to flow the

water in unitsof feet. The difference between section intercept

at right and left equals the top width.

3. E071 - BACKWATER COMPUTATION WITHOUT CONSIDERING THE MESH SIZE.

As mentioned in E081, a smaller mesh size is used and a longer time is

required. Especially, if a short distance between two stations is used

and the mesh size is smaller than 25 feet, then a much longer computing

time is required. Therefore, an uneaual mesh size with only ten meshes

between two stations are used is applied to the program development.

Due to the uneven error propagation, the accuracy of the result is slightly

decreased, but a smaller computing time is expected.

EXAMPLES OF APPLICATION

Example 1: Simple Geometric Channel

As Figure 1 shows, a set of numerical values such as b=2'. d=l1 , x=l 1

and Manning coefficients n = 0.03 are used in this design channel section.

Two techniques are used to partition the entire channel section into three

subchannels. First, a vertical partition without considering the conditions

given by equation 4 is used to divide the entire channel section into two

right triangular and one rectangular subchannels. The results are shown as

dotted lines in Figure 1. The conveyance calculated by SR and MR methods

are equal to 108.18 and 123.83, respectively. The results obtained by the

MR method is 14.5 percent higher than by the SR method. This result is

also consistent with the theoretical description as stated in conclusion 1.

Second, the conditions given by equation 4 are used to partition the entire

channel section into two triangular and one trapezoidal subchannels. As

19 -

mentioned in a previous section, the values of A, P, P-j , P? and P3 can be

directly calculated from the record data. The values of Ap Ag arid A3

which can be obtained based on the condition given by equation 4 are equal

to AP-|/P, AP2/P, and AP^/P, respectively. The results are shown as inclined

dash-lines in Figure 1, and the value of x1 is 1.757'. The conveyances

calculated by both methods are all equal to 108.18. This implies that the

SR method is independent of the technique used to partition the subchannels.

If a channel with a wide and shallow cross section is considered where the

hydraulic radius approximates the mean depth, then the conveyance calculated

by both methods is not significantly different. For instance, let b equal

100' in the above example, and without considering the condition given by

equation 4, the conveyance calculated by the SR method is 4943, and by the

MR method, it is 4978. The difference between the two methods is less than

1 percent.

Example 2: Water Surface Profile Computation in C-123:

A canal such as C-123 (Corps of Engineers, 1966) located in Broward County,

Florida, is used co illustrate the statement given by conclusion 2.

Manning's n value used to design the canal is 0.03, which was reported by

the Corps of Engineers (1953). This canal was opened by the FCD in September

1972. The roughness coefficients of this canal werealso re-evaluated by

Taylor and Tai (1974). The results of the roughness coefficients studied in

April, May, and July are shown in Table 1. The field data of' stages and

discharges in those three studies are also used to illustrate the Wi-ter surl.jce

profile calculation. The roughness coefficient varies until the elevation of

the computed water surface at the upstream end approaches the historical record.

As illustrated in Conclusion 1, if the condition given by equation 4 is used

to partition the subchannels, then both the SR and MR methods give the same

results. Therefore, only a vertical partition technique without considering

20 -

the condition given by equation 4 is used in the MR method. The results of

the elevation of computed water surface are listed in Table 1. Two conclusions

can be drawn from Table 1: First, if the elevation of computed water surface

is expected to approach the historical data, then the roughness coefficient

computed based on the MR method is higher than the measured data. It is

higher by about 7 to 14%, and based on the SR method is within 4.4% difference

as compared with the measured data. This 4.4* difference is still within

the 95% statistical confidence limits. Hence, the roughness coefficient

computed based on the SR method does not distort the actual roughness

coefficient significantly. Second, if the approximate roughness coefficients

are known, then the upstream elevation computed, based on the MR method, is

lower than the historical elevation difference by about 15*. However, based

on the SR method, it is only a 2% difference, which is also within the 95%

statistical confidence limits. Hence, the SR method is more reliable than

the MR method in this example of backwater profile calculation. The results

of conveyance computed by both methods are listed on Table 2. As can be

seen from Table 2, if the same approximate roughness coefficients are used

in both methods, then the conveyance computed by the MR method is never less

than that by the SR method. Therefore, the elevation of the computed water

surface based on the MR method is never lower than that by the SR method.

EXAMPLE 3: WATER SURFACE PROFILE IN C-24 CANAL

A canal such as C-24 located in St. Lucie County, Florida, is another

example used to exemplify the statement given by Conclusion 2. The total

discharge is obtained by field observations. Manning's n value, which is

equal to 0.03, was used by the Corps of Engineers. The vertical coordinates

partitions, without considering equation 4 conditions, are used to perform

21

the subchannel cross sections. The results of the water profile calculation

based on both the MR and SR methods are shown in Figure 4. As can be seen

from Figure 4, the water surface profile calculated by the MR method is one

foot lower than that by the SR method. This result is consistent with the

statement given by conclusion 2 that the stage of backwater profile computed

by the MR method is lower than that of the SR method. Although the difference

of stage is only one foot in this 20 miles of C-24, the error is as large

as 15 percent because the total elevation difference is only 6.6 feet. This

shows that the water surface profile computation is significantly affected

by the technique used to partition the channel cross section.

EXAMPLE 4: DESIGN CHANNEL WITH DIFFERENT ROUGHNESS COEFFICIENT MATERIALS

A design channel as shown in Figure 2 with b=20', d=3', and x=3' is

constructed with a concrete bottom float finished, and the side walls are

built with dry rubble. Chow (1959) indicated that the roughness coefficients

are 0.015 for float finished concrete, 0.025 for cement rubble masonry. If

the conditions of equations 37, 38, and 39 are used to estimate the subsection

area as the dash line indicated, x'=10.98'; the values of CTR and HTR are

all equal to 6816. If an equivalent n=0.02 is used in equation 35, the HTR

value is 6223. The difference between 6816 and 6223 is about 9 percent.

This result indicates that if an equivalent n value is not available in a

compound channel, but an assumption of the same mean velocity is used in the

entire channel, then the HTR method can be used to estimate the discharge

based on individual parts of construction materials. However, if the subsection

channel is divided as a dotted line with x=3', the result of the CTR method

is 8695, which will be higher than 6816 by about 28 percent and higher than

6223 by about 40 percent. This result implies that if an equivalent roughness

- 22 -

coefficient is not available, the HTR method is more reliable than the CTR

method.

DISCUSSION AND SUMMARY

Based on these studies of computation for hydraulic elements in open

channel cross section, four different techniques were demonstrated, i.e.,

homogeneous technique (SR) and composite technique (MR) for constant

roughness coefficient, homogeneous technique for varied roughness coefficient

(HTR) and composite technique for varied roughness coefficient (CTR). The

results of the theoretical proof and numerical exemplification showed that

the conveyance computed by composite technique is not less than by the

homogeneous technique. If a mean velocity is assumed equal in the entire

cross section, then the SR or HTR method is more reliable because this method

is relatively easy to use and the calculating result is also independent

of the technique used in partitioning the boundary between subchannels. A

design channel with different constructing materials for the channel bottom

and side walls, especially when an equivalent roughness coefficient is not

available during the time of designing, the HTR method is suggested to estimate

the primary discharge because the results obtained from the MR or CTR methods are

not unique. In other words, the MR or CTR methods are strongly dependent upon

the technique for partitioning the subchannel section. If a mean velocity

is obviously unequal in the whole cross section, for example, a designed channel

with one depth central channel and two shallow channels, or an alluvial

channel, the composite technique is more reliable because the mean velocities

in the central and side channels are distinctly different.

This study also concluded that the different techniques used to partition

the channel cross section will affect the water surface profile calculation.

- 23 -

For instance, theC-24 canal at St, Lucie County, Florida, will have about a one

foot elevation difference between the SR method and MR method. This one foot

is about 16 percent of the total elevation difference.

Based on the study of C-123 canal backwater profile computation, the SR

method is more reliable. Therefore, the FCD backwater profile computation

program is based on the SR technique. Three computer programs are developed

in this backwater computation. The first is called E070 which is used to

develop the channel cross section, elevation control, roughness coefficient

classification, wetted perimeter, and top width of each stage. The second

is called E081 which is used to compute the backwater profile computation with

an equal mesh size assignment. The third is called E071 which is also used

to calculate the backwater profile calculation without considering the mesh

size assignment.

REFERENCES

1. Chow, Ven Te, "Integrating the Equation of Gradually Varied Flow",Proc. Paper 838, Proceedings, ASCE, 1955, Vol. 81:pp 830-1-830-32.

2. Chow, Ven Te, "Open Channel Hydraulics", McGraw-Hill Book Co., Inc.New York, N.Y. 1959, pp. Ill, 136-140.

3. Corps of Engineers, "Central and Southern Florida Project, Part VI,Section 5, Channel Roughness", Department of the Army, Jacksonville District, Corps of Engineers, Jacksonville, Florida, May 1953.

4. Corps of Engineers, "Central and Southern Florida Project, EvergladesNational Park Water Supply—Canal 123", Department of the Army, Jacksonville District, Corps of Engineers, Jacksonville, Florida, November, 1966.

5. HEC-2, "Water Surface Profiles", the Hydrologic Engineering Center,Corps of Engineers, U. S. Army Computer Program: 723-X6-L2O2A, 1971.

6. Henderson, F. M., "Open Channel Flow* Macmillan Company, New York,N.Y., 1969, pp: 19-21, 144-148.

7. Hildebrand, F. B., "Introduction to Numerical Analysis”, McGraw Hill BookCompany, Inc., New York, 1956.

24

8. Horton, R. E., "Separate Roughness Coefficients for Channel Bottom andSides", Engineering News Record, Vol. Ill (22): pp: 652-653, Nov. 30, 1933.

9. Keifer, C. J, and M. H. Chu, "Backwater Functions by Numerical Integration",Transactions, ASCE, 1955, Vol. 120: pp: 429-442.

10. Kinori, B. Z., "Manual of Surface Drainage Engineering',' Vol. 1, America’1Elsevier Publishing Company, Inc., Mew York, M.Y., 1970, pp: 36-90.

11. Lansford, W. M. and W. D. Mitchell, "An Investigation of the BackwaterProfiles for Steady Flow in Prismatic Channels", University of Hi inu i - Engineering Experiment Station Bulletin No. 381, Urbana, Illinois,1949, P. 29.

12. Pickward, W. F. "Solving the Equations of Uniform Flow", Journal of theHydraulic Division, ASCE, 1963, Vol. 89 (HY4): 23-37.

13. Prasad, Ramanand, "Numerical Method of Computing Flow Profiles", Journalof the Hydraulic Division, ASCE, 1970, Vol. 96 (BY!):75-86,

14. Rockafeller, R. T., "Convex Analysis", Princeton Un-’versity Press, PrincetonN. J., 1970, pp: 23-31.

15. Shih, S. F., "Commentary on Modified Monte Carlo Application to GroundwaterMovement - The Simultaneity Procedures", Water Resources Research,Vol. 10(4): 885-887.

16. Shih, S. F., and R. L. Hamrick, "Hydraulic Representation of Flow CrossSections",Journal of Drainage & Irrigation, ASCE, 1976, Vol. 102 (;Rii

17. Spiegel, M. R., "Advanced Calculus", Schaum Publishing Company, New Ye,A.,1963, pp: 106.

18. Taylor, R. L. and C. S. Tai, "Roughness Coefficients in C-123 Canal’,’Hydrology Division, Resource Planning Department, Central and Soutnern Florida Flood Control District, West Palm Beach, Florida, Dec. 1974.

Table I. Comparison of the results of the elevation of water surface computed based on the single section representation (SR) and multiple section representations(MR).

Scat i ons Wate r Surface Elevation. M S.L. - Ft.(f rom May 22, 1974 April 24, 1974 July 25, 1974downs t ream SR MR SR MR SR MRft.) O,Q37"O.O37 0.041 0-035 0.035 0.039 0.025 0.025 0.028

IIU*1

CD o cfs Q=690 cfs Q=1190 cfs

811+50 6.75 6.75 6.75 7.03 7.03 7.03 9-96 .9-96 9.96736+00 6.94 6.90 6.93 7.25 7.20 7.24 10.14 10.09 10.12735+00 6.94 6.90 6.93 7.25 7.20 7.24 10.14 10.09 10.12308+00 8.39 8.06 8.31 8.85 8.49 8.78 11.40 1 1 .09 11.34

307+00 8.390=5308.07

cfs8.31 8.85

cfs8.78 1 1 .41

Q=11701 1 .09

cts] 1.3^

214+50 8.76 8.37 8.66 9-23 8.81 9.16 11.80 11.40 11.722 1 *++00 8.76 8.37 8.66 9.23 8.81 9.16 11.80 11.40 11.72

5=510 f s 6=580 cfs 0=1165 c f s

162+00 9.17 8.74 9.07 9-62 9.17 9.53 12.1 1 1 1 .69 12.05161+00 9.18 8.76 9.08 9.64 9.18 9.55 12.13 11.72 12.07109+00 9.33 8.90 9.24 9.78 9.32 9.70 12.28 11.86 12.23108+00 9-33 8.90 9.24 9.78 9-33 9.71 12.28 11.86 12.2357+00 9.40 8.97 9.32 9.86 9.40 9.79 12.36 11 .94 ,2.3255+50 9.4o 8.97 9-32 9.86 9.40 9.79 12.36 11.94 12.32

2+87 9.45 9-02 9.37 9.91 9.45 9.84 12.41 11.99 12.370+62 9.45 9-02 9-37 9.91 9.45 9.84 12.41 11 .99 12.370+00 9.45 9.02 9.37 9.91 9.45 9.84 12.41 11.99 12.37

Record Downstream 6.75 7.03 9.96Data Upst ream 9.43 9.86 12.39Measured n va 1 ue 0.0377 0.0341 o.b26"i

"Roughness coefficient used to compute the backwater profile.

Table 2. Comparison of the results of the conveyance computed by single section representation (SR) and multiple section representat ions (MR) .

Conveyance, *10^

Stations May 22,. ,974 April 24, 1974 July 2[i, 1974ft. SR * MR SR MR SR MR

0.037 0.037 0.041 0.035 0.035 0.039 0.025 0.025 0.028811+50736+OO 1.178 1.344 1 .2,5 1.291 1.473 1.325 2.473 2,884 2.579

735+00 1.055 1.197 1.085 1.160 1.316 1.187 2.260 2.610 2.340

308+00 1 .015 1.128 1.038 1.129 1 .253 1.150 2.184 2.457 2.230

307+00 0.959 1.054 0.983 1 .075 1.179 1.098 2.03, 2,261 2.075

214+50 0.826 0.910 0.851 0.927 1 .019 0.952 1.765 1.961 1 .807

214+00 O.699 0.752 0.711 0.795 0.85, 0.805 l .625 1 .737 I.616

162+00 0.574 0.597 0.574 0.662 0.688 0.660 1.482 1.534 1 .425

161+00 0.779 0.799 0.763 0.889 0.9,0 0.869 1.856 1.902 1 .786

] Q9+O0 0.972 0.988 0.941 1.103 1.119 1.064 2.214 2.273 2.130

10 8+00 1 .141 1.171 1.114 1 .299 1.322 1.257 2.570 2.652 2.484

57+00 1.318 1.350 1.283 1.490 1.522 1 .445 2.919 3-024 2.83,

55+50 1.5,0 1.544 1.467 1 .704 1.739 1.650 3309 3.429 3.209

2+87 1.700 1.737 1.650 1.482 1.954 1 .854 3-696 3.831 3.583

0+62 1 .985 2.002 1.919 2.257 2.277 2.181 4.651 4.685 4.408

0+00 2.261 2.262 2.183 2.592 2.594 2.501 5.515 5-527 5.212

Average 1.045 1.137 1.056 1 .140 1.269 1.175 2.276 2.496 2.291

“ Roughness coefficient u$ed to calculate the conveyance.

