What this calculator does
A valve that stops a moving column of liquid has to absorb its momentum somewhere, and it goes into pressure. Whether you face the full surge depends on one comparison only: is the closure faster than the pressure wave can travel the pipe and come back? This tool makes that comparison and gives the governing peak.
How to use it
- Enter the velocity the liquid is actually moving before the event.
- Enter the length of pipe the pressure wave has to travel.
- Enter the pressure-wave