Question

The loss of head due to sudden enlargement in a pipe is expressed by: (where symbols have their usual meanings)

• A. $\dfrac{(V_1^2 - V_2^2)}{2g}$
• B. $\dfrac{(V_1^2 - V_2^2)}{g}$
• C. $\dfrac{(V_1 - V_2)}{2g}$
• D. $\dfrac{(V_1 - V_2)^2}{2g}$

Hint:

For sudden enlargement, head loss is proportional to the square of velocity difference across the section.

Answer 1

The Correct Option is D

Step 1: Recall the formula.
The head loss due to sudden enlargement in a pipe is given by: \[ h_L = \frac{(V_1 - V_2)^2}{2g}. \]

Step 2: Explanation.
This is derived from applying Bernoulli's equation and considering the energy loss due to mixing of flows at the expansion section.

Step 3: Conclusion.
Thus, the correct formula for head loss due to sudden enlargement is $\dfrac{(V_1 - V_2)^2}{2g}$.