Question

An earthen trapezoidal channel (n = 0.025) has a bottom width of 5.0 m, side slopes of 1.5 horizontal: 1 vertical and a uniform flow depth of 1.10 m. In an economic study to remedy excessive seepage from the canal two proposals, (a) to line the sides only and, (b) to line the bed only are considered. If the lining is of smooth concrete (n = 0.012), calculate the equivalent roughness in the above two cases for a bottom slope of 0.005

Answer 1

Answer:

A. 0.020

B. 0.018

Explanation: check the attached file

Answer 2

Answer:

a. n=0.020  b. n=0.018

Explanation:

a.

Case 1: To line the sides only

n=(Σn₁¹°⁵P₁)^2/3/P^2/3

n = equivalent roughness

n₁=corresponding roughness coefficients

P=length

At the bed: n₁=0.025 and P₁=5m

At the sides: n₂=0.012 and P₂= 2*1.1*√1+1.5²=2.2*1.8=3.96m

P = P₁+P₂=8.96m

Equivalent roughness, n = [5*(0.025)^1.5+3.96*(0.012)^1.5]^2/3/(8.96)^2/3

n= [(5*0.00395)+(3.96*0.0013)]^2/3/4.317

n=0.0249^2/3/4.317

n=0.0842/4.317

n=0.0195

n=0.020

b.

Case 2: To line the bed only

P₁=5m   n₁=0.012

P₂=3.96 n₂=0.025

P=8.96

Equivalent roughness n= [5*(0.012)^1.5+3.96*(0.025)^1.5]^2/3/(8.96)^2/3

n=[(5*0.0013)+(3.96*0.00395)]^2/3/4.317

n=0.0221^2/3/4.317

n=0.078/4.317

n=0.018