Q.96 A rectangular channel 3 m wide carries water at a depth of 1.2 m. The bed slope of the channel is 0.0025. Calculate the hydraulic radius of the channel.
- A0.627 m
- B0.667 mCorrect
- C0.637 m
- D0.617 m
Solution
Concept
Hydraulic radius is the flow area divided by the wetted perimeter.
Formula
R = A/P = b y / (b + 2y)
Step-by-step solution
1. Area A = b × y = 3 × 1.2 = 3.6 m². 2. Wetted perimeter P = b + 2y = 3 + 2 × 1.2 = 5.4 m. 3. R = A/P = 3.6/5.4 = 0.667 m.
Explanation
For a rectangular channel, the wetted perimeter is the bed width plus the two side depths. Dividing the area 3.6 m² by the perimeter 5.4 m gives R = 0.667 m. The bed slope is not needed to find R.
Why the other options are wrong
A (0.627 m), C (0.637 m) and D (0.617 m) do not match the correct ratio 3.6/5.4 = 0.667 m. They are distractor values.
Shortcut
R = by/(b + 2y) = 3.6/5.4 = 2/3 ≈ 0.667 m.
Common mistake
Adding the top width to the wetted perimeter, or using the bed slope in the calculation.
Correct answer: B) 0.667 m