- 25

26

Figure 1. Natural channel section with constant Manning's n.

F- - - H

Figure 2. Design channel cross section.

Figure 3 Example of overbank flow

ii

27

DISTANCE IN MILES

Figure 4. Comparing water surface profiles of C - 24, St. Luice County, Florida.

E070-1

APPENDIX I: USERS MANUAL FOR E070

FOR PROGRAM TO BUILD TAPE FILE OF SECTION GEOMETRY AND CHARACTERISTICS

FROM CROSS-SECTION DATA

E070

(BLDWS)

CENTRAL AND SOUTHERN FLORIDA FLOOD CONTROL DISTRICT

E070-2 -

PROGRAM LIMITATIONS

]. Limit o£ 500 stations with section data in any one run.

2. Limit of 68 range and elevation points per section.

3. Limit of 5 coefficient classification codes in the range of 1 to 5 inclusive.

4. Limit of 5 pairs of ranges for any of the 5 classification codes (must all be on the same card).

5. Limit of 50 distinct elevations.

MOTES: Error messages are printed and processing is discon­tinued if any of the above limitations are exceeded.

A warning message is printed if the coefficient classification ranges do not extend over the width of the section; however, processing will continue.

REQUISITION FOR COMPUTER WORK

Est. Time - - One minute is needed, approximately, for one cross section in natural channel or for five cross sections in designed channel.

Category - - Production Run

Job Run No. - E-070

Output Tapes- 11 - Tape No. is assigned by user

Disks - - 6100

- EO7O-3

USER’S INPUT DESCRIPTION

MISCELLANEOUS NOTES

CARD ORDER

The first input cards must be a "CN" card followed by an "EL" card.

The "CL" card must be present before "RE" cards are encountered.

The "CL" card(s) may be present at intervals throughout the run; how­

ever, for a "CL" card(s) to apply to a given station, the "CL" card must

be placed between the "ST" card and the "RE" card(s) for that station. All

"RE" card(s) processed will use the last "CL" card(s) encountered for coeffi­

cient classification ranges.

The "EL" card(s) may be present at intervals throughout the run; how­

ever, for an"EL" card(s) to apply to a given station, the "EL" card must be

placed after the "ST" card for that station. AH "ST" card(s) processed will

use the last "EL" card(s) encountered for the elevation limit and end slopes.

The very last card of the run must be an "EN" card.

The section data must be entered in an upstream order, also the ranges

on the "CL" card(s) must be in the same order as the ranges on the "RE" cards

(increasing in magnitude from left to right or right to left.)

FORMAT INFORMATION

Symbols used to indicate the proper method for numbers or letters entered

in card columns shown are -

RJ - Indicates that a whole number must be right justified in card columns shown.

DI(XX-XX) - Indicates that the decimal point is implied between the card columns shown

A - Any alpha-numeric character

E070-4

Do not indicate any decimal points on data sheets.

NOTES: "CL" card(s)

If at any time during the course of a run, a previously defined coeff

cient classification code is no longer used - insert a "CL" card with that

code present and the range fields blank at the point where it has been dis

cont inued.

E070-5

USER'S INPUT DESCRIPTION Card Format Information

"CN" Card (Canal name card)

C.C. Symbol Description

1-2 A "CN"6-11 A Contains canal name

"EL" Card (Elevation limit and end slope card)

C.C. Symbol Descri ption

1-2 A "EL"5-13 DI(10-11) Elevation limit to which the end slopes are

extended.17 RJ 1-SIopes are extended from end points of

section.O-Slopes are extended from high points on ends of section.

18-25 RJ Horizontal extension of slope for each footof elevation to the elevation limit.

"CL1* Card (coefficient classification card)

C.C. Symbol Descripti on

1-2 A "CL"4 RJ Coefficient classification code5-12 □1(11-12) '20-27 DI 26-27) ' Starting range for the area of the35-42 DI(41-42) ........... ..section for which this coefficient50-57 DI(56-57) classification applies.65-72 DI(71-72)

13-19 DI(18-19) ]28-34 DI(33-34) ] Ending range for the area of the43-49 DI(48-49) ]........... ..section for which this coefficient58-64 01(63-63) ] applies.73-79 01(78-79) ]

"ST" Care (Station Card)

C.C. Symbol Description

1-2 A "ST"5-13 01(12-13) Station of section in feet.

E070-6

"RE" Card (Range and elevation card)

Symbol Descri ption

1-2 A "RE"5-13 01(10-11) ]20-28 DI(25-26) ]35-43 DI (40-41) ]............ .Range of point at which elevation is50-58 DI(55-66) ] given.65-73 DIC70-71) ]

14-19 DI(17-18) ]29-34 Di(32-33) J44-49 01(47-48) 3.......... ■Elevation of point for corresponding59-64 Dl(62-63) 3 above range.74-79 01(77-79) 3

"EN" Card (End of data card)

C.C. Symbol Description

1-2 A "EN"

Note - Blank code in C.C. 1-2 indicates to use previous code encountered for this card.

E081-1

APPENDIX 2: USERS MANUAL FOR E081

PROGRAM TO CALCULATE WATER

SURFACE PROFILE FROM SECTION

CHARACTERISTICS ON TAPE FILE

EO81(WSPRF)

E081-2

PROGRAM LIMITATIONS

1. Limit of 20 initial stages.

2. Limit of 20 discharge changes with corresponding station values

3. Limit of 20 roughness coefficient changes with corresponding station values.

REQUISITION FOR COMPUTER WORK

Category - - Production Run

Job Run No. - - E0S1

Input Tape - - ll=Assigned No. of tape from Job Run No. E070

Disks - - 6100

USER'S INPUT DESCRIPTION

Miscellaneous Notes

For each of the number of initial stages selected, the program

will calculate the water surface profile using the given discharge

and roughness coefficient information.

Symbols used to indicate the proper method for numbers entered

in card columns shown are:

RJ - Indicates that a whole number must be right justified in

card columns shown.

DP - Indicates that the number must have a decimal point indicated

in one of the card columns shown.

- E081-3

USER'S INPUT DESCRIPTION

Card Format Information

PARAMETER CARD

C.C. Symbol

1-10 DP

11-20 DP

21-30 DPCONTROL CARD

C.C. S ymbo1

4-5 RJ

9-10 RJ

14-15 RJ

18-20 RJ

23-25 RJ

Note: For the last

Description

Alpha value, a positive value is required. If a negative value, e. g.(-I.O), is used, the alpha value will be changed with corresponding section characteristics -

+1.0 - upstream run ; -1.0 - downstream run.

Ax, between 25.0 and 100.0 are recommended.

(not station

Description

Number of stages

Number of discharges to change in run including initial discharge

Number of friction coefficients to change in run including initial friction coefficients

Position or location of station in run to start profile calculation

Position or location of station in run to end profile calculation

two entrys use the position number or location of stationvalue) in an upstream order.

INITIAL STAGES CARD(S)

C.C. Symbol Description

1-10 DP

11-20 DP

21-30 DP

31-40 DP

41-50 DP

Initial stages to be used in runs.

- E081-4

C.C. Symbol

51-60 DP

61-70 DP

71-80 DP

Use as many stage cards

DISCHARGE CAKD(S)

C.C. Symbol

1-10 DP

Description

Initial stages to be

necessary. No imbedded

Description

Station value (feet) be cbanged.

used in runs.

blank fields allowed.

at which discharge is to

11-20 DP New discharge at the above station.

ROUGHNESS COEFFICIENT CARD(S)

C.C. Symbol Description

1-10 DP Station value (feet) at which roughness coeffi­cients for each classification are to be changed

11-20 DP New roughness coefficients at the above station. A positive value is required; if a negative vahr

21-30 DP e- g. (-1.0), is used, the roughness coefficients will be changed with corresponding depth of flow

31-40 DP (This program at present time was developed only for marsh area, if user wants to use this varia-

41-50 DP ble roughness coefficients in other area, please contact personnel in Water Planning Division)

51-60 DP

Note: At least one discharge and roughness coefficient card containing starting station value must be present in run.

Station values on these cards must be in order of run, either upstream or downstream.

- E081-5

PLOT CARD

c.c. Symbol Description

5 RJ Plot codeBlank or 0 - Do not plot water surface profile 1 - Plot water surface profile

11-20 DP Horizontal scale of plot

21-30 DP Vertical scale of plot

Note: One plot card must be present after roughness coefficient card(s). Use

as many new parameter cards with succeeding cards as necessary. The last card

must be present as a blank form.

E07V1

APPENDIX 3: USERS FOR EO71

PROGRAM TO CALCULATE WATER

SURFACE PROFILE FROM SECTION CHARACTERISTICS ON TAPE FILE

E071

(WSPRF)

The input used in this program is the same as E081 except the columns from

21 to 30 in the first card is not considered. In other words, the same set

of E081 cards can be run in E071 because the data between columns 21 and 30

is automatically not used in E071.

- AC4-0 -

APPENDIX 4: E070 COMPUTER PROGRAM

COSY V3.3 - MSOS 75.0 09/05/75 ' 'eo7o deck/ 1=01.l

PROGRAM 5LD*S

01 MFns [ON El70)»R{70>.«ODE(7) .*040)79) .CL (5.5. = ) • I C I 5)0 IMfns ION I CODE ( 7 > • I'-> I A f 15 ) .NC A AL ( 5) » I 57 H ( IO ) , J PC* < ] )DATA ( ( k ODE ( I) » I = 1.7) =2HST . 2HRE , 2HC1'1« 2hFN • 2HF L « ?H .=mCL> oat A ( ( I CODE <I) .1 = 1.7)=7 < 0 > > .< NT=1 1 ) . ( I TC <I) .T = ].G)=5(0) )DATA ((((CL(I.J.K).r = 1.5).J=l'5),K = l*3'=50(0.0)).(I-|l UK=lH )

300 FORMAT(lH].17HILLEGAL CARO CODF)301 FORMAT(Ini.57HSTATIOM CARO ENCONNTfrEO WITH NO PREVIOUS CANaL NAME

I CARO)303 FORMAT( |H1.F2HSTATION CARO FNCQ' INTE°ED WITH NO PREVIOUS ELEVATION

II TMf T FARO)= 1)0 FORMA T ( 1 rio » 1 0 ( 1 H« ). 1 = H CHANNEL STATION =,]5ai,?6H = FLOOD PLAIN

ISTATIOm =. 15A1.2X, 10 ( lH*-1) )510 FORMAT I 1H0.33HCRITICAL. ELEVATION OOFS MOT APPLY)511 FORMAT(1H0.20HCRIT JFAL ELEVATION =.F6.=)

3t)4 FORMAT ( IhI .66PRAN0E ANO ELEVATION ''ARD FNCOtJNTEREo W T T H N0 PREVIOU

IS STATION CARO)3C5 FORMAT (lHl .R5HPANC.F AND ELEVATION CARD ENCOUNTERED 91th NO pREVIOU

IS COEFFICIENT CLASSIFICATION CARD)13 FORMATf1HO,55HALLO^AMLF NUNHFP OF pan&f ANO ELEVATION POINTS FXCFF

I DEO)501 FORMAT < 1 Hl .SHFANAL .Ml)502 FORMAT(1HO»17HFLFVATION LIMIT =.El0.2)5p3 FORM A T ( 1 H'J » R 1 HR ANDES FOR COEFFICIENT CLASSIFICATION NO..12.2H =/

1 1H .4x,5(E9.?,1H-.ER.R.1H,.2X))

CC read data card

C10 READ(HP,200)KARO200 FORMAT (R0A1)

CALL RACK(KARO. 1,2, fRCK. 1 )ISAVE=*DO 20 ^=1.7

IF (IPFK ( I ) -KODF (K))?''.21.2020 CONTINUE

WRITE(51.300)GO TO 999

r

C DETERMINE TYPF of CARO

c21 IE (K- 5)41.42.414? K=lSAVr41 CO T0(j*2,3.A..5*l'7).Kr

C STATI m1 CARDC1 IE(ICOOE(3))22.22.2322 WpITR (51 . 301)

GO TO QH923 IE(1 CODE(5) )25.25,52 25 WR I TE { 5 1 • 30.3 )

GO TO R99 52 100=1

IE (If DOE (1)1 ?u,24.2S24 STATN = SC7E I (KARO.5. 1 1.". I )

DO 243 L=14.22IE (KAR', (L) -I9LNK ) 24 1.24 9.241

240 CONTINUESTATm-statn 00 TO 24?

01 n 01 on no? 0" 00 3 0 ■' 0 0 h 0 ''005 0 A A 0 k

0 0 0 0 ' f) i, 0 14

0 0 0 0 R o n o; o n n n i i nf' n 12

0 ? n 1 3 0 i n 1 a (1 <i 1 1 5 0 " 0 1 5 0 0 017 Oi 0 1 3

0 r 0 1 9 0 ■'020

00 021 UT022 V 0 f) 2 3 00 0 24

0 0 0 25 0 4 0 2H fi 102 7 (|i024 01029 0 0 0 30 Of 031 01032 00033 0 00 3a 01035

<j 1C 35 (110 37

0 0 0 =4 f)io > 4 Of 0-C i,o 04 I 0i(j4 = i) 0 0 a 3 0 0 0AA 01 0 i. =0,1 0 c 5 O') f)4 ? 0 i 0 Art

