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: Formula Identification.
The head loss associated with a sudden pipe enlargement is expressed as: \[h_L = \frac{(V_1 - V_2)^2}{2g}.\]

Step 2: Derivation Rationale.
This formula is derived by applying Bernoulli's equation and accounting for the energy dissipation from flow mixing at the expansion point.

Step 3: Final Statement.
Consequently, the accurate formula for head loss in a sudden enlargement is $\dfrac{(V_1 - V_2)^2}{2g}$.