In a long pipe, when the flowing water is suddenly brought to rest by closing the valve or by any similar cause, there will be a sudden rise in pressure. The magnitude of pressure rise depends on
- Athe speed at which the valve is opened
- Bthe velocity of flowCorrect
- Cthe diameter of the pipe
- Dthe thickness of the pipe wall
Solution
Concept
Factors governing water-hammer pressure
Formula
Δp = ρ c V (instantaneous closure)
Step-by-step solution
1. The pressure rise is proportional to the velocity brought to rest. 2. It also depends on the speed at which the valve is CLOSED and on the elasticity of the pipe; the pressure rise is largest for sudden closure.
Explanation
The most direct dependence is on the velocity of the water that is stopped: the greater the velocity of flow, the greater the pressure rise (Δp = ρcV).
Why the other options are wrong
The speed of opening the valve is irrelevant to the closure surge. Diameter and wall thickness only modify the wave speed.
Shortcut
Δp ∝ V.
Common mistake
Choosing the opening speed.
Correct answer: B) the velocity of flow