24eaded1-b1b8-4333-9d6b-5fe8000e3271 458 5 7 decimal

GVF: STANDARD STEP EXAMPLE - Open Channel Flow - 2nd Ed. - Haniff Chaudhry, page 164

]]>

Image

0.00000379 0.00000828 + 2 / 0.000006035

5.0046 0.00583 + 5.0104

5.0104 0.01670 + 5.027

1. DATA

]]>

Q 30 m 3^s / * :

S 0.001 :

B 10 m * :

n 0.013 :

SS 2 :

y.1 5 m * :

z.1 0 :

x 0100020003000400051 mat m * :

percent (#1) ％ 1100 / :

y.start 5 m * :

2. GENERAL EQUATIONS USED IN THE ANALYSIS

]]>

Wetted Perimeter y P B 2 y * (1 SS 2^+ sqrt * + :

Hydraulic radius y R y A y P / :

Area y A y B y SS * + (* :

Velocity y V Q y A / :

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

Friction slope y Sf y V n * y R (23 /^m 13 /^s / * / (2^:

y Vh y V (2^2 g.e * / :

Total Energy y z H z y + y V (2^2 g.e * / + :

<---- Eqn 1

]]>

3. SAMPLE CALCULATIONS

]]>

ΔXX 01000 m * 1000 m * 1000 m * 1000 m * 51 mat :

Z 01 m * 2 m * 3 m * 4 m * 51 mat :

Section 1-Known y.1 5 m *

y.1 Z 1 el H 5.0046 m *

y.1 Sf 0.000003379

----------------------------------------------------------------------------------------------

Section 2-Guess depth: First start with "ystart". 
Then copy y_2_calc value here repeatedly until both are equal y.2 4.00157 m * :

y.2 Z 2 el H 5.01041 m *

y.2 Sf 0.0000083

Sf.avg_2 y.1 Sf y.2 Sf + 2 / : 0.00000583

h.f2 ΔXX 2 el Sf.avg_2 * : 0.00583 m *

Calculated value H.2 y.1 Z 1 el H h.f2 + : 5.01041 m *

Guess Value y.2 Z 2 el H 5.01041 m *

Compare this with y2 y.2_calc H.2 Z 2 el - y.2 Vh - : 4.00157 m *

y.2 y.2_calc - abs 0.0001 m * ≤ OK black light green 1 3 mat Retry red yellow 1 3 mat if

----------------------------------------------------------------------------------------------

Section 3-Guess depth: First start with "ystart". 
Then copy y_3_calc value here repeatedly until both are equal y.3 3.00732 m * :

y.3 Z 3 el H 5.0271 m *

y.3 Sf 0.0000251

Sf.avg_3 y.2 Sf y.3 Sf + 2 / : 0.00001669

h.f3 ΔXX 3 el Sf.avg_3 * : 0.01669 m *

Calculated value H.3 y.2 Z 2 el H h.f3 + : 5.0271 m *

compare with y.3 Z 3 el H 5.0271 m *

Compare this with y3 y.3_calc H.3 Z 3 el - y.3 Vh - : 3.00732 m *

y.3 y.3_calc - abs 0.0001 m * ≤ OK black light green 1 3 mat Retry red yellow 1 3 mat if

Main Program: The basic logic is balancing Total Energy (TE) between 2 sections by repeated iterations

]]>

TE is a function of z & y

]]>

xx sl StdStep j 1 xx rows range j 1 ≡ Δxx j el 0 : zz j el 0 : yy j el y.start : TE1 j el yy j el zz j el H : TE2 j el TE1 j el : sf j el yy j el Sf : sf_avg j el 0 : hf j el Δxx j el sf_avg j el * : ar j el yy j el A : pr j el yy j el P : hr j el yy j el R : vv j el yy j el V : vh j el yy j el Vh : dif j el 0 : NN j el 0 : 151 line Δxx j el xx j el xx j 1 - el - : zz j el zz 1 el xx j el sl * + : NN j el 0 : yg y.start : TE1 j el yg zz j el H eval : sf j el yg Sf eval : sf_avg j el 0.5 sf j 1 - el sf j el + (* eval : hf j el Δxx j el sf_avg j el * eval : TE2 j el TE2 j 1 - el hf j el + eval : ΔTE 0.0001 m * : TE1 j el TE2 j el - abs ΔTE ≥ yg TE2 j el zz j el - yg Vh - eval : sf j el yg Sf eval : sf_avg j el 0.5 sf j 1 - el sf j el + (* eval : hf j el Δxx j el sf_avg j el * eval : TE2 j el TE2 j 1 - el hf j el + eval : TE1 j el yg zz j el H eval : dif j el TE1 j el TE2 j el - : NN j el NN j el 1 + : 81 line while yy j el yg : 121 line if ar j el yy j el A : pr j el yy j el P : hr j el yy j el R : vv j el yy j el V : vh j el yy j el Vh : 61 line for xx m / - yy m / ar m 2^/ pr m / hr m / vv m s / / vh m / zz m / TE1 m / Δxx m / - hf m / TE2 m / dif NN augment eval 21 line :

TE y z H ≡ z y + y V (2^2 g.e * / + ≡

See Eqn 1

]]>

Calculations at control point

1. y_start known

2. TE1 = TE2 Total Energy using y_start

3. Similarly, calculate other initial canal parameters

4. dif = 0 Diffrence in TE at start

5. NN = 0 Number of iterations at start

]]>

<--- yg = y_start

]]>

Guess Depth to start first iteration

]]>

<--- TE1 = Total Energy (TE) corresponding to 'yg' using Eqn 1

]]>

<--- sf = Friction slope corresponding to 'yg'

]]>

<--- sf_avg = Avg. Friction slope between two sections

]]>

<--- hf = Head loss due to friction between two stations

]]>

<--- TE2 = TE after deducting "hf" from TE in previous station

]]>

<--- ΔTE = Tolerance for energy balancing in iterations

]]>

<--- Start of 'while' loop

]]>

y TE z - V 2^2 g.e * / - ≡

<--- 'yg' re-calculated from TE2 within 'while' loop, from Eqn 1

]]>

By re-calculating 'yg', Iteration continues while abs(TE2-TE1) ≥ ΔTE

]]>

<--- yy = final 'yg'

]]>

Calculation of other final canal parameters

]]>

<--- Resulting matrix

]]>

title x y A P R V Vh Z H Δx hf H_Calc Dif NN augment :

Image

Text book solution

]]>

Ans x S StdStep :

Ans title Ans stack :

NN = Number of iterations

]]>

NOTE:

The "while loop" solves by repeated iterations, and hence, trial calculations are not shown.

]]>

Ans x y A P R V Vh Z H Δx hf H_Calc Dif NN 05100 32.361 3.09 0.3 0.005 0 5.005 00 5.005 001000 - 4.002 72.041 27.896 2.583 0.416 0.009 1 5.01 1000 - 0.006 5.01 0 m * 22000 - 3.007 48.161 23.449 2.054 0.623 0.02 2 5.027 1000 - 0.017 5.027 0 m * 23000 - 2.038 28.682 19.113 1.501 1.046 0.056 3 5.093 1000 - 0.066 5.093 0 m * 24000 - 1.263 15.825 15.65 1.011 1.896 0.183 4 5.447 1000 - 0.353 5.446 0 m * 12614 mat