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

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

${R}_{H}=\frac{{A}_{W}}{{P}_{W}}$

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

Here,

B = Width = 6 m

y = Depth = 0.80 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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