13. You may aknow about the recent hurricane and heavy rain that happened in Tex

Question

13. You may aknow about the recent hurricane and heavy rain that happened in Texas. We must calculate the capacity of water channels so that in case of heavy rain we can manage the water level properly. The following picture is a parabolic cross-section of a channel: Water surface Y-X We can calculate the discharge factor for flow through an open channel by the following equation: 2 3 As it can be seen in the previous picture, y is the maximum water depth to breadth of the channel at the top of the water. In both MATLAB and Excel determine the discharge factor for y started from 0.3 m to 1.02 meter with the steps of 0.04

Explanation / Answer

Given below is the matlab code for the question

format short
y = 0.3: 0.04: 1.02; %values of y from 0.3 to 1.02 in steps of 0.04

%calculate intermediate values so the formula looks simple
a = sqrt(16.*y.^2+1);
b = a + 4.* y;
c = 1 ./ (4.*y) .* log(b);
K = 1.2 ./ y .* (a+c) .^ (-2/3);

%make a table of y values and corresponding discharge factor K values
table = [y' K']

output
=====
table =

0.30000 2.22607
0.34000 1.91220
0.38000 1.66469
0.42000 1.46509
0.46000 1.30123
0.50000 1.16473
0.54000 1.04959
0.58000 0.95146
0.62000 0.86704
0.66000 0.79384
0.70000 0.72990
0.74000 0.67370
0.78000 0.62402
0.82000 0.57985
0.86000 0.54041
0.90000 0.50502
0.94000 0.47315
0.98000 0.44432
1.02000 0.41817

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