0 5 04 4 Of 05'J

C " n 51 0 0 0 5 = 0 0053 0 005a

0 o 0 5 5 01 o 5 5 0 0 05 7 0 o 0 5 3 0110 4

0 C 0 5 0

241STATM=5GET(KARD.14.2?•0.1) ' AC4-2 -

00061242 DO 250 L-23.3C 0P062

IF(KARD(L >“IHLNK)251.250.251 00063

?50 CONTINUE 00064

CRFlV=-9999.OF30 00 065GO TO 252 00066

251 CRFLV=SG£T(KAPD.23.30.0.01) 00067252 CALL STAT(STATN.TSTA) 00068

CALL STAT(STATM.ISTR> 00069WPITE(61.500)ISTA,IST8 06070IF ( CDF|,V*9998. OF30) 25 3.253.254 00071

253 WRJTF(61*510) 0007?GO TO 555 - 0073

254 WRITE (61.51 1 ) CRELV 00 074255 I CODE(I) = 1 C0075

N=0 00076GO TO 10 00077

C 00078

C PROOFS PREVIOUS STATION 00079C ohobo

c CALCULATE GEOMETRY On OB 1

c 00082

25 CALL DFSCT(N.E.R.ELrMT.KODFL.SL) 00083r 00084c ROUTINF TO CHECK FOR SECTION COVERAGE WITH COEFFICIENT RANGES 00085

c 00086CALL COFCH(R(1).P(N).CL*IC) 00087

c 00088c CALCULATE SECTION CHARACTERISTICS 00089

c 0,0090CALL SCHARIN.E.R.CL.IC.STATN.STATM,CRELV> 00091GO TO(24.30).IGO 00092

c 00093c RANGE ANO ELEVATION CARO 00094

c 00095

2 IFdCOOE(l) )31.31.29 0009631 WRITE(61.304) 00097

GO TO 999 00098

29 IF(ICODE<7)161.61.3? 00099

61 WRITE(61.305) ootooGO TO 999 00101

32 N=N*1 00102M = N*4 OC 103

MK = -9 0010400 33 L=N.M 00 105MK=MK*15 00 106IF(L-70) 11.11.12 00107

12 WRITE(61»13) 001 08• GO TO 9999 00109

11 R(L)=SGET(KAPD.MK-i.mk*7.0.001> 0O110E(H=SGET(KARO.MK.R.mk*13.0.01) 001 11

IF ( R > >33.34.33 0O112

34 IF(F (L)) 33.35.33 00113

33 CONTINUE 00114

N = M 00115

GO TO 36 0O116

35 N=L-1 00117

36 ICOOE<2)=1 00118

GO TO 10 00119

c 00120

c CANAL NAME CARO 0012100122

3 CALL MOVE (KARD.6.1 1 .f-'CAAL* 1 ) " AC4-3 -WRITE(61,5011NCAALREWIND NTWRITE(NT)NCAAL

00123 00 129 00125 00 1 25

ICODE < 3> =1 0 0 1 2 TGO TO 10 00 l 25

C Or. 1 29

Cc

ENO OF DATA CAPO 001 30 00131

9 IGO=? Of)l 32GO TO 25 00 133

30 ENO EH_E NT 00139999 REW I NO NT Of 1 35

GO TO 9999 00136

C 00137

C ELEVATION LIMIT CARO 00132

c Of 1 39

5 EL IMT = 5GET(KAPD.5,13,0.00 1 ) 00 190K0DEL=5GET(KARO,17,17,1.0) 00191

SL=SGET(KARO,18.25,1.0) 00 192WRITE(51.502)ELIMT 00193ICODE(2)=1 00 199GO TO 10 00 195

C 00196C COEFFICIENT CLASSIFICATION CARO 00197

c 001987 11 =SGFT ( K ADD, *+, 9,1.0) 00199

IC(II)=0 00150

MK = -9 00151DO 50 ,1=1.5 00152mk=mk + 15 0 0 15 3PR I =5GFT(KARO.MK-l»MK+6,0.1 ) 00 159RR9=SGFT( K ARD ♦ MK + 7 ♦ M<+■ 1 3 » 0 •1) 001 55IF(RR1)51,5?,5 1 00 156

52 IF(RR?)51,53,51 00157

51 MM=IC ( I I)+1 00158CL(11.mm,1)=RP1 00159CL(11,mm,2)=RR2 00160IC(II)=IC(II)+1 00161

50 CONTINUE 0016253 ICOOEfn =1 0 016 3

J=IC ( I I ) 00169IF(J)10,10,71 00165

71 WRITE (*1 .503) II , UCL ( I I.MM. ID) ♦ TD=1.2) .MM=1 .J) (in 166GO TO ,0 00 167

9999 CALL FxIT 00168

ENO 001 69 00170

SUBROUTINE COFCH(RL,RR»CL,IC) 00171

300 FORMAT(1H0,120(1M»)/) 001 72

302 FORMAT(in ,96HRANGFS FOR COEFFICIENT CLASSIFICATIONS ARE NOT CONTI On] 731GUOUS OR 00 NOT EXTEND REYONO SECTION LIMITS) 00179DIMENSION CL(5,5.?),rC(5),XR(50) 00175

N=0 0017600 in J=l,5 00177NC=IC(J) 00 178

IF (NO 10,10,11 00179

11 DO 10 1=1.NC GO 1 30XR(N+1)=CL (J, I »1 ) cm siXR(N+2)=CL(J,I.2) 00 1 82N=N*2 0 018 3

10 CONTINUE 00139

CALL Sf)PT 1 (N« XR, 1, '-0185IF (RL-xR{1>>50,60,60 00136

60 IF (RR-XR(N>)70.70,50 0013770 IF(N-2)99,99,20 0013320 K = N-1 00139

DO 30 T=2,K,2 00190IF(A0S(XR(I)-XR(I*11)-0.01)80,30,30 00191

90 CONTINUE 00]92GO TO 99 00193

50 WRITE<6l»300) 0 0,94WRITE(61,302) 03,95WRITE (61,301 ) < XR( I > , 1 = 1 ,N> 00196

3i,l FORMATflH .12F10.1) On,97WRITF(61,300) 00,99

99 RETURN 00,99Enn 00300

on?mSUBROUTINE DFSCT(N.F,R.FLINT,KQDEL.SL) 0n?0?DIMENSION E(1)»W(1>♦XL(70>»YL(70>,XR(70>,YR(70> 0o?03

300 FORMAT (1H0.27HINPIIT RANGES ANO ELEVATIONS) 0G204302 FORMAT(1 HO,36HSECTI ON UN-DEFINED ON LEFT HAND SIDE, 00205303 FORMAT(1HO»37MSECTION UN-DEFINED ON RIGHT HAND SIDE, 002063C4 FORMAT(1HO,13,29H POINTS AMOVE ELEVATION LIMIT) 0020759 FORMAT ( 1HO,90HALLO'VA3LF NUMBER OF oANGF AND ELFVATTON POlNTb E*CEE 00203

1DED WITH ADDITION OF CALCULATED POINTS) 002093C5 FORMAT(1H0.40HRE-DEFINED SECTION RANGES AND ELEVATIONS) 00210C 00211C SORT POINTS IN ASCENDING ORDER AY RANGE 0021?C 00213

CALL S0RT2(N,R,E, 1 ) G(j214C 00215c print input Range and elevation data 00216C 00217

WRITE(41.300) 00218DO 56 1=1,N 00219WRITE<61.3G1>R(I)»F(T, 00220

56 CONTINUE 00221301 FORMATflH .2F10.2) 00222C 00223C SORT POINTS IN ASCENDING ORDER AY Fl EVATION O0?24

C 00225CALL S0PT2(N*E«R»1) 00226

C 00227C USING RANGE OF LOWEST ELEVATION - PLACE POINTS ON LEFT OR RIGHT 0D228C 00229

L=0 00230

M=n 00231DO 10 1=1,N 0^232IF(R(I,-R(1>)11,11,12 00233

11 L=L*1 00234XL(L)=R(1) . C()235YL(L>=P'(I> ’ 00236

GO TD 10 00?37ip M=M+1 00233

XR(M,=p(T) 0o?3RYR(M)=F(I> 00240

10 CONTINUE 00241C 0024?C DETERMINE IF SECTION UN-DEFINED 00243£ 00244

IF,L-l)13.13,14 0024514 IF(M)is,15.16 00246

13

IS

Ccc

16ccc30

31

3?

33

99

CCC29

36

35C

Cc

37 39

ccc38

4?

41C

CC

4C44

WPITE(61,30? ) - AC4'5 - 0024700243L=L + 1

XL (LI=XL (L-l)- (5LIMT-YL(L-l> I*SL 00249YL (L)=FLIMT 00250

no TO 16 C0251WRITF <6l.303) 0f)25J

M=1 O0?53XR (m> = xL ( 1 ) ♦ (EL TMT-YI (I)>*SL 00554YR(M)=FLIMT 00?55

0 0 256TEST FOR EXTENSION OF SLOPFS ON FAR LEFT OP RIGHT 00257

00258IF (KOOFL)39.29.30 0 0 259

00260EXTEND SLOPES FROM FAR LEFT ANO RIGHT 0 0261

00262CALL SoRT2(L»XL,YL»2) 00263IF(YL<L>-ELIMT>31.32,32 0 0 264L=L*1 00265YL(L)=FLIMT 00266XL<L)=XL <L-1>-(ELIMT-YL(L-I> MSL-0.001 00267CALL 5ORT2(M,XR.YR»1) 00268IF ( YR(M)-EL I MT>33.99.99 00269M = M+ 1 00270XR(M)=XR(M-l>♦(EL I MT-/R(M-l>)*SL*0.001 00271YR(M>=RLIMT 00272«=L 0 0 273J = M on?74GO TO 34 00275

00276ELIMINATE POINTS TO LEFT OF HIGHEST ELEVATION ON I .HS 0027?

00278K = Q 00279DO 35 1=1.L 0G280IF ( XL (I)-XL(L) )35.36.36 0028 1K=K + 1 00282XL (K> =XL ( I ) 00283YL(K)=YL(1> 00284CONTINUE 00285

00286ELIMINATE POINTS WITH EQUAL ELEVATIONS ON FAR LHS 00^87

OC 288CALL 9QRT2(K,XL.YL.?) 00289IF(YL(K>-YL(K-1>>35.39.38 00290K = K-1 00291GO TO 37 00 292

00293ELIMINATE POINTS TO RIGHT OF HIGHEST ELEVATION ON FAR RHS 00294

0 0295J = 0 00296DO 41 1=1.M 00297IF(XR(T>-XR(M)>42.42.41 00290J=J* 1 00299XR(J>=XR(I) 00300YR (J)=YP(I> 00301CONTINUE 00302

00303ELIMINATE POINTS WITH EQUAL ELEVATIONS ON FAP RHS 00304

0 0 3 05CALL S0RT2(J,XR,YR,1i 0C2Q6IF(YR(J)-YR(J-1>>98,44.90 0O307J=J-1 00308

GO TO i.0 - AC4-6 -Oi) 309

9a L = K 00 31 0M = J 0 0 31 1GO TO 30 0 0 312

c C031 3c truncate any area arove elevation limit ON ROTH SIDES 0 0 314c 00 315J"* SORT points ON LHS IN DESCENDING ORDER RY PANGE AND RE-CALCULATE 00316c POINTS ABOVE ELEVATION LIMIT ON EAR LHS 0031 7c 00 3 H34 L = < 003,9

IF(YL(L>-pLIMT)17,17,18 0A32018 L=L-1 OOT21

IE(YL(L,-ELIMT)19,17.13 0032219 XL(L*1>=XL<L*1, + (XL(L>-XL(L*1))MYL(L*1> -ElIMT)/(YL(L*1>-YL(L)) 00323

YL(I*1)=ELIMT 00324L=L*1 U H325

C 00326c SORT POINTS ON RHS TN ASCENDING ORDER RY range and 0^327c POINTS ABOVE ELEVATION LIMIT ON EAR RHS 00328c 0 0 32917 M = J 00330

IF ( YP(m)-FLIMT121,21,22 0033122 m=m-i 00332

IE(YR (M)-ELIMT123,21,22 0Q33323 XP(M+1)=XR(M+1)-<XP<M,1)-XR(M))»<YR(M«-1) -ELIMT)/(YP(M+1)-YR(M)) 00334

YR(M+l)=ELIMT 00335M=M*1 00336

C 00337C RE-SET ELEVATIONS ABOVE ELEVATION LIMIT ON I HS 00336C 0 033921 K = 0 00340

DO 20 1 = 1.L 0C341IE(YL(I)-EL I MT 120,20,24 00342

24 YL(11=ELIMT 00343K=K*1 00344

20 CONTINUE 0 0 345C 00346C PE-SET ELEVATIONS ABOVE ELEVATION LIMIT ON RHS 00347c '0 348

DO 25 I=1,M 00349IE(YR(I)-ELIMT)25,25*26 00350

26 YR ( I )=ELIMT 00351K=K+ 1 00352

25 CONTINUE 00353IE (027,27,28 00354

28 WRITE(61,304)K 00355C 00356C PLACE REMAINING POINTS IN RANGE AND ELEVATION ARRAYS 00357C 0035627 DO 50 1 = 1 ,L 00359

IM=L+1-I 00360R ( J ) =X| ( IM) 00361

80 E(11=YL(IM) 0 0 362DO 60 1=1 ,M 00363J = L*I 00364R(J)=XR ( I ) 0 0 365

60 E <J)=YP( I) 00.366N=l.*M 00367CALL AMXMN(E,N,EMAX.EMIN) 00368

L = 0 00369K=N-1 00370

DO 70 T=?.KIF(E d)-E < I * I > > 70.71 .70

- AC4-7 - 0 3 371 00372

71 IF(F(I)-EM IN)70.70.72 0037 3

72 L = L + 1 00 3 74LL=N*L 00375E(LL)=F(I)-0.0001 00 3 76

R(LL>= R ( I ) 00 U770 CONTINUE "0 37H

N = N + L 00 T74IF (N-70)57.57.58 00 380

58 WRITE(61.59) 00381STOP 0O382

57 CALL S0PT2(N.R.E.1) 0P383

WRITE(61.305) 0 0 384DO 55 1=1.N 00335

WRITE(61.301)P(I).F(I) 00336

55 CONTINUE 00 387

RETURN 00383END 00389

00390SUBROUTINE schar<n.ei ev.range.cl . IC . STATN,STATM.CRELV) 0 0 391DIMENSION ELEV(1).RANGE(1, .CL <5. 5.?).IC(5).Y3(70) 00392DIMENSION TW(50.5).Wp(50.5> 00393DATi (f'T = ll) 00394

300 FORMAT(1H0.59HTQP WIDTHS BY M CLASSIFICATION AT EACH DISTINCT EL 00395lEVAT IQ.') 00396

302 FORMAT(1 HO.66HWETTFD PERIMETERS BY N CLASSIFICATION AT EACH DIST 00397

1 INCT El EVATION) 00 393

C 00394c DETERMINE DISTINCT ELEVATIONS 00400c

DO 10 T=1»N

0040.100402

Y3(I)=rLFV (I ) 0040310 CONTINUE 00404

CALL SoRTl(N.Y3.2) 00405L = 0 00406DO 20 1=1.N 00407IF(I-N)12.11.11 00408

12 M=I+ 1 00409DO 13 J=M,N 00410IF <Y3(I)-Y3(J)>13.20.13 00411

13 CONT INI jE 0041211 L=L + 1 0 0413

Y 3 (L ) =Y3( I) 004 1420 CONT INuE 00415

LLL=L 004 1 6C

initial ize top wJdth and wetted00417

c perimeter arrays 00418c 00419

DO 30 K=1.LLL 00420DO 30 J=1.5 00421T W(K.J)=0.0 00422WP(K.J)=0.0 00423

30 CONTINUE 00424M = N-1 00425

c 00426c ENTER [OOP FOP DETERMINATION OF TOP WIDTH AND WETTED °ERlMETEP 00427c EOP EACH DISTINCT ELEVATION 00428c

DO <.0 k = 1«LLL0042900430

c 00431c CALCULATE TOP WIDTH AND WETTED PERIMETERS FOR EACH CLASSIFICATION 00432

c AT THIS DISTINCT FI EVATION D gh- 3 3c

DO 50 J=l*5004 34 004 35

IF(IC1J))50.53,51 0043651 NC =IC(J) 03437c 0 P4 36c CALCULATE TOP WIDTH AND WETTED PEPTEETER EDR EACH PAID OF RANGES 0 0 4 .3 9c WITHIN This CLASSIFICATION at THIS distinct elevation 0Q443c

