The 'Joukowski' pressure rise due to water hammer when a valve closes instantaneously is:
Choose the correct answer
ΔP = ρ × V² / 2 (dynamic pressure only)
ΔP = ρ × c × ΔV — wave speed c (~1000 m/s for steel pipe) × density × velocity change; very large for fast closure
ΔP = c × V only (no density term)
ΔP is always less than 0.1 bar
Correct Answer
B. ΔP = ρ × c × ΔV — wave speed c (~1000 m/s for steel pipe) × density × velocity change; very large for fast closure
Why is this the answer?
Joukowski (1898): ΔP = ρ × c × ΔV where ρ = water density, c = wave speed = √(K/ρ) modified for pipe elasticity (typically c = 800–1200 m/s for steel pipes), ΔV = change in velocity at valve. For instantaneous closure from V to 0: ΔP = ρcV. Example: ρ=1000, c=1000 m/s, V=2 m/s → ΔP = 2×10⁶ Pa = 2 MPa. Wave travels upstream at speed c. Protection: slow valve closure (T > 2L/c — critical time), surge tanks, pressure relief valves.
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