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

Head loss in 100 m length equals 1.00 m.

Step-by-step explanation:

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

`Q=(1)/(n)(A^(5/3))/(P^(2/3))S_(f)^(1/2)`

For a asphalt rectangular channel we have

Area of flow =
`3.0* 2.0 = 6m^(2)`

Wetted Perimeter =
`3.0+2* 2.0=7.0m`

manning's roughness coefficient = 0.016

Applying values in the above equation we get

`33.84=(1)/(0.016)* (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)=(H_(L))/(L)\\\\\therefore H_(l)=0.01* 100m=1.00m`