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