Question

Define the hydraulic radius in terms of wetted perimeter and area.

• A. $R = \frac{P}{A}$
• B. $R = \frac{A}{P}$
• C. $R = A \times P$
• D. $R = \frac{1}{AP}$

Hint:

Remember: Hydraulic radius = Area / Wetted perimeter.

Answer 1

The Correct Option is B

Concept: Hydraulic radius is an important parameter in fluid flow, especially in open channel flow.
Step 1: Definition.
Hydraulic radius is defined as the ratio of the cross-sectional area of flow to the wetted perimeter.
Step 2: Formula.
\[ R = \frac{A}{P} \] where $A$ is the area of flow and $P$ is the wetted perimeter.
Step 3: Physical meaning.
It represents the efficiency of the channel in conveying water; larger $R$ means less frictional resistance.
Step 4: Evaluating the options.

• $R = \frac{P}{A}$ $\rightarrow$ Incorrect
• $R = \frac{A}{P}$ $\rightarrow$ Correct
• $R = A \times P$ $\rightarrow$ Incorrect
• $R = \frac{1}{AP}$ $\rightarrow$ Incorrect

Step 5: Conclusion.
Thus, hydraulic radius is given by $R = \frac{A}{P}$.