#618 Water flows down a wide and shallow rectangular

Water flows down a wide and shallow rectangular - civil engineering

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Free Chegg Question

Water flows down a wide and shallow rectangular channel of concrete (n=0.015) laid on a slope of 0.004. find the depth and the rate of flow in SI units for critical conditons in the channel

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Free Chegg Answer 1

For thin film flow, the critical slope is defined as:

S_c = (g*n²)/(y_c)^1/3

where:

g = gravity = 9.81 m/s²

n = 0.015

y_c = critical depth

Rearranging the equation:

y_c = [(g*n²)/S_c]³

substituting in values and solving:

y_c = [(9.81*0.015²)/0.004]³ --> y_c = 0.168 m

Next note the critical velocity is found by the following relationship:

(V_c²/g) = (A_c/T_c) --> V_c = sqrt[(A_c/T_c)*g]

where:

T_c = the top width = b

A_c = flow area = b*y_c = 0.168*b

V_c = critical velocity

substituting in values and solving:

V_c = sqrt[(0.168*b/b)*9.81] = sqrt(0.168*9.81) --> V_c = 1.284 m/s