Slow Valve Closure (Allievi Formula) Water Hammer Calculator

Determine hydraulic head rise (ΔH) and transient peak pressure for slow valve closures where closure time exceeds the pipe reflection period (tc > 2L/a).

Conduit & Valve Deceleration

Pipeline Length L (m):

Steady State Head H₀ (m):

Initial Flow Velocity v₀ (m/s):

Wave Speed a (m/s):

Valve Closure Time t_c (s):

Closure Characteristic:

Slow Closure Head Rise

Max Transient Head H_max:

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Surge Head Rise (ΔH):

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Peak Transient Pressure:

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Reflection Period (2L/a):

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Closure Safety Assessment:

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Frequently Asked Questions

What is the Allievi formula for slow valve closure?

Lorenzo Allievi demonstrated that when closure time tc > 2L/a, negative reflected relief waves return to the valve before it fully shuts, reducing the pressure spike to approximately ΔH ≈ (2·L·v₀)/(g·tc).

Why do butterfly and gate valves cause unexpected water hammer during slow closures?

Quarter-turn valves and gate valves do not reduce flow linearly with angle. Flow barely drops over the first 70% of closure, then abruptly chokes in the final 15% of travel, acting like a sudden rapid closure.

What is two-stage valve closing and why is it effective?

Two-stage actuation quickly closes the valve from 100% open down to ~20% open in 5–10 seconds, then crawls through the remaining 20% over 30–60 seconds. This avoids shockwaves while rapidly minimizing reverse flow.