6c64c6bb-bfb6-4dd4-885f-14030e2bb6ff 177 5 7 decimal

1. Example:Main Canal Design - To Find FSD, Vel, Froud Number etc, for Open Channel flow

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Note:Input values highlighted. Default Units - SI

1. Input

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Q.d 10 m 3^s / * :

Design discharge

Q.ol 12 m 3^s / * :

Overloaded discharge

Bed width

BW 4 m * :

Bed slope

S.0 0.00018 :

Side slope

Z 2 :

percent (#1) ％ 1100 / :

Manning's "n"

n 0.015 :

Free board

FB 0.75 m * :

2. General Equations used

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Area y A y BW y Z * + (* :

Perimeter y P BW 2 y * 1 Z 2^+ sqrt * + :

Hydraulic radius y R y A y P / :

Velocity y V Q.d y A / :

Top width y T BW 2 Z * y * + :

Manning's Eqn y Vm 1 n / y R (23 /^* (S.0 sqrt * m 13 /^s / (* :

3. Find Normal Depth y₀ & Critical Depth y_c

It is advisable to plot variation of depth vs. Q to estimate the guess depth (y_g). We see that there

are two values as solutiins, ie. yy=-3.5m & yy=1.5 m approximately. Hence, take y_g = 2 m.

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Guess depths yy 4 - 2 - 1 - 012 2.5 71 mat m * :

j 1 yy rows range QQ j el yy j el A yy j el Vm * : for

QQ m 3^s / 15.73 0 4.68 - 0 4.26 16.48 26.16 71 mat

Hence, assume y.g 2 m * :

XYPlot.XLimMin 1 el 5 - :

XYPlot.XLimMax 1 el 4 :

Settings for X-Y Plot

(Many thanks to "Mezentsev"

for the latest plug-in).

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XYPlot.YLimMin 1 el 5 - :

XYPlot.YLimMax 1 el 30 :

XYPlot.XTick 1 el 1 :

XYPlot.YTick 1 el 2.5 :

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yy QQ augment Q.d 2 1 sys yy QQ augment Q.d 2 1 sys

3.1. Find Normal depth

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3.2. Find Critical depth

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Critical Flow Eqn for 
Trapeziodal sections F1 Q.d 2^y.c T * g.e y.c A (3^* / 1 ≡ (:

Normal depth Eqn. to solve F Q.d y A y Vm * ≡ (:

Use symbolic optimization F Unknowns y 11 mat

F1 Unknowns y.c 11 mat

guess depth y.g 2 m *

guess depth y.g 2 m *

Try y_g=1m and we get

-3.68 m (-ve) which is

not admissible

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Normal depth y.0 F y.g FindRoot : 1.559 m *

Ctitical depth y.c F1 y.g FindRoot : 0.738 m *

Normal velocity V.0 y.0 V : 0.901 m s / *

Critical velocity V.c y.c V : 2.476 m s / *

Check calculations Q.0 y.0 A V.0 * : 10 m 3^s / *

Check calculations Q.c y.c A V.c * : 10 m 3^s / *

4. Find flow conditions

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Froud Number at yo Fr.0 Q.d 2^y.0 T * g.e y.0 A (3^* / : 0.076

Froud Number at yc Fr.c Q.d 2^y.c T * g.e y.c A (3^* / : 1.07642

Using Formatted label

Fr.0 1 < Sub-Critical Flow black light green 1 3 mat 1 Fr.0 ≤ 1.00001 < Critical Flow red light green 1 3 mat Super Critical red yellow 1 3 mat if if Fr.c 1 < Sub-Critical Flow black light green 1 3 mat 1 Fr.c ≤ 1.00001 < Critical Flow red light green 1 3 mat Super Critical red yellow 1 3 mat if if

Slope of given channel S.0 0.00018

Critical slope for given canal parameters S.c n Q.d * y.c A y.c R (23 /^* m 13 /^s / (* / (2^: 0.003038

Ratio of Sc/So S.c S.0 / 16.88

5. Advanced Method - suitable for programming (using "FindRoot")

5.1. General Equations used

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Area y b z A1 y b y z * + (* :

Perimeter y b z P1 b 2 y * (1 z 2^+ sqrt * + :

Hydraulic radius y b z R1 y b z A1 y b z P1 / :

Manning's Eqn y b z SL V1.m 1 n / y b z R1 (23 /^* (SL sqrt * m 13 /^s / (* :

Top width y b z TT b 2 z * y * + :

Velocity y b z V1 Q.d y b z A1 / :

Eqn to find normal depth for 
trapezoidal section b z q SL F7 q y b z A1 y b z SL V1.m * ≡ (:

b z q SL F7 Unknowns b q SL y z 51 mat

Eqn to find critical depth for 
Trapeziodal sections b z q FF1 q 2^yy.c b z TT * g.e yy.c b z A1 (3^* / 1 ≡ (:

Eqn 1: This is useful for

programmimg as shown below

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b z q FF1 Unknowns b q yy.c z 41 mat

guess depth

b z q SL yy yy b z q SL F7 yy FindRoot :

b z q y yy.c b z q FF1 y FindRoot :

Critical depth for Trapez. section for Qd yy.c0 BW Z Q.d 1 m * yy.c : 0.754 m *

Depth for critical slope. Before 
you use this, you must know Sc BW Z Q.d S.c y.g yy 0.738 m *

Normal depth for Trapezoidal section yy.0 BW Z Q.d S.0 y.g yy : 1.559 m *

Critical slope for given canal for Qd n Q.d * yy.c0 A yy.c0 R (23 /^* m 13 /^s / (* / (2^0.002807

