What is the normal depth in a 4.5-foot wide rectangular channel that conveys a discharge of 185 cfs and has a bed slope of 4% with a manning's roughness coefficient of 0.016?

normal depth is 2.7 ft

Explanation:

Given data

wide = 4.5 foot

discharge Q = 185 cfs

slope S = 4%

roughness coefficient n  = 0.016

To find out

What is the normal depth

solution

we consider height is d

so area A = 4.5 d

perimeter = 2d + 4.5

so Rn = 4.5d / 2d+4.5

and discharge formula is

Q = 1/n A (Rn)^2/3 ×(S)^1/2

185 = 1/0.016  × (4.5d)  (4.5d / 2d+4.5)^2/3 (0.04)^1/2

d² = 0.731 ( 2d + 4.5)

d² + 1.462 d + 3.289 = 0

solving this equation we get

d = 2.7 ft

normal depth is 2.7 ft

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