L = 1r' 044 1 0C449

DO 60 I=1.NC 0 044 3jc,n = i 0C444

c ■04^5c pun along section td calculate top width and wfttfd perimeter CG4h6c fop each pair of ranges within this classification at this 00447cc

DISTINCT ELEVATION 0044600449

DO 70 [_j = l»M 0Q450GO TO(73♦74), IGO 0 3 451

c or. 452c FIND STARTING INTERSECTION 00453c 0045473 IF(CL(J,I,1>-RANGE(L J) ) 85*71,71 0045585 IF (CL ( J, I ,21 -RANGE (L J) ) 60.60,91 0 045691 IGD = 2 00457

RG1 =RANC,E (LJ) 00458EH=ELFV(LJ) 00459GO TO 92 00460

71 IF(CL <J,I,1)-°ANGE<LJ♦1) )81,70.70 0046181 I GO = 2 00462

PGl=CL(J.1,1) 00463ELI=ELFV(LJ)*(ELEV(L 1*1)-ELFV(LJ))/(RANGE(LJ♦1>-PANGE(LJ))* 00464

1(RGl-RANGE(LJ)) 004659? RG2-RANGE(LJ*1 I 00466

EL? = ELFV <LJ*1> 0 0467c G0468C DETERMINE IE THIS LINE SEGMENT IS DM OP 0ELOW THIS DISTINCT 0 0469C elevation 00470C 0047183 IF ( EL 1-T3(K) )72,72*75 0047272 IE(EL2-Y3(K))76,76,78 01)4 7 3C 03474c DETERMINE if SECOND CLASSIFICATION falls WITHIN THIS LINE SEGMFNT 00475

c 0047676 IF(CL(J,1,2)-RG2)61,61,62 00477c 00478c SECOND CLASSIFICATION FALLS within this line segment 0 0479

c 0048961 IE(CL(J,I,2)-RG1)14,14.15 0048 115 PG2=CL(J,I•2) 004 62

EL2=FLFV(LJ)*(ELEV(L !* 1)-ELEV(L. 1))Z(RANGE(LJ* 1J -RANGF(LJ>)» 00483

1(RG2-R&NGE(LJ)) 00484TW(K,J)=TW(K,J)*RG2-PG1 00485WP(K,J)=WP(K,J)+SQRT((EL1-EL2)»«2+<RG2-RG11**2> 00486

14 L=L-1 00407

IF (L ) 16.16*60 00488

16 L = l 00409

GO TO ^0 00490

C 00491

c ACCUMULATE TOP WIDTH AND WETTED PERIMETER FOR THIS LINE SEGMENT 00492

c 0049 3

62 TW(K,J>=TW<K,J)*PG2—RG1 00494

wp(K,J)=WP(K* J)+ SQRT((EL1-EL2)»*2*(RG2-RG1)»*?) - AC4-9 - 0049532 RGI=RANGE(LJ*1) 0 04 96

EL1=ELFV(LJ+1) 004R7GO TO 70 0049s

75 IF(EL2-Y3(K))77,8?,8? 0 04R.LC oosotC line segment intersects this distinct elevation with negative 00501

c SLOPE 0050<c 005077 RGI=RG1♦(RG2-RG1)*(EL 1-Y3(K))/ (EL1-EL2) 005d

EL1=Y3(K> 0050cGO TO 76 0050(

78 IE(EL I-Y3<K))64,82,8? 0050'C 0050cc LINE SEGMENT INTERSECTS THIS DISTINCT ELEVATION WITH POSITIVE 0Q501c SLOPE 005l(c 005164 RG2=RG1♦(RG2-PG1)«{Y3(K)-EL 1)/(EL2-FL1) 005b

EL2=Y3(K)' 0051:GO TO 76 005P

C 0051-c FIRST CLASS RANGE PREVIOUSLY ENCOUNTERED - CHFCK FOR SECOND 0051(c 005174 RG?=RAnGE(LJ+1) 005b

EL?=ELEV(LJ+1) 005bGO TO 33 0052(

70 CONTINUE 005260 CONTINUE oo5?;50 CONTINUE 005240 CONTINUE 0052<

WRITF(61,300) 0052'WRITE(61,301) (Y3(K),(TW(K,J),J=1 ,5),K = l,LLL) 0052!WRITE(61»30?) 0052WRITE(61,301) <Y3(K),(WP (K,J),J=1,5),K=1»LLL) 0052'

301 FOPMATdH ,F1<) .2,5F2P .5) 0052'WRITE(NT)STATN,ST ATM,CRELV,N,(RANGE(I) ,ELFV (I) ,I = 1,N1 • LLL, 0053

1(Y3(K),(TW(K»J),WP(K.J>,J=1»5),K=1,LLL) 0053return 0053END 0053

AC5-0

APPENDIX 5: E081 - COMPUTER PROGRAM

COSY 73.3 - MSOS V5.0 09/09/75 - AC5-1 -

EOS] DECK/ 1=01.LPROGRAM wSPPF 0'001DIMENSION 0(49)»SI(?G),NCAAL(6> * EC ( ^) ,XFC(20 * 5 >.SQ <40)•SFC(20 > •J ; 0 0 >

DIMENSION Y3(?'5O) ,AP(2,50.5) .TW (2,50.5) .9(70) • F (70) -J r 9 0.3DIMENSION TOPW(?).CO(2) ,ARE A(?).STATN(?),LL (?) 9 ;• r,*DIMENSION ISTA ( 15) , ST ATM (2) , CPFL V ( ?) . JCC (? . 5) . ICC (2 ) .SNC ( 20 ) C o 0 s

DIMENSION IHUF(1?S) , I A(?0) "'■DOCOMMON O.SI .NCAAL.FC. Y3,Ta(. AP, Wh . CO , APF A , ST A TN . 1 « Ol'OO 1

COMMON I A D 0 0 sCommon R ,F .NT , ALFA .URDWN, NO« NS . NST 1 »NST? , NST, NOST , WS ,UPE • 7 At_E. S I T 0 n 0 09COMMON IFPP»IO,IS.DEPTH,I ST.SO.XFC,SEC.NFC.ICC.SNC.NCr 0 '.'CIOEQUIVALENCE (7STA,I A(1) ) , (7WS,I A(3) i , (7DPTH,I A(5) ) , <7 TOP.I A(7) ) . Du 0 1 1

1 ( 7 AP , I A ('») ) , ( 7CO . I A ( 1 I ) ) , ( AC APE « I A ( 1 3 1 ) , ( A C VOt. , I A ( 1 S ) ) IN (1 1 22 , (SLPL, I A(17) ), (SLPP.I A(19) ) (n 0 1 3

301 FORMAT (1HP. 12HDISCHAPGE = .ElO.p 0 6 0 1

30? FORMAT (] HQ, 29HR0UGHNESS COEFFICIENTS = ,5E1<1.3) OOP is

999 CALL LOCATE(PC,86.MMM) :' p is

WRITS (4 0)MMM 0 0 0 17

CALL DqPENIIHUF.40,29,6) 0 A o ] 8

JPEC=O 9' '■ 0 1 9

C 0 9 0 2 0

C READ WATER SURFACE CROEILE CONTROL DATA (U 921

Ccall wsreo

0 ’10 2? 9 " 9 2 3

r L?C24

c

c

LOOP FOR EACH STAGE 0 61)25 0 C f> 2 6

no 3o iS=i.ns 0 0 02 7

c 0 r 0 2 8

c SET DISCHARGE AND FRICTION COEFFICIENTS AT INITIAL STATION 0 9 029

cDiD 1C J=l,5

060 it

P < 0 3 1

FC(J)=xFC(1 , J) 06 0 32

JCC(1•J)=ICC<1,J> 06 0 33

JCC(2. J) =ICC ( I , J > 3AQ34

10 CONT IN1 IE 0 96 35

TQ= 1 Q0 035

c 006 37

c read initial section data ano rrimt headings

r

REWIND NT

Of:9 3900 04W

c

RFAD(NT)NCAAL 900410'042

c DETERMINE IF TAPE TO PE PEAD UPSTREAM OP DOWNSTREAM 0 0 04 3

cIE (UP.DWN) 74,75,75

0 0 044 0 9 045

79 NT AD = NST2-1 00046

DO 75 K=1.NTAP 09047

READ(NT) Op 048

76 continue 0D049

GO TO «1 0 n 0 5 0

75 IE (NST1 - 1 )61 ,A 1 ,«? 06051

82 NTAP=NSTl-1 0005?

DO S3 K=1.NTAR 00053

READ (NT) 39054

S3 CONTINUE 09055

si READ(NT)STATNf1>,STATM<l>.CRELV(1),uRE-(R(I),E(I).I=1.NRE),LLl, 0 A 056

](Y3{1,k),(TW(1.k,M),AP(1,K,M),m=i,S),k=1,LL1) 00057

WS=SI(IS) 00 058

LL ( 1) =|.L 1 9 6 06 9CALL WSTAP 0 0 050

jrr-? - AC5-2 -«cc = 2

W 1I ■ : ) 6 J

c \i ,36 'c T4ANSFFP TO ROTTDM OF | OOP fF cop,IP PwrCF.-jj Li ' C 54c i' ■ • n tD -)

GO TO( 14.30 ) ,WPP i < ■ i 6 6c , ,,»67c DFTFP.1TNF SECTION DJTFPCEPTS FOR TNTTI Af. STATION • ft 6 Hc • I " 1 n 4

14 CALL - 0 I NT ( . rJPL , p , p , SLPL .StPP ) 8 4 17 j

c 3, C 7 IcI*

DETERMINE SFCTION CHARACTERISTICS fop I N I T I AI STATION i <, n 7 >

CALL "'-CHP(LL ( ! ) . DEPTH.Y3.W.AP.FC. 7 T OP , /CO • / A P . CPRL 7 t 1 ) . ICC. 1 ••' ' n f 1r IJ 74

] ALFA . 7ALF > - '3 75c • ' Wc PRINT AND STQPF INITIAL STATION DATA ' ' n 7 /

i ft 7CAI L MAT ( ZSTA. 1ST* ) . ‘ 1 ' 4WR I TF > 61 . 3«B ) 1ST A . 7hS . /(}PTH, ZT DP, 7 A R . 7 'MO. AC A RF . A C^OL * c LPL • Si. PP • 3 '• 4 8 i.l

] 7alf '■ 16 1388 FORMA T (1 HP.15 A] ,2Fh.’.FFll.^.’flF.s.Fh,?) c 0 4 ?

IvFC=1RFC+1 6 ; 0 6 3CAI L OPUT f IRIJE, IRFC. I A I T n0A4

C l r 186C FMTFP ITERATION PROCESS for TmTS CHANNr|. J f 5 8 6

c , 1 6 7c k! '! 0 8 8c LOOP mo EACH STATION 1 '■ 0 8 4c

no z.'-' iST=l.N5Tf i,4 '■) ;0 4 I

c. (\ 14 2c ENTER INTERPOLATION AND ITERATION PROCESS FOP THIS STATION ■J 8 4 3c 4f I’-44

IF (NPOi./n) 77,78.78 b 045

77 DO 81 4=1.2 f ' C 4 6PAWSPACE mt 4 • > f 4 7

«r> CONTINUE ) ' P 4 878 PEAD(NT)STATM (?).SI ATM(2) .CPF) 4 (?) ,nRP .(R(|).F(J),I=i ,nrF )«lL?' C : ft 44

1 ( Y3 ( ?.K ) . (Trt (?.K ,M) . AP (2.K.M) .m-i ,c ) ,k = ] ,L.L? ) •••11.LL. (?)=! L? t • 1"1

c Co ) 12C DETERMENT if OHANNFL DESIGNATION TO RF CHANGFn AT THIS STATION j 1 0 3

cIF(KCC-NCC>42.4?»46

■'ll 04C 11 06

4? IF ( APS {SNC(KCC)-STATM(2) )-P .0 1 )4 3.43,46 <• 0)0643 DO 45 J =1 • 5 J ? 1 0 7

JCC (2,0 =ICC(KCC.J, « ■ ! 0 845 CONI I ni lE I ' I 0 4

KCC=KCC+1 »s 1 1 ,46 CALL ^CINKSTATM.CPFI V, JCC) •t > 1 1 I

GO T0(44p..H1)*IFPP tf'; 1 1 2

r ! 13C

C

CALCULATE SECTION InTPPCEPTS AT THfS tfATEP SUOFACF L 1114 ■',.115

344 CALL SCINT(RS.MPF.P.p.SLPL.SLhh) J C 1 1 6CA) L STAT (ZSTA . ISTa ) f 3 1 1 7WPTTF(hl,388)ISTA.74S,/DPTH.7TOP,7AO,/ro.AfAPF,ArPOL,5LHL.SLPP. J ? 1 1 6

1 7 A)_ F If' 1 1 4IQrc=lofC+1 o r!2>CA|.L Dpi IT ( IPiJF , IRFC . I A ) 1 i)21

c '■ 1 2?

C<~

21 11

cc

c1 2 22 1 3

15

AO30

20 1

996

IC

1 1

1220

30

31

32 99

- AC5-3DETERMINE IF OISCHAPHF IS TO nr C*-)AhGFD AT TRIP STATION i. H 2 3

H 1

IF( IO*)-NO)21*21*1? ? K 1 25

IF ( AHS (SO ( 10+ 1 ) -STAT^H 1 ) ) - 0.01, 1 1 • 1 1 * I 1 >6

10=19*1 i, '■ 1 27-

i^P I Tr ( 6 1 * 30 1 ) 0 ( I 0 ) 0 <■ ) 2 3

Z 1 1 29DETFP”TNE IF FOICTI9D CCFFF IC IE'! T S TO =>E CHANGED AT Tn(S STATION „, 1 3

Pl U ■01 l 12IF (JFC-NFC) 22.22’AO

IF < AHS (SEC ( JEC) -STApH I ) >-0.01)1 3,l7.A2 P 1 3 3

DO ]5 1=1.5 'Pl 39

EC ( J, ='<FC (JFC.J) 9 <• 1 35

CONTINUF V 1 3 6

JFC=JFC*1 A , 1 37

WP I TF(61 . 332)FC IP 1 1“

CONTINUE C ' 1 39

CONTINUE (Pl 9!?

