Question

A 500 mm-diameter concrete pipe is laid on a slope of 1m per 500m and is required to carry water at the rate of 0.04m^3/s.Determine the normal depth of flow.Use roughness coefficient n=0.013

Answer 1

Q= flow rate = 0.04 $m^3/s$

R= hydraulic radius

s= slope ($\frac{1}{500})$

n= manning's coefficient of roughness= 0.013

$R= \frac{A}{p} = \frac{weted area}{weted perimeter} = \frac{0.5h^2}{3.412h}$

$Q=VA$

$V= \frac{1}{(n)} (R^ \frac{2}{3}S ^ \frac{1}{2})$

$Q= \frac{1}{(n)} (\frac{0.5h^2}{3.412h})^\frac{2}{3} \times (\frac{1}{500})^\frac{1}{2} \times 0.5h^2$

$0.04= \frac{1}{(0.013)} (\frac{0.5h^2}{3.412h})^\frac{2}{3} \times (\frac{1}{500})^\frac{1}{2} \times 0.5h^2$

solving for h,

h , normal depth is equal to, h= 0.1854 m