Question

Hydraulic radius in the Manning's equation is given as

• A. Wetted perimeter/Cross-sectional area
• B. Cross-sectional area/ Wetted perimeter
• C. Cross-sectional area/Depth of flow
• D. Cross-sectional area/Bottom width of channel

Hint:

Hydraulic Radius $R = \frac{\text{Area } (A)}{\text{Wetted Perimeter } (P)}$. Hydraulic Depth $D = \frac{\text{Area } (A)}{\text{Top Width } (T)}$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The hydraulic radius ($R$) is a geometric property of open channel and closed conduit cross-sections governing boundary shear friction resistance.
Key Formula or Approach:
\[ R = \frac{A}{P} \]
where \(A\) is flow cross-sectional area and \(P\) is wetted perimeter.

Step 2: Detailed Explanation:
By definition in fluid mechanics and open channel hydraulics:
The Hydraulic Radius (\(R\)) is defined as the cross-sectional flow area (\(A\)) divided by the wetted perimeter (\(P\), the boundary length in direct physical contact with the fluid):
\[ R = \frac{A}{P} \]
(Hydraulic depth \(D = A / T\), where \(T\) is top water surface width).

Step 3: Final Answer:
Hence, the hydraulic radius is Cross-sectional area/ Wetted perimeter, matching option (B).