Topic: Fluid Mechanics
The hydraulic diameter, $D_h$ of a rectangular duct with sides 'a' and 'b' is
- A. $D_h = \frac{4ab}{2a+b}$
- B. $D_h = \frac{2ab}{a+b}$
- C. $D_h = \frac{2ab}{2a+b}$
- D. $D_h = \frac{4ab}{a+b}$
Answer: B. $D_h = \frac{2ab}{a+b}$
Explanation: Hydraulic diameter is defined as $D_h = \frac{4A}{P}$, where $A$ is the cross-sectional area and $P$ is the wetted perimeter. For a rectangular duct, the area is $A = a \times b$ and the perimeter is $P = 2(a+b)$. Substituting these gives $D_h = \frac{4ab}{2(a+b)} = \frac{2ab}{a+b}$.