Head loss due to sudden enlargement in a pipe: write the correct formula
A pipeline of diameter d₁ along AB carries liquid and is suddenly enlarged at B to diameter d₂ for the downstream length BC.
Assume steady incompressible flow with negligible losses other than the separation loss at the enlargement.
Choose the expression for the head loss across the sudden enlargement.
Difficulty: Easy
Correct Answer: h = (v₁ − v₂)² / (2g)
Explanation:
Concept/Approach
At a sudden enlargement, eddies form and energy is lost due to separation. The standard expression for the loss is based on the velocity change only.
Step-by-step Head loss across enlargement = Loss of velocity head due to separationhe = (v₁ − v₂)² / (2g)
Common pitfalls
Do not use (v₁² − v₂²)/(2g); that would be the net change in velocity head, not the separation loss.
Discussion & Comments