CALL DCLOS(IRUF) , I A 1

PEAD(60,201) IPLOT «HSCAL* V5CAL P 1 P

FORMAT(15 * 5X.2F10.3) t'l 1 A 3

IF ( I PL O T ) 99 9.9 9 9.9 9 A j Q , A '*

CALL PLOTS(0*0,9) 0 o 1 m-5CALL 9SPLT (NOST.NCAAt , HSC AL * VSf AL *1 iPDWN ) 0 7 | t* 6

CALL PLOT(0.0 - 0.0.999) (P , A 7

GO TO 99Q 3r 1 A7

END CL I A 9CP l 5?

SldPG'JTplE SC I NT ( WS » h , p, f . SL.PL T • SL dpT) ; e i s i

OIMFNSlON P(1)*F(1) or 1 52

DO l-\ k = 1*N f.r,lS3

IF HS-F (K > ) 1 0,1 I , I? 9.J15A

CONTINUE 0'>l55

SLPLT=n.O CP 155

GO TO ?0 C 3 157

SLPLT = p (K> 00 152

GO TO 20 0)i ] 595LPLT=p(K-l)♦(F(K-l)-WS)/<F(K-l)-F(K))»(R(K)-9(K-l)) 0 -i 1 PCDO 3? K=1,N 0 3161

L=N-<*, 0 3162IF(WS-C <L),39.31*32 0 3 16 3

CONTINUE C516A

SLPPT=9.0 0.3 165

GO TO 99 0 0166

slppt=p (L) 0 916 7

GO TO 99 0 9 1 66SLPPT = p <L > + ( dS-E (L> > / (F (1..* 1 ) -F (I > ) ’(P (L + 1 > -R <L >> Q'3 1 69

RETURN 0 0 1 7 J

END C 0 1 71 30 172

SUAROUTINF WSPLT (NOST.NCAAL. pSCAL *VSCA|_ .ijpown, on 73

DIMENSION I STA(15)»NCAAL(6) 00176

DIMENSION IRUF(125) .f a(20).MSG(11) 09 175

DIMENSION LCHAR(32) , TPL1 (15) .IP1.2I7) 09 1 76DATA ( ( IPL 1 (I) * 1 = 1 *5) =AHELF.V.AHA TTQ.Ahn In«4H FFE.AHT ) (Pl 77DATA( (JPL2<I,* 1 = 1»7)=AHWATP.AHR St 1. AHRF AC. AHE PR.AHOeTL* 4HE FO. 00173

ii HP ) on 179DATA (mSG=41HSFT PEN ON PLAIN PAPER AGATNST RIGHT STOP) 00 130

FOU I VALENCE (STA. IA ( 1,) * (WS.1A(3) ) . (DEPTH.I A(5) ) CO 161FORM A T ( 1 h 1 * 59HPR0F I Lr 9ILI NOT rJT TN ?7 INCHES WTTh GIVEN VEPTlCA 0 9 1 62

L SCALP) Ou 1 M3

CALL FACTOR(O.S) 0»j 1 6 A

300

CALL DOPEN( I3>IF.4<1,Pr ,6) - AC5-4 - 0 J1 AS

C u ' 1C DETERMINE MAXIMUM AMD MINIMUM STATION VALUES G'187C C r 1 A A

CALL DoET(I RUE»1»I A) (UH)STl^STA J •, I v<.CALL OGET(I RUE•NOST. I A) (.,'IMIST2=5Ta imp?

IE(STl-ST?)27.28,28 )i.H3

27 SGN=J . 0 )GO TO ?9 yiHS

28. SGN=-1.0 i; r. >96C i97

C DETFRMINE MAXIMUM ANO MINIMUM ROJTDm EfEVATlON ANO WATER SURFACE •'><■ 1 08C CCIUN

39 WSMX=-Q999,0-30 K?5‘:W5MM = *P99P.0E V) p o20 1

UO 17 K=l.NOSf GO2 02CA) L DGET(IRUF.K,I A) 0<j?Cl3IF ( wS-WSMX ) 18. 1 8.19 LTPQ4

19 WSMX=WS n>?0518 IE( (WS-OEPTH)-WSMN)26«17.17 ?r?0626 WSmn=WS-DEPTH C 2207

17 CONTINUEC G,, 2 f)UC DETERMINE IE PLOT Will. FIT ON PLOTTER WITH GTVEN SCA| fS O'»?10

C 0OP11

XM JN= T F IX ( WSMN )-VSCAI 0G212XMAXzIFIX(tfSMX)+VSCAI j<?13X INCH= < XmAX-XmJn) / VSCA1 0 0 21*

IF(XINCH-27.0) 10.1C . 1 1 <021511 WRITE(61 .300) 0C216

GO TO 9999 Cv217C 0 0? ISC POSITION PEN. PLOT AMD LABFL ELEVATION AXIS 00219C g o 2 2:10 call SFTMSG(11.MSG) 00221

CALL EPLOT(1,3.0*2.0) C0222CALL SC ALE(1.0»1.0/VSCAL.0.0 • 0.0) ^0223CALL EGPID(1.o•0* 0•0»VSCAL/2.g.IF IX(X INCH)»2) '0 224CALL EPLOT(1 .0,0.0.0) 00225CALL SCALEfl.0.1.0*0.0.0,0) 00226Y=-1.OS 00227YV=XMIN-VSCAL 0fl228N=XIMCH+1 00229DO 12 *=1«N 00?30Y = Y ♦ 1 . n O '1?! 1YV=YV+VSCAL C23?CALL PUTDC(YV.2.LCHAP,1,6) 00233CALL ECHAP(-0.70.Y.O.I.0.1.0.0.LCHAP.6) 0n?34

1? CONTINUE • 09235CALL A4AH IPLl . 1 .5.LCHAR, 1 ) 00236CALL ECHAP(-0.90.1.0.0.2.0.2.1.5707.LCHAR.17) 0"?37

r 0^?38C PLOT ANO LABEL STATION AXIS 00239C 0 0240

CALL EPLoT ( 1 . n . 0.0.0 ) 0C2MCALL SCALE(1.0/hSCAL.1.O.ST1»SgN-0.5*hSCAL.P.0) nn?42DO 13 K=l.MOST 0?43CALL OGET(IBUE.K.IA) 00244CALL FPLOT(?.STA»SGN.0,0) 0)245CALL EPLOT (1 . ST A*SGN. . 04) 0QP46

- ACS-S -CALL EPLOT(?»STA«SGN.-0.04) n j?47CALL STATISTA ,ISTA) T'i ’4 ft'CALL ECHAR ( ST A»SGN*0 . i-5*HSC Al_ •-1 .60 • 0 • 1,0.1 »1 .5707, 1ST A » 1 5 ) f),7?49

CALL FpLOT(1.STA’SGN.0.0) Or 2Su

13 CONTINUE O'dSL

CALL AhA1 ( IPl2,1.7,LCHAR,1) ii f, 25 2

CALL MDVE(NCAAL,).6,I CHAP,27) I) ; 25 3CALL ECHAP(ST1*5GN+H5CAL,-2.0,0.2,0.2-0.0,LCHAP.3?) CP 254

r .7? 255C PLOT WATER SURFACE PROFILE 0 2 2 5 6

CALL EDLOT (1 ,ST 1 ttSGN,. 0 )C0ft57

Of 25ft

CALL SCALEd ,0/HSCAL. 1 ,0/VSCAl »ST 1»SGN,XMIN) f25*

no 20 «=i.ndst n -> ft 6 ij

CALL DGET(I HUE,K,I A) C-7 26]IF{K-l)2^,24,25 2f-?62

24 CALL FpLOT<1«STA*SGn.WS) u f 26 325 CALL ppLOT < ? ’ STA*Sf,N. WS ) CO 26ft

CALL Pi JTDC < WS, ? • LCH AR , l,e>) ft 0 265

CALL ECHAP<5TA*SGN + 0.05«H5CAL•WS K.C5*VSCAL»0.1»0.1»1•5707 * 0 7 ?661LCHAR.6) 0 "?ft7

CALL FPLOTd.STA&SGM.WS) 0 2 268

20C

CONTINUE Of 269 0 2 270

c PLOT -UTTOM ELEVATION PROFILE CC?71c

DO 3A r=q»NOST00 77?JV73

L-NOST-K* 1 (?.}?74CALL DGET (IHUF»L,IA) 0 2 2 75

IF (K-d 34.34,35 0 2 27634 CALL EPLOT(1,5TA»SGN,-DEPTH ) 0(277

GO TO 36 0227ft

35 CALL DASLNLXSTA, XWS-XD°.ST A*SGN.WS-DEPTH•C.25.HSCAL) 0027436 CALL PUTDC(WS-OEPTH,p,LCHAP,1.6) Of ?ftO

CALL FCHAP (STA»SGN*0’.35«HSCAL.^5 -DEPTH -0,65&VSC At.»0 • 1,0 » 1 • 0 f 2 ft 1

1 I .5707,LCHAP,6) 0C?ft?XSTA=STA»SGN 0 a ? ft 3xws=ws 0 0 284XDP=DEpTH 0 0 285

30 CONT TNI IE Oi’ftrtftCALL EPLOT(1, ST?fiSGN + 3.0*H5CAL•XMIN) Of 2ft7

9999 CALL EPLOT(999,0.0,0.L) 00?ftft

return (j 22ft 9end 0 ??90

0 0 29 1StjRPOtlTlNE WSTAP 0 0 29?DIMENSION Q (40 ) .SI (?!■) , NCAAL (6 ) . FC (S I . XFC ( 20,5 ) , SO <40 ) *SEC (20 ) O f 29 31)1 MENS ION Y3(2,50).AP(?.50.5).T9(2.SO.S).P(70).F(7 0) 00294DIMENSION TOPW(2) .CO (?) .AREA(2) .STATN(2),LI (?) 0 0 295

COMMON Q , SI • NCAAL,EC•Y3,TW,AP, TnDW,CD.AREA.STATN,|i 0 0 296COMMON 7STA,ZWS,7DPTh,ZTOP,7AP•7CO.ACARE«ACVOL•SLPL»SI °R 2f?97COMMON R,E.NT.ALFA.UPDWN,NO.NS.MST1.NST2.NST.MOST.WS.NRE.7ALF.SIT 0 3?4ftCOMMON I ERR,IO, IS,DEpTH,I ST,SO,xEC,SFC.NFC 02299

3C4 FORMAT(IHI*SIX,6A1//1H ,33X»11 HD ISowARGF =.F9,0.2X. 0 33001 1SHINITTAL STAGE =, F6 .?/] H0,43X , ??HROI JGHNESS COEFFICIENTS) CO 30 1

25 FOPMATdH ,41.x , 14HCL ASS IFIC AT I ON, I2.3H = ,F7.4) 00 3 O' 222 FORMAT(1HO,13X.5HWATFP.14X.3HTop,3CX,2(13H ACCUmULATpD>»3X, Of 30 3

1 ISHSECTION INTERCEPTS/1H ,6X,7HSTATI0H.5X.13HSTAGE DEPTH,5X Of 3 042 SHW I OtH , ft X • <+H APE A , 6 X • 24HCON VE Y A NCF SURFACE AREA.5X,6HVOLUME, CO 3053 ft X • 4HI EF T , bX • 5HR I GHT , 4 X » 5HALPH A ) 0 7306

900 FORMAT ( 1H0,17HINITIAI. STAGE OF .F7.2.27H RFLOW HOTTO*’ ELEVATION OF 043071 .F7.2) 0 0 30ft

ROl FORMA T (1 HO . 1 7H INI T I At STAGE OF .E7.R.23H AROVF TOP EI.rVATION OF . it r 3C'41F7.?) >)' 31 (;LL1=LL ( 1 ) '"'nilWRITF(Si,3"4)NCAAL.O(TO).WS ' 11200 23 JJL=1»S t,' 1 i 3IF (EC < JJL ) ) 23-23 ,?4 !t 314

24 WO ITE(61.25) J.JL .FC ( JJL) <'■ ■ 1 1 B23 FONT I Mi)F . 11 6

W P I T F(Si .22) 3 I 1 7C. cc DFTFPMTNE jf INITIAI STAGE OUT OF PANGF I.l 1 3 1 4c 1 3-".

IF(WS-Y3( I -LL11)11.11.12 ■ 32!

11 WRITS .400) i)S.Y3< 1 .1.L1 ) ,-,322

77 I FRO = 2 ' 3? 1

pF Tl IP 'i 3 24

1? IF ( WS —Y3 ( 1 , I ) ) 1 4 « 1 4.1 5 • -■’3 25

IS WRITS (M .~>Pl >W5.Y3(1 • 1 ) 0 12S

GO TO 77 V,. 12 7

14 IFPP=1 f t32S

r 0 vN

c EJND DFPTh AT JMITIA' STATION Of 3 30

c 0 '331

0FPTH = v/S-Y3 ( 1 .LUI ) <3 1332

c C '333

c determine SECTION ChAPACTEWISTICS AT initial STAGE tj '3 34

c U )335

7QPTH =0EPTH ft ,i 336

ZSTA =STATN(1) Or 337

ZWS = WS O', 3 is

aCApf =s.;i V 0 3 3m

ACVOI =3.0 Or 34 j

PETURN ‘i 3 34 1

ENO SO 3-4 2 ( 3 34 3

SUBROUTINE WSREO ■3 :) 34401MENS JON 0 (40) ,Sl I? ■) .NCAAL(S) .EC) .XEC ( ?u.5) .SO(40) .SEC(20 ) r '345

DIMENSION Y3 ( 2.50) .AP 12.5 3.5).TW(2.R0.5) ,R(70),E(70) 0)34e

DIMENSION TOPW(?) .CO(2),AREA(2) ,STATN{2) .LL <2) . 1CC(2Q,5).SNC<2C1 C ,.'34 7

COMMON O.si.NCAAL.EC.Y3.TW.aR. rOPW.CO.4fFA.STATN.lt 0 3 343COMMON ZSTA.ZWS.ZOPTM.ZTOP.zap,7C0,ACARE,AC VOL * SLpL » SI PR Cn 344COMMON R.E.NT«ALFA.UPOWN.NO.NS.MSTl.NST2.N5T.MOST.MS."'RE.ZALF.SIT Or 35 C

COMMON I ERR.10,[S,CERTS,I ST•SO,*EC•SEC»NFC»iCC.SNC.NCr 0. ' 35 I

NT = 1 1 ' , 35 2

PEAD(SO.201)ALFA.UPOWN.SIT 03353

201 FORMAT f8E10.3> Of 3 54

IE CJPOWN)SC.6U,50 0 7,355

so CALL fxIT 0,7 356

50 READ(SO,2a2lNS,NO,NFC.NST1,NST2.NCC ',357

202 FORMAT(615) 03353

READ (SO.201) (SI (IS).[S=1.NS) U';354

DO 10 t0=1*N0 0C360

10 READ (So .2i, ] ) SO ( I 0) , 0 I 10) -■ 3b 1

DO 20 TC=1.NFC 0 3 36?

