Question

A 3.0-m wide rectangular asphalt channel discharges 33.84 m^3/s of water with a depth of 2.0 m. What is the head loss in 100 m length of channel?

Answer 1

Answer:

Head loss in 100 m length equals 1.00 m.

Explanation:

The head loss in an open channel is calculated using manning's equation as follows

$Q=\frac{1}{n}\frac{A^{5/3}}{P^{2/3}}S_{f}^{1/2}$

For a asphalt rectangular channel we have

Area of flow = $3.0\times 2.0 = 6m^{2}$

Wetted Perimeter = $3.0+2\times 2.0=7.0m$

manning's roughness coefficient = 0.016

Applying values in the above equation we get

$33.84=\frac{1}{0.016}\times \frac{6^{5/3}}{7^{2/3}}S_{f}^{1/2}\\\\\therefore S^{1/2}_{f}=0.1\\\\\therefore S_{f}=0.01$

Now we know that

$S_{f}=\frac{H_{L}}{L}\\\\\therefore H_{l}=0.01\times 100m=1.00m$