Question #179417

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

Expert's answer

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

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