20 READ(SO.2')HSFC(1C) . (XEC( TC.J) • J=l.c) o '-3b 1

TEfNCC)1.1.2 0 4 3 04

? DO 3‘. NC=1»NCC ■)36S

30 PE AD (SO, 20 3) SMC (NC) , ( ICC (NC. J) , J= 1 , ■=1 0 f. 36S

2C3 EORMAT(Ellj.3,10I5) s) n 367

1 NST=NST?-N5T1 0 363

nost=nst*i i, j 364

RE TUR'J 0 3 370

F'-ji- AC5-7

FM1

SU3QO:IT I NE WSCHR <INPFX .DEPTH. Y 3 , T AP . Pf , TOPW »CO • ARF A • C^t 1. V . JCG * I •

[ALFA.AlF1D 1 MFN5 JON Y3 ( 2 *50 » ♦ T-. < 2,50 , S ) .flP(?.4(l.S) . F f ( 5 , . ICF ( 9. u )DIMENSION APR (51 .VFl(Fj

WS = DFPTH*Y 3 ( I • IMDFX)DO 14 k = 2 *INOP xIF(mS-y3 ( 1 .K) ) 1,.. 1 1 . 1 1

..9 ‘‘ 3 7 ’ U! 9/2 (' ■. 3 7 3■ 1 174

L " 9 7 , ■■375 -977

0 1 • 3 7 4

< 3 ?'->

10 CONTINUESTn°

C '• 3 4 0 !) 1! 9 4 1

11 RATIO=(W5-Y3(I»K))/(Y3(I»K-1>-Y3(I ,K ) )

T0Ot>l = 0.0C O = 0 . nA r F a = n , 0no u=i.5IF (CREl O + RHQH.f'FTO) 42.42.41

V 94 2 9 - 3 3r. '3-t if 344 C' 9 3 5 4 0 -'3 4 7

41 IF (W5-<~DFLV) 43,43*42 C -‘3 4 4

43 IF(JCC( I*j> )4 c * 4 5 * 4 2 0; 344

42 IE(FC(J)121*44*21 0 \ 3 4 0

21 IF(T2(T*K-1*0)140*40*29 C '! 341

2? Tp- ( T9 ( I , K -1 * J 1 -T W ( I * < * J1 1 *R A T I n* T J f T , «■ * J)AR=(TP*Tw(I*K.J))/?,■ MWS-Y3< T *K1 1IF (K — If''DFX)?3*2z**94

0 ''3/9 O'’ 343

j 9 4423 M=TNNFy-l

DO 3 { 1 =K * MAR = AR+(Tw(I*L*J)+TW(T.L*l*J)}/7.0<>fY3(T*L)-Y3(f.L+l))

A 114 70 '>134 ? 947

30 CONTINUE 0 Y3PP

24 'mR= ( AD ( I ,K-1 * J1 - AP ( I ,K * J) ) ^R4T IO*AD ( I .<* J)

ARD(J)xARTODiv = TOPw *TPARF£ = ,*dfa*APIF (FC(J) )51 .52,52

0 0 349V ? 4 0 Li

0 9U0 V

0,54-12 J'!4i) 3

51 D=AR/Td

FN=1.541 3-1.054 71 3.49G1 79»0»«2-0 . l'24972«n»*3*-0.0 173095»D»«4-

1 0.04 1 ?1-<1«D* *5 + 0. COCO 34 1 199CO=CO+1 .42 6* < AR4>« (5.4/3.01 /WP«« (2.0/3.0) 1 /FN

GO TO 25

0 94 04 0?405 0 4 0 5

f .94 C 7

0 ■ if 0 4

52 CO=CO*1*4rt6« <AP»«(5.0/3.0)/WP*»(2.0/3.A) )/F C CJ)

FN=FC(J)0 34of e 9 411.‘

25 VFL (J) = ( ( A»P (J)/WP) »xH2.0/3.0) ) /Fn

GO TO 90

0 4 411 ■) 412

4 4 ADR ( J) -<) . fj

VFL(J)=0.0

<3413 0 0 4 1 4

20 CONTINUETF(At.FA) 24,27.27

C 4 15 '10 4 14

?5 AR]=0.0A YFF = !) . 0A R = 0.0DO 24 1= 1 .5API -AP1 ♦ APR(J)AYF|_ = VFL ( J, »*3.0»APP ( J) + A7FL

r< 4170 4414 0 r 4 1 4 0 0 490 0 -I f 2 1 O',422

25 AVR = VFF <J)ttARR(J) ♦A VPALF = AVFL»AR1-»AWI/(AVR*AVR«AVR)GO TO 99

Of 42 3 lr 0 4 9 4

C -'42527 A|_F = Al.FA 0 94 24

29 RETURNENO

SiJRQOUT I ME RCINT (5TATM.CRFLV* JCP)0 I MENS ion Q (40 ), SI (?-') .NCAAL (6) *FC (F ), XFC (20.5 ) *SQ <40 1 ,SFC (20 ) DIMENSION Y3<2,50),Ap(9.50.5).TN(2.^O.5),D(70).F(70)

0-427 J ,,4?S

0.0424 C '14 3? U9431 C, 0 4 32

?70

*02368

?64

53 3

533r»

c

11IP

Ccc43

469Ccc611

23

Cccc6flCcr

534

OP-'FNSION TOP"/<?) .CO (21 . APFA (P • (?) «LL. (?) • alff (5,01 MF NS ION ICC(20.5 J .SNC(20) .ST ATM<21 .CPELV(2) .JCC(2.5iCOMMON 0.61.NCAAL.FC.Y3.T9,AP. TORW,CO.APE A,STATM.I ICommon ZST A./WS . 70PTH. 7TOP. 7AP.7CO. aCAOF. ACVOI. ,SLpL . F| op

COMMON p»F,NT,ALFA,UJD9N»NO,NS.NST1 .NST?.NST.MOST.w$. ■ >rF.ZALF.SI 7COMMON IEPP. io. IS.OFPTH. IST.SO.XFC^FC.NFC. ICC.SNC.NcrFQPMATf1H0.3BHUNAHLF TO COMVERGF AFTER 20 ITERATIONS)FORMAT ( J HO . 1 FMOEPTH oiJT OF RANGp)FORMAT(IhO.7HOFPTH =.F6.2/1H , =>0H I TFR AT I ON INTERVAL =.I3/1h .

1 ?SMI NTEPPOL4TI ON INCREMENT =.Flo.?/lH ,2'iHRFACh bottom SLOPE =.2 F1S.7/1P .28M0ISTANCE FROM LAST STATION =.F10.3/lH .llHTOP NIOTh 3=.F]S.7/1h .1RHCONVFYANCt =.E1S,7/Ih .FHAPFA =.E15.7i

FORM AT ( 1 HO » 37HSUPFR-CR IT I CAL F|..OW AT A DISTANCE OF .Fi-.S.1 lAR PAST LAST STATI-on/JH .HHTop mTDTh =.E13.6.7h Apfa -. f. j 3. 6,2 13H CONVEYANCE =»F13.6)LL1=LL(1)LL?=LL(2)

DETFPMfNE RFACH CONTROL DATA

PE ACM-AfSS (ST ATN ( 1 )-S T A TN < 21 )Nir=PF aCH?SIT + rt.5 FNT T = iJTTOX=REACH/FNIT IF (> i°OwN ) 53? * 532.513 SL0PE=(Y3(?»LI.?)-Y3( 1 .1.L1 1 )/PEACH 00 TO S3<+SLOPE=(Y3(l»LLl)-Y3(?.LL2l)/REACH

enter iteration process fop thif rfach

00 55 M=1.nit ICOiJl =nSTApT = FLOAT (M UNIX fF (UPD^N) 11,12.1?5TART=START-DXYSTRT=OFPTH100=1.

CHECK FOR EXCESS NUMHFR OF ITERATIONS

ICOIJT=TCOOT* 1IF (ICOUT-201 68,68.964M0= 1

ERROR nlSCOVEPEO - PRINT DATA TO ThIS ROINT WITH pfRTTNENT DATA

GO TO(1.2,.MO WRI TF(61.9701 GO TO l WRITF(61.90?)WRITE (61.968) DEPTH. m.[)X, SLOPE. ST ART •XTOPW.XCO.XAR IE?R=?RFTURN

calculate initial ano ending station tor widths, areaf and CONVEYANCES fop INTERMEDIATE POINT calculations

do 95 1=1.2

CHECK FOR ALLOWAHLF RANGE OF DFDTH

/,

.43 3

' >4 34'u 35

/ 4 36•417

' ' Z+ 0 «U ■ 4 3

/,•<'

1 .441 ' r4-+? ’'^3

5 1 4 4 4 ' '44 5

4 46 r ■. 44 7

C ' 4 ■+ 6 0 '44 4 4.456 5'451 C 14 6 R r- ';45 3 C ,14.54 04 55

0 6 456 r ,45 76 4458

0 1459 0-',46V 0 >461 3 T462 k>i'-46 3 0 3464 04465 3 3466 C '4 67

3 '.468 6-4 469 0 4470

5 14 71,1472

014 73 1, '.4 74 0 04 75 :J 0 4 7 6 Ci 3 4 7 7 0 44 76 pi 474 ■• <•> 4 8 k>

(j 14 6 1 Uf48?

3f48 3 Ci 4 4 84 G G 4 85 0 4486 C',487 04488 Cf 489 0>)p90 i -14 41 04 492 0">493

(14444

- AC5-9 -INDFX=LL ( I 1 0 ■’> a 4 5IF (DEPTH>44.44,<+5 0 j 4 96

-*5 IF( (DFDTH + Y3 <I, INDFX, )-Y3(1,I))46.4^,44 Ij 1.4-U

44 MO=? J ’’ 6 9 ■<GO TO 61 0 P t, H ■?

96 C4L L wSCH-J (LL ( I ) » DEPTH. Y3.TW, AP,FC, TQPW ( I) . Cr> ( T ) . A -F A ( T ) , t r1CRELV{fI»JCC,1•ALFA»ALFF(I) ) C>r 5" 1

4 0 CONTINUE ;C5 >2

C O'150 3c FIND TOP WIDTH, AREA AMD CONVEYANCE AT INTERMEDIATE POINT OcSOt,c

XTDP /(= ( TOPW (2) -TOPW ( 1 > ) /PE ACH^STAPj JOPw ( 1 )0 ''SOS Or 60b

XAP= ( APE A (?) - APE A ( 1 t » /PE ACH«ST A PT♦ A PE A ( 1 ) (1.15 0 7XCO=(CO(2)-CO(1))/PEACH*START+co(1) Or S08XALF=(ALFF(?)-ALFF(1))/PEACH»STAPT+ALFF(1) r * s o p

c 0,.5 10c CALCULATE SLOPE at THIS DEPTH 0^511c

SE- (Of IO) >X CO) oc-2o ' 5 1 2 045 13

FRQD2= (XALF*Q(IQ)**2*XTOPW)/3?.?/XAP/XaP/XAP 0 15 14IF(FPOO2-1.0)224,225.225 0,15 15

224 SLOP2=(-1.0*5 IGN(1.0.UPDWN) )*(SLOPF-SE)/(1.C-FPOD2) Yf 5 16GO TO ?26 ' ">517

225 FPOD2=n.01 0 YS 1 HWRITE(61,964)ST ART,XTQPW,XAP,Xfn 045 1960 TD ??4 0 C 5 2 C

226 IF(I GO)19,19.21 00521C 0 352?C SAVF CALCULATED SLOPE OF FIRST ITERATION CY52 3c C052419 SLOP1=SLOP2 00525

lGD=l 00526C 03527c CALCULATE NEW DEPTH flf.528c

TEMP=SLOP?0052900533

DEPTHSYSTRT+(SLOP 1+SL0P2)/?.0*OX 00531GO TO 68 00532

21 IF(ABS(TEMP-SLOP2)-0.00001) 555.555.556 0f533556 TEMP = S|_OP? 00534

DEPTh=ySTRT*(SLOP 1♦SLOP?)/2.0«DX 00535GO TO 43 (1 OS 36

555 IF (UPDWN)4,5,5 005374 XTOPW=(TOPW(2)-TOPW f1 > >/REACH*(ST APT*DX)+TOPW(I) 0 0538

X AP= {APEA (2 )-AREA (1) ) /PEACH*(ST APT+ DX ) *AREA (1 ) 0 05 39XCO=(CO(2)-CO(1)1/PFACH»(START *nx)+CO(1) 00540XALF=(ALFF(2)-ALFF()) )/REACH*(ST APT*DX)+ALFF(11 0:i54l

5 WS=(Y3(2«LL2)-Y3(1,LL1))/PEACH*(M*DX)+ Y3( 1,LL1)+ (3FPTH 0 054255 CONTINUE 00543C 00544C FIND WATER STAGE AT FNDING STATION FOR THTS DFPTH 00545c

WS=DEPTH*Y3(2.LL2)0054600547

c 00548cc

TPANSEFR ENDING STATION DATA TO INITIAL STATION 00549 0 0550

STATN(1)=STATN(2) 00551CRELV(1)=CRELV(2) 0355,2LL ( 1) =t_L (21 03553INOEX=i.L (21 00554DO 65 K=l,INDEX 00555Y3(1»K)=Y3(?,K) 33556

b<=>

66

DO 65 M =1.5

AP(1«K,M> = AP(?.K «M) T^{1*K«M)= TW CONTINUE00 66 m=1.5JCC(1.M)=JCC(?»M)continue

- AC5-10 -

C U C

CO

C

CALCULATE AREA ANO VOLUME HETWPEN STATIONS

SREAR= f 7T0P**TOPW) /P.-'WAPS (STATM<?j-STATM( I ) > /A356 0 .(1 V0UJM={ZAP + XAR)/a.P*A5S(ST ATM(-STATM(I) >743560.0 STATN(1>=STATC(2)

STOkE CALCULATED DATA AT THIS STATION

ZSTA =STAT’I(?)7i#S =WSZoPTh xnEPTHZTOP =XTOP^ZAP =XA«7C0 = XCOzale=xaleacvol=acvol*volumACADE =ACARF ♦SPEARIEPR=1RETURNENO

: t558 0;'55k> Of'660 0 ;i 561

0C562 0 >56 3 ■orssp(; ft 'O 6“i 'Ct766 L o 5 6 7 0 ',568j 0 6 -<Co 73

0 571; o s 7 >

0 57 3

0 ?574 ■-),i575 0 (j 5 7 6 "3577 0^578 0^579 OC580 00S81 (J 0582 00 58 3 0 0 584

- AC6-0 -

APPENDIX 6: E071 - COMPUTER PROGRAM

- AC6-1:OSY V3.3 - MSOS 75.0 09/08/75E071 OFCK/ 1*01.1.

