The head loss in a sudden expansion from 6 cm diameter pipe to 12 cm diameter pipe, in terms of velocity v₁ in the 6 cm diameter pipe is
- A(15/16) v₁²/2g
- B(3/4) v₁²/2g
- C(1/4) v₁²/2g
- D(9/16) v₁²/2gCorrect
Solution
Concept
Borda–Carnot loss
Formula
hL = (v₁ − v₂)²/2g
Step-by-step solution
1. v₂ = v₁ (A₁/A₂) = v₁ (6/12)² = v₁/4. 2. hL = (v₁ − v₁/4)²/2g = (3v₁/4)²/2g = (9/16) v₁²/2g.
Explanation
The loss is based on the relative velocity (v₁ − v₂).
Why the other options are wrong
Other options use wrong velocity differences.
Shortcut
hL = (1 − A₁/A₂)² v₁²/2g.
Common mistake
Using v₁²/2g × (1 − 1/2)².
Correct answer: D) (9/16) v₁²/2g