Normal depth, for Rect. section BW 0 Q.d S.0 y.g yy 2.581 m *

Critical depth for Rect. section BW 0 Q.d 1 m * yy.c 0.861 m *

Froud Number at normal depth Fr1.0 Q.d 2^yy.0 BW Z TT * g.e yy.0 BW Z A1 (3^* / : 0.076

Froud Number at critical depth Fr1.c Q.d 2^yy.c0 BW Z TT * g.e yy.c0 BW Z A1 (3^* / : 1

Critical depth for Trapez. section for Qol yy2.c0 BW Z Q.ol 1 m * yy.c : 0.839 m *

Critical slope for given canal for Qol n Q.ol * yy2.c0 A yy2.c0 R (23 /^* m 13 /^s / (* / (2^0.002735

Program to find FSD, Vel, Froud Number for a range of bed widths b z q1 sl q2 Find_Y j 1 b rows range y_rect j el b j el 0 q1 sl 1 m * yy : FSD1 j el b j el z q1 sl y_rect j el yy : FSD2 j el b j el z q2 sl y_rect j el yy : AA1 j el FSD1 j el b j el z A1 : AA2 j el FSD2 j el b j el z A1 : YC1 j el b j el z q1 1 m * yy.c : YC2 j el b j el z q2 1 m * yy.c : SC1 j el n q1 * YC1 j el b j el z A1 YC1 j el b j el z R1 (23 /^* m 13 /^s / (* / (2^: SC2 j el n q2 * YC2 j el b j el z A1 YC2 j el b j el z R1 (23 /^* m 13 /^s / (* / (2^: SCR1 j el SC1 j el S.0 / : SCR2 j el SC2 j el S.0 / : VV1 j el q1 AA1 j el / : VV2 j el q2 AA2 j el / : T1 j el b j el 2 z * FSD1 j el * + : T2 j el b j el 2 z * FSD2 j el * + : fr1 j el VV1 j el g.e AA1 j el T1 j el / * sqrt / eval : fr2 j el VV2 j el g.e AA2 j el T2 j el / * sqrt / eval : sp j el - : 191 line for A b m / FSD1 m / YC1 m / VV1 m s / / SC1 SCR1 fr1 sp augment eval : A A FSD2 m / YC2 m / VV2 m s / / SC2 SCR2 fr2 augment eval : 31 line :

First find depth for rect. section using Eqn 1, by using z=0 & guess depth = 1m. This will result in a +ve result.

Then use y_rect as guess depth to find FSD. If we do not use this step, we may get -ve values for FSD.

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---- FSD for Q_d, using Eqn 1

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---- FSD for Q_ol, using Eqn 1

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Areas for Q_d& for Q_ol

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Critical depths for Q_d & for Q_ol

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y b z A1

Critical slopes

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g.e 9.80665 m s 2^/ *

Ratios of

for Q_d & for Q_ol

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Velocities

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Top widths

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Froud numbers

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---- Space

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Define range of bed widths; 
This input can be modified 
suitably in ascending order bb 3 3.25 3.5 3.75 4 4.25 4.5 4.75 591 mat m * :

Ans bb Z Q.d S.0 Q.ol Find_Y :

title BW FSD1 YC1 V1 SC1 SC1/So Fr1 - FSD2 augment :

title title YC2 V2 SC2 SC2/So Fr2 augment :

title1 m m m m/s - - - - m m m/s - - - augment :

title title title1 stack :

Ans title Ans stack :

6. Results

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Suffix 1: Canal parameters for Qd

Suffix 2: Canal parameters for Qol

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Q.d 10 m 3^s / *

Q.ol 12 m 3^s / *

Critical slope for given canal for Qd n Q.d * yy.c0 A yy.c0 R (23 /^* m 13 /^s / (* / (2^0.002807

for

BW 4 m *

Ans BW FSD1 YC1 V1 SC1 SC1/So Fr1 - FSD2 YC2 V2 SC2 SC2/So Fr2 m m m m/s - - - - m m m/s - - - 3 1.70823 0.85558 0.91235 0.0028 15.53053 0.27594 - 1.86412 0.94733 0.95677 0.00273 15.15566 0.27897 3.25 1.66851 0.82759 0.90988 0.0028 15.5388 0.27609 - 1.823 0.91765 0.95454 0.00273 15.15797 0.27913 3.5 1.63044 0.80137 0.90718 0.0028 15.55297 0.27622 - 1.78347 0.88975 0.9521 0.00273 15.16578 0.27927 3.75 1.59394 0.77679 0.90428 0.0028 15.57254 0.27632 - 1.74546 0.8635 0.94946 0.00273 15.17854 0.27938 4 1.55895 0.75373 0.90119 0.00281 15.59686 0.27639 - 1.70892 0.83878 0.94663 0.00274 15.19571 0.27948 4.25 1.52542 0.73206 0.89792 0.00281 15.62559 0.27644 - 1.67381 0.81548 0.94362 0.00274 15.21728 0.27955 4.5 1.49327 0.71169 0.8945 0.00282 15.65811 0.27647 - 1.64005 0.79351 0.94046 0.00274 15.24243 0.2796 4.75 1.46245 0.6925 0.89093 0.00282 15.69411 0.27648 - 1.6076 0.77275 0.93714 0.00275 15.27102 0.27963 5 1.4329 0.6744 0.88724 0.00283 15.73317 0.27646 - 1.5764 0.75313 0.9337 0.00275 15.30252 0.27964 1114 mat

Critical slope for given canal for Qol n Q.ol * yy2.c0 A yy2.c0 R (23 /^* m 13 /^s / (* / (2^0.002735

for

BW 4 m *

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