PROGRAM WSPRF **00 1DIMENSION Q(40).51(2*) »NCAAL(6>.FC(5),xFC(20.5),SO(40).SFC(20) 0*002DIMENSION Y3(?»50).AP(?.50.5)•TW(2.50*5).R<70)*F(70) 00003DIMENSION T0PW(2)»CD(2)*ARFA(2>.STATN<?).LL(2) 00004DIMENSION ISTA(15).ST ATM(2).CRELV(2) .JCC(2.5).ICC(20.5).SNC(20) 00005DIMENSION IRUF(125).I A(20) 00006COMMON Q.SI»NCAAL»FC«Y3•TW»AP• TnPW.CD. APFA .STATN.t 1 00007COMMON IA 0000-4COMMON R.E.NT.ALFA.UPDWN.NQ.NS.NSTl•NST?.NST♦NOST•wS,nRE 00009COMMON IERR* IO. IS.OEPTH. IST.SO. XFC.SFC.NFC, ICC.SNC.Nr/' 00010EOUIVAiENCE (ZSTA.IA(U).<7WS.IA(3)).(7DPTH.IA(5)).(7TOP.IA(7)). 0*011

1 (7AR,IA(9)).(ZCO.I A(11>).(ACARE.I A(13)) .(ACvOL. IA( 15)) 000122 . (SLpL.»1A (17) ) . (SLPR.IACI9) ) 00013

301 FORMAT<1H0.12HDI5CHARGF = .FI0.1) 00014302 FORMAT(lHg.24HROUGHNFSS COEFFICIENTS =.5F1O.3> C0015999 CALL LOCATE(40.88.MMM) 00016

WRITF (i>0 ) MMM 0001 7CALL DOPEN ( 10NF . 40 * 70 * 6) 0fj0l8IREC=O 00019

C 00020C READ WATER SURFACE PROFILE CONTROL DATA 00021C 0*022

CALL WSRED 00023C 00024C LOOP FOP EACH STAGF 0l)025C 00026

DO 30 IS=1.NS ' 00027C 00028C SET DISCHARGE AND FRICTION COEFFICIENTS AT INITIAL STATION 00029C 00030

DO 10 1 = 1.5 00031FC(J)=XFC(1»J> 00032JCC<1.J) = ICC(1 *J) 0OO33JCC(2.J)*ICC(I•J) 00034

10 CONTINUE 00035IQ=1 00036

C 00037c read Initial section data and print headings ooossc 00039

REWIND NT 00040READ(NT)NCAAL 00041

C 00042C DETERMINE if TAPE TD RE READ UPSTREAM OP DOWNSTREAM 00043c 00044

IF(UPDwN)74.75.75 0004574 NTAP=NST2-1 00046

DO 76 k=1.NTAP 00047READ(NT) 00048

76 CONTINUE ‘ 00049GO TD 81 00050

75 IF (»jST 1-1) 81.81.8? 0005112 NTAP=NSTl-l 00052

DO 83 k=1.NTAP 00053REAO(NT) 00054

33 CONTINUE 0005531 READ(NT)STATN<1).ST ATM(1).CPELV(1).NRE.(R <I),F (I).1=1.NRE).LL1. 0 0 056

1(Y3(1*K).(TW(1.K.M).AP(1.K.M).M=1.S)*K=1.LL1) 00057WS=SKIS) 00058LL(1)=LL1 00059CALL WSTAP 00060

KCC = 2 CC TRANSFFR TO BOTTOM OF LOOP IF ERROR PRESENTC

GO TO ( 14.30* IFRR cC DETERMINE SECTION INTERCEPTS FOR INITIAL STATIONC14 CALL SC I NT(WS,NRE.R.E.SLPL .SLPR )CC DETERMINE SECTION CHARACTERISTICS FOR INITIAL STATIONC

CALL WSCHR(LL(1)»DEPTH»Y3*TW«AP•FC.7TO°*ZCO*ZAR«CPFLV(1)*JCC*1) CC PRINT ANO STOPE INITIAL STATION DATAC

CALL STAT'(ZSTA, ISTA)WRITE(Sl,388)ISTA.ZW^ , ZDPTH,ZTOD,ZAR,ZCO,ACARF* ACVOL.SLPL.SLPR

38 8 FORMAT(1 HO,15A 1.2F8»9,5EI 3.6»2F12.0IREC=IRF.C*1CALL DPUT(IRUF,IREC.I A)

CC ENTER ITERATION PROCESS FOR THIS CHANNELCCC LOOP FOR EACH STATIONC

DO 40 fST=l*NST CC ENTER INTERPOLATION ANO ITERATION PPOCFSS FOP THIS STATION

CIF(UPOWN,77*78,78

77 DO Si] M=l»2 BACKSPACE NT

80 CONTINUE78 READ(NT)STATN<?),STATM<2) .CRELV(2),NRE,(«(I),E<I),I=1.NRE) ,LL2»

1 <Y3 <2»K> , (TW(2.K.M) , AP(2,K,M) , M=1 ,c;) *K = 1 , LL2)LL(2)=LL2

CC DETERMINE IF CHANNEL DESIGNATION TO BE CHANGED AT THIS STATIONC

IF(KCC-NCC)42.42.4642 IF(ARS(SNC(KCC)-STATN(2,1-0.01)43,43.4643 DO 45 J=1.5

JCC(2.J,=ICC(KCC,J)45 CONTINUE

KCC=KCC*146 CALL POINT(STATM.CRELV*JCC)

GO TO(949.30),IERRCC CALCULATE SECTION INTERCEPTS AT THIS WATER SURFACEC949 CALL SCINT(WS.NRE.R.F.SLPL.SLPR)

CALL STATtZSTA .ISTA)WRITE(61♦388)ISTA.ZWS.ZOPTH.ZTOR.ZAP.ZCO.ACARE.ACVOL.SLPL.SLPR IREC=IREC+1CALL DPUT(IAUF.IREC.IA)

CC DETERMINE IF DISCHARGE IS TO BE CHANGED AT THIS STATIONC

IF(10+i-NO>21.21.12

0006 t 09062 00063 00064 06065 00C66 000^7 0C066 0 0069 06070 000 71 00072 00073 0u074 09075 00076 00077 00078 00074 00080 00081 000^2 00083 00084 00085 00086 0f)f)8 7 0 0088 00089 OnORQ 0 0091 00092 09093 00048 0009c 00096 00097 00098 00095 on 1 00 ooioi 00102 0 010 3 0 0 1 04 001 OS 00106 00107 ooioe 00 1 os 00 11 c 00111 00112 00113 00118 001 is 001 i6

001 IT 00118 00119 00120 00121 C0122

- AC6-3 -21 IE(ABS(SQ(10*1)-ST ATM(1)>-0.01>11,l1,1211 IQ=IQ*1

WRITF(61*301)Q<IQ)CC DETERMINE IF FRICTION COEFFICIENTS TO RE CHANGED AT THIS STATIONC12 IF ( JFC-NFC>22 * 22*4022 IF(ABS(SFC(JFC)-STATN(1) >-0.01)13.13,4(113 DO IS .1=1,5

FC(J)= XFC(JFC* J)15 CONTINUE

JFC=JFC*1 WRITE(61*302)FC

40 CONTINUE30 CONTINUE

CALL DCLOS(IBUF)READ (60*201)IPLOT*HSCAL*VSCAL

201 FORMAT{I5*5X«2F10.3)IF (IPLOT)999.999*998

998 CALL PLOTS<0*0.0)CALL WSPLT (NOST.NCAAL.HSCAL,VSCAL.IJPDWN)CALL PLOT(0.0*0.0*999)GO TO 999 END

SUBROUTINE SCINT(WS*M*R*E*SLPLT*SLPRT)DIMENSION R(1)*E<1>DO 10 K=1*N IF (WS-r(K)) 10* 11*1?

tO CONTINUE SLPLT=0.0 GO TO 20

11 SLPLT=P(K>GO TO 20

2 5LPLT=P(K-1)*(E(K-l)-WS)/(E(K-l)-E(K))*(R<K)-R(K-l,>0 DO 30 K=1,N

L=N-K+1IF(WS-f(L))30*31*32

0 CONTINUE SLPRT=0.0 GO TO 99

1 SLPRT=R(L)GO TO 99

2 SLPRT=p(L)*(WS-E(L))/(E(L*l)-E(L))»(R(L*l>-R(L))9 RETURN

END

SUBROUTINE WSPLT(NOST.NCAAL. HSCAL*VSCAL»UPDWN>DIMENSION 1STA(15)»NCAAL(6)DIMENSION IBUF(125)*TA(20)*MSG(11)DIMENSION LCHAR(32),IPL1(15)»IPL2(71 ‘DATA ((IPL1(I)»1=1.5)=4H£LEV.4HATI0.4HN IN.4H FEE.4HT )DATA ( ( IPL2( I) * I=1»7)-4HWATE»4HR SU.4HRFAC*4HE PR .4H0F TL * 4-HE FO*

1 4HR )DATA (mSG=41HSET PEN ON PLAIN RAPER AGAINST RIGHT STOP)EQUIVALENCE (STA,IA(1)).(WS.I A(3)).(DEDTH»IA(5))

)0 FORMAT(1H1.59HPROFILE WILL NOT FIT IN 27 INCHES WITH GIVEN VFRTICA IL SCALE)

CALL FACTOR(O.S)CALL OOPENtIBUF,40*20.6)

DETERMINE MAXIMUM AND MINIMUM STATION VALUES

00123 0 0 124 00125 00126 00127 00128 00 1 29 00130 00131 00132 00 133 00 134 031 35 00136 00137 00138 00139 00140 00141 00142 00143 00144 00145 00146 00147 00148 00149 00150 0015] 00152 CO 1 S3 00154 00155 0 0156 00157 00158 00159 00160 00161 00162 00163 00164 00165 00166 00167 00 168 00169 00170 00171 00172 00173 00174 00175 00176 00177 00178 00179 00180 00181 00182 00183 00184

cCALL DGET ( IBLJF* 1 * I A)ST1=STACALL DGET(I9UE,NOST* I A)ST?=STflIE(ST 1-ST2)27.28 . 28

901 85 00 186 00 187 001880 0)89 00 190

27 SGN=1.0 00191GO TO ?9 00 192

28 SGN=-1.0 00193C 00198c DETERMINE MAXIMUM AND MINIMUM AOTTQM ELEVATION AND WATER SURFACE 00195c 00 19629 WSMX=-9999.0E30 00 197

WSmn=+9999.0E30 OC 198DO 17 K=1*NOST 00199CALL DGET(IBUE*K,IA) 00200IE (WS-WSMX>18.18*19 00201

19 WSMX=WS 0020218 IF((WS-DEPTH,-WSMN126*17*17 0020326 WSMN=WS-DEPTH 0020817 CONTINUE 00205C 00206c DETERMINE IE PLOT WILL FIT ON PLOTTER WITH GIVEN SCALPS 00207c

XMIN=IFIX(WSMN)-VSCAL0020800209

XMAX=IEIX(WSMX)*VSCAl 00?10XINCH= (XMAX-XMIN)/V5CAL 0021 1IF(X INCH-27.0)10*10*11 00212

11 W9ITE(61 * 300) 00213GO TO 9999 00218

c 00215c POSITION PEN* PLOT AND LABEL ELEVATION AXIS 00216c 0021 710 CALL SFTMSG(11*MSG) 00218

CALL EPLOT(1♦3•0♦2•0> 00219CALL SCALE ( 1 • 0 * 1.0/VSCAL* 0.0»0.0) 00220CALL EGRID(1»0.0»0.0,VSCAL/2.0.1EIXfXINCH)*2) 00221CALL EPLOT(1*O.0*0.0) 00222CALL SCALEIl.0*1.0*0.0*0.0) 00223y=-i.05 00228yv=xmin-vscal 00225N=XINCh*1 00226DO 12 K=1*N 00227Y = Y* 1.0 00228YV=YV+VSCAL 00229CALL PUTDC(YV.2.LCHAP*1*6) 00230CALL ECHAR(-0.70 *Y* 0.1 * 0.1 * 0.0*LCHAP»6) 00231

12 CONTINUE 00232CALL A4A1(IPL1*1*5*LCHAR*1) 00233CALL ECHAR(-0•90 * 1.0*0.2*0.2*1.5707*LCHAR,17) 00238

c 00235c PLOT AND LABEL STATION AXIS 00236c

CALL EPLOT(1*O.0*0.0)0023700238

call scale<1.o/hscal*i.o*sti*sgn-o.5»hscal»o.o) 00239DO 13 K=1,NOST 002^0CALL DgET<IRUF*K*IA) 00281CALL EPLOT{2*STA*SGN«0.0) 00292CALL EPLOT(1»STA’SGN* 0,09) 00293CALL EPLOT(2»STA«SGN*-0.0A) 00288CALL STATISTA *TSTA, 00285CALL ECHAR{STA«SGN + 0.05*HSCAL*-1.60*0*1 *0.1 * 1.5707*ISTA* 15) 00296

- AC6-5 -CALL EPLOT ( 1 *STA*SGN*Q.O) " AC6-5 -

13 CONTINUECALL A4A 1 (IPL2.1.7 *LCHAR.1)CALL MOVE (NC A AL * 1 • 6 ♦ |_ CHAR » 27 >CALL ECHAR(ST]*SGN*HSCAL♦-?.0♦0.2*0.2* 0.0 *LCHAR* 3?)

PLOT jJATER SURFACE PROFILE

’4?5

?0

14

15 56

10

>999

104

'512

*00

CALL EPLOT(1*ST1»SGN.O.O)CALL SCALE(1.0/rtSCAL* 1.0/VSCAL* ST 1*SGN.XMIN)DO 20 k=1,NOST CALL DGET(IRUF*K.I A)IF(K-l)24-24.25CALL EPLOT(1.STA»SGN.WS)CALL EPLOT<2*STA»SGN,WS)CALL PUTDC(WS,2»LCHAR»1 * 6)CALL ECHAR(ST A*SGN*0 . Cl5*HSCAL» WS ♦ 0•05*VSCAL.0,1.0.1 * I.5707,

1LCHAP.6)CALL EPLOT(1.STA*SGN*WS)CONTINUE

PLOT floTTOM ELEVATION PROFILE

no 30 <=1*NOST L=NOST-K* 1CALL OGET(IBUR.L*I A,IF(K-1)34,34,35CALL EPLOT(1«STA»SGN*WS -DEPTH )GO TO 36CALL DASLN(XSTA,XWS-XDP*STA*SGN,WS-nEPTH,0.?5.HSCAL)CALL PUTDC<WS-DEPTH*P*LCHAP*1»6>CALL ECHAR(STA«SGN + 0.05*HSCAL*WS -DEPTH -0.65«VSCAt »0.1 * 0.1 *

1 1 * 5707 *LCHAR*6)xsta=sta*sgn

xws=wsXDP=DEPTHCONTINUECALL FPLOT ( 1 . ST?«-SGN ♦ 3.0*HSC AL . XM IN)CALL EPLOT(999*0.0»0 ,0)RETURNEND

SUBROUTINE WSTAPDIMENSION 0(40).SI(20).NCAAL(6)*FC(5)*XFC(?0*5)*SO(40>.SEC(20) DIMENSION Y3(2*50)*ao(2*50*5)*TW(2.5O*5> *R(70)*E(70)DIMENSION TOPW(2)*C0(21* AREA(2)*STATN(?)*LL(2)COMMON O*SI.NCAAL.FC.Y3.TW*AP. TORW.CO.AREA.STATN.il COMMON ZSTA,ZWS*ZDPTH*ZTOP*ZAR.7CO* ACARE» ACVOL . slpl * Sl_PP COMMON R.E *NT * ALEA.UPDWN*NQ*NS*NSTI»NST2»NST »NOST»WS*NRE COMMON IERR.10.IS.DEPTH.IST * SO.XFC* SEC.NECFORMAT(1H1.51X.6A1//1H .33X»11 HOISCHARGE =.F9,0.2X.

