Question

Calculate the hydraulic radius of a channel with a wetted perimeter of 8m, a width of 6m, and the following depths taken...


Calculate the hydraulic radius of a channel with a wetted perimeter of 8m, a width of 6m, and the following depths taken on a transect: .80m, .65m, .70m, .72m, .10m, .05m, 1.55m, 1.04m, 1.10m, .80m, .10m, .15m

Answer

Given:-

The wetted perimeter of the channel = 8 m 

The width of the channel = 6 m 

To determine:-

The hydraulic radius of a channel for different depths

Considering the channel section as a rectangular channel section 

So,

The hydraulic radius of a rectangular channel section can be calculated using the formula

RH=AWPW

Here,

RH = Hydraulic radius 

AW = Wetted cross-sectional area of the channel

PW = Wetted perimeter

Now,

Putting, the width of the channel = 6 m and wetted perimeter of the channel = 8 m 

For,

a) Depth of water = 0.80 m 

The hydraulic radius will be 

RH=AWPWPutting, Aw=B×y

Here,

B = Width = 6 m

y = Depth = 0.80 m 

RH=6×0.808RH=4.88RH=0.6 m

Similarly,

S.No Width Depth Wetted perimeter Hydraulic radius
a) 6 m 0.80 m 8 m 0.6 m
b) 6 m 0.65m 8 m 0.487 m
c) 6 m 0.70 m 8 m 0.525 m
d) 6 m 0.72 m 8 m 0.54 m
e) 6 m 0.10 m 8 m 0.075 m
f) 6 m 0.05 m  8 m 0.0375 m
g) 6 m 1.55 m  8 m 1.1625 m
h) 6 m 1.04 m  8 m 0.78 m 
i) 6 m 1.10 m  8 m 0.825
j) 6 m 0.80 m  8 m 0.6 m
k) 6 m 0.10 m  8 m 0.075 m
l) 6 m 0.15m 8 m 0.1125 m

Hence,

The hydraulic radius of a channel for different depths are:-

Depth Hydraulic radius
0.80 m 0.6 m
0.65m 0.487 m
0.70 m 0.525 m
0.72 m 0.54 m
0.10 m 0.075 m
0.05 m  0.0375 m
1.55 m  1.1625 m
1.04 m  0.78 m 
1.10 m  0.825
0.80 m  0.6 m
0.10 m  0.075 m
0.15m 0.1125 m
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