1 ISHINITIAL STAGE =.E6.2/1 HO*43X*2PHROUGHNESS COEFFICIENTS)FOPMATdH *41X* 14HCLASSIEICATION. I2.3H = .E7.4)FORMAT<1HO*18X.5HWATEP*14X.3HT0P»30X*2(13H ACCUMULATED)*3X.

1 18HSECTION INTEPCEPTS/1H .6X»7HSTAT ION*5X* 13HSTAGE DEPTH.5X2 5HWIDTH.8X.4HAREA.6X*24HC0NVEYANCE SURFACE AREA.5X.6HV0LUME*3 ax,4HLEET.6X*5HRIGHT)

FORMAT(1 HO•17HIN ITIAL STAGE OF ,F7.?*27H RELOW BOTTOM ELEVATION 1 *E7.2)FORMAT(1 HO * I7HIN ITIAL STAGE OF *E7.?*23H ABOVE TOP ELEVATION OF

1F7.2)LL1=LL ( 1 )

OF

00P47 0Q748 00249 002S9 Pn?Sl 09252 09253 00254 30?S5 0 0 756 00?57 00258 00259 C026C 00261 00262 0(i?63 0C264 00765 00266 00767 00268 00269 00270 00271 00272 00273 00274 00275 00276 00277 00278 00279 00280 00281 00282 00283 00284 00285 'J0286 0C287 00288 00289 00290 00291 00292 00293 00294 00295 00796 00797 00298 00299 00300 00301 0030? 00303 00304 00305 00306 00307 00308

'01

- AC6-6WRITE(61•304)NCAAL.O(IQ),WS 00 309no 23 )JL=1.5 0031 0IF(FC( JJL))23,23.24 00311

24 WR!TE(6l,25)JJL.EC(JJL) 0331?23 CONTINUE 00313

WRITE(6l,22) 00314C 0 n 3 1 5c DETERMINE if INITIAL STAGE OUT OF PANGE 00316c 00317

IE(WS-y3U,LL1> ) 11.11.12 0031«11 WRITM61.900) WS.Y3 ( l.LLl > 00 3 1 977 IERR=? 00320

RETURN 0032112 IE(WS-Y3(1,1>)14.14,15 0032?15 WRITE(61*901)WS,Y3(1«I) 00323

GO TO 77 0932414 IE»R=1 ''■0325C. 00326C FIND DEPTH at INITIAL STATION 00327C 0032B

DEPTH=wS-Y3<1,LL1) 00329C 00330C DETERMINE SECTION CHARACTERISTICS aT INITIAL STAGE 00331C 0033?

ZDPTH =DEPTH 00333ZSTA =STATN(1) 00334ZWS -WS 00335ACAPE =0.0 00336ACVOL =0.0 0H337RETURN 00336END 00339

00340SUBROUTINE WSRED 00341DIMENSION 0(40).SI(20).NCAAL(6)*FC(5).XEC120.5).50(40).SEC(20) 00342DIMENSION Y3(2 * 50),AD(2»50 * 5),TW(?.50.5) »R(70)♦E(70) 00343DIMENSION T0PW(2).CO(2,.AREA(2),STATN(2)»LL(2,•ICC(20.5),SNC(20) 00344COMMON Q.SI.NCAAL.FC.Y3.TW.AP. TOpW, CO» APEA , ST ATN »|.l 00345COMMON ZSTA.ZW5.ZdPTH.ZT0P.ZAR.7C0. ACARE.ACVOL.SLPL.5I.PR 00346COMMON R, E, NT, ALE A. IJPDWN , NQ, NS, NST 1 , NST2 »NST » NQST, WS, NPE 00347COMMON IERR.IQ.IS,DEPTH,1ST.SQ,XFC.SEC.NFC.ICC,SNC.NCT 00346NT=11 00349READ(60,201)ALFA,UPOWN 00350

201 FORMAT(8E10.3, 09351IE(UPDWN)50.60,50 00352

60 CALL EXIT 0035350 RE AD(60»202)NS,NQ,NEC»NST1•NST2,NCC 00354202 E0RMAT(6I5) 00355

PEAD(60*201) (SI( IS),IS = 1.NS) 00 356DO 10 tQ=1,NQ 00357

10 READ(60,2Ol) SQ(IQ).Q(IO) 00356DO 20 IC=1,NFC 00359

20 RE AD(60,201)SEC(IC),(XEC(IC* J)*J=1»5, 003601E(NCC)1.1,2 00361

2 DO 30 NC=1,NCC 0036230 RE AD(60,203»SNC(NC) , (ICC(NC,J I ,J=1,5) 00363203 FORMAT(E10.3*1015) 003641 NST=NST2-NST1 00365

NOST=NST*1 00366RETURN 00367END 00366

00369SUHROUTlNE WSCHR(INDEX,DEPTH.Y3,TW.AP.FC.TOPW,CO,AREA,CRELV,JCC.I) 00370

- AC6-7 -DIMENSION Y3(2,5P),TW(?,5n,5),AP(2,50,5).FC<5).JCC(2,5) W5=DEPTH*Y3(I,INDEX)DO 10 k=2,INDEX IF (WS-Y3(I,K>)10*11.11

0 CONTINUE STOP

1 RAT 10=(WS-Y3(I ,K))/(Y3(I,K-1>-Y3 <I.K))TDPW=0.0 co=o.o AREA=Q.0 DO 20 J=l,5IF ( CRFLV*9998,OE30)4?,42,41

1 IF(WS-CRELV)43 * 43.423 IF(JCC{I,J))20.20.4?2 IF(FC(J))21.20,211 IF(TW(I,K-1,J))20,20»222 TP*(TW(I,K-1.J)-TW(I.K,J))#RATTO*TW(I.K,J)

AR = (TD*TW( I.K, J) ) /?.('« (WS-Y3 ( I.K) )IF (K-INDEX)?3,24.24

3 M=INDEX-1 DO 3f> L = K,MAR=AR+(TW(I,L•J,*TW(I»L*1.J>>•0*(Y3<I,L)-Y3(I,L*1))

0 CONTINUE4 yP= < AP ( I,K-l.J)-AP( I,K,J) )*RATin*AP(I,K,J)

TOPW=TOPW*TPAREA=APEA*AR IF (FC(J)>51.52,52

1 D=AR/TPFN=1.5613-1.08471*D*0.490179*D**2-0.124972»D**3*0.0173095*D**4-

] 0.0012181*0**5*0.0000341199*D**6C0=C0*l.486*(AR**(5.0/3.0,/WP**(2.0/3.0)>/FN 60 TO ?O

2 CO=CO*1.486*(AR**(5.0/3.0)/WP**(2.0/3.0))/FC(J)0 CONTINUE

return

END

700268

SUBROUTINE RCINT(STATM,CRELV.JcoDIMENSION 0(40).SI(?0).NCAAL(6).FC(S),XFC(?0.5).SO(40),SFC(20) DIMENSION Y3<2,50>,AP(2,50.5),TW(2,50,5),R(70),E(70)DIMENSION TOPW(2).CO(2).AREA(2).STATN(2).LL(2) dimension icc(2o,5>,snc(20>,statm<2i.crflv(?),jcc<2.5)COMMON 0,SI .NCAAL,FC.Y3.TW.AP. TOPW . CO , ARE A , STATN »(_ iCOMMON ZSTA,ZWS,ZDPTM,zTOP,?AR,7CO,ACARE.ACVOL.SLPL,Si PR COMMON P,E,NT,ALFA.UPDWN,NQ.NS.NSTl.NST2.NST,NOST-WS.NRE COMMON I ERR,IO,IS,DEPTH,1ST,SO,XFC,SFC.NFC.ICC.SNC.NCC FORMAT (1 HO, 38HUNARL.E TO CONVERGE AFTER 20 ITERATIONS)FORMAT(IHO,13HDEPTH OUT OF RANGE)FORMAT(1H0.7HOEPTH =.F6.2/1H ,20HITFRATI ON INTERVAL =,I3/1H ,

1 25HINTERPOL AT ION INCREMENT =»F10.2/lH .20HREACH BOTTOM SLOPE =,2 EI5.7/1H .28HDISTANCF FROM LAST STATION =,F10.3/lH .llHTOP WIDTH 3=,F15.7/1H ,12HCONVFYANCE =,E15.7/1H .6HARFA =,E15.7)

FORMAT(IHO.37HSUPER-CRITICAL FLOW AT A DISTANCE OF ,F10.3»1 18H PAST LAST STATION/Ih .llHTOP WIDTH =,E13.6»7H AREA =,E13.6,2 13H CONVEYANCE =.E13.6)LL1=LL(I)LL2=LL(2)

DETERMINE REACH CONTROL DATA

REACH=ABS(STATN(1)-STATN(2)) DX=REACH/10.0

00371 00372 00373 0 0 374 00375 00376 00377 00378 00079 00^«0 00381 0038? 00383 00384 0OT85 00386 00387 00388 00389 00390 00391 00 392 00393 00394 00395 00396 00397 00398 00399 00400 00401 00402 00403 00404 00405 00406 00407 00408 00409 00410 00411 00412 00413 00414 00415 0 Q4 16 00417 00418 00419 00420 00421 00422 00423 00424 00425 004^6 03427 00428 00429 00430 00431 00432

64

- AC6-8 -

533

532ccc534

IE(UPDWN)532*532.533 SLOPE-(Y3(2,LL2>-Y3 (1»LL 1 > >/REACH GO TO 534SLOPE=<Y3(1, LL1)-Y3(2.LL2) )/REACH

ENTER ITERATION PROCESS FOR THIS PEACH

1 1 12

CCc43

969CCC611

23

DO 55 m=1,10 ICOIJT^"START-CLOAT(M )«DX IF(UPOWN) 11.12.12 STAPT=START-OX YSTRT=OEPTH IGO=O

CHECK FOR EXCESS NUMBER OF ITERATIONS

ICOUT=ICOUT+1IF (ICOlJT-20 ) 6«.65.969MQ=l

ERROR DISCOVERED print data TO THIS POINT WITH PERTINENT DATA

Cccc

68Ccc

GO TO(1.2).MOWRITE(6l.970)GO TO 5WRITE(61.902)WRITE(61»968)DEPTH.M.OX.SLOPE.START.XTOPW.XC0.XARIFRR=2RETURN

CALCULATE INITIAL AND ENDING STATION TOP WIDTHS. AREAS AND CONVEYANCES FOR INTERMEDIATE POINT CALCULATIONS

DO 90 r=1.2

CHECK FOR ALLOWABLE °ANGE OF 0EpTH

45 44

46

90Ccc

INDEX=LL ( I )IE(DEPTH)44.44,45IE f(DEPTH*Y3(I.INDEX) )-Y3(1.1) )46,46*44 mo=2GO TO 61CALL WSCHRILL(I)* DEPTH,Y3*TW♦ AP.EC«TOPW<I),CO(I)»AREA<I)*

1CRELV( I) , ICC * T)CONTINUE

FIND TOP WIDTH* AREA ANO CONVEYANCE AT INTERMEDIATE POINT

XTOPW=(TOPW(2)-TOPW(1)>/REACH»START+TOPW(1) XAP=(AREA(2)-AREA < I ) )/REACH»START +AREA(1) XCO=(CO(2)-CO(1))/REACH’START+CO(1)

ccc

CALCULATE SLOPE AT THIS DEPTH

SE-(O(TO)/XCO)»»2FRDD2=(ALEA*Q(IQ)**2*XTOPW)/32•2/XAP/XAR/XAR IE(ER0D2-1.0)224*225*225SL0P2=(-1.0*SIGN(1.0.UPOWN) > *(SLOPE-SE)/(1.0-EROD2) GO TO ?26 FRDD2 = 0.01WRITE(61,964)START,XTOPW.XAR*XCO

00433

0 04 34

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004 39 00443

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00457 00458 00459 00460 00461 0 0462 0046 3 00464 00465 00466 0046 7 00468 00469 00470

00471 00472 00473 00474 00475 00476 00477 00478 00479 00480 00481 00482 00483 00404 00485 00486 00487 OC48’0 00409 00490 0 0491 00492 00493 00494

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- AC6-9 -226CCc19

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GO TO 2?4IF(IGO)19*19*21

SAVE CALCULATED SLOPE OF FIRST ITERATION

SLOP1=SL0P2 IGO=1

5554

555CCc

ccc

65

66CCc

ccc

CALCULATE NEW DEPTH

YLAST=DEPTHDEPTH=YSTRT*(SLOP1*SLOP2)/2.0*nxIF{ABS(YLAST-DEPTH)-0.001>555*555*43IF(UPDWN>4*5»5XTOPW=(TOPW(2)-TOPW M) >/REACH*(START*DX > +TOPW( I)XAR=(AREA(2)-AREA(I))/REACH*<ST ART *DX)*APEA (1)XCO=(CO(2)-CO(1)>/PFACH*(START + OX> *CO{I )WS = ( Y3 (2*LL2> -Y3 ( 1 ,LLl > ) /REACH*(M*nX )+Y3 <I*LL1) *DFPTh CONTINUE

FIND WATER STAGE AT ENDING station FOR THIS DFPTH

WS=OEPTH*Y3(2*LL2)

transfer ending station data to initial station

STATN(1)=STATN(2)CRELVd > =CRELV (2)LL{1)=LL(2>INDEX^lL <2>DO 65 K=1*INDFXY3fl*K)=Y3(2.K>DO 65 M=l,5AP(1*K,M)-AP<2 *K*M)TW<1*K,M)=TW(2.K*M)CONTINUEDO 66 M=1 * 5JCC(1*m>=JCC(2*M)CONTINUE

CALCULATE AREA AND VOLUME BETWEEN STATIONS

SRFAR={ZTOP*XTOPw)/?,ft*ABS(ST ATM{?)-ST ATM(1))/43560.0 VOLUM=(ZAR* XAR)/?.O*ABS{STATM(?>-ST ATM(1)1/43560*0 STATM{l)=STATM (2)

STORE CALCULATED DATA AT THIS STATION

ZSTA =STATN(2>ZWS = WSZDDTH =DFPTHZTOP =XTOPWZAP =XAPZCO =XCDACVOL=ACVOL+VOLUMACAPE =ACARE *SREARIERR=1RETURNEND

00495 00496 00497 00498 00494 1)0900 00501 0050? 0O503 00504 00505 00506 00507 00905 0'509 00510 00511 00512 00513 00514 0n515 00516 00517 00518 00519 00520 00521 00522 00523 00524 0 0 525 0 0 526 0Q527 00528 00529 00530 00531 00532 00533 00534 00535 00536 0C537 00538 00539 00540 00541 00 54? 00543 00544 00545 0 0546 00547 00548 00949 00550 00551 0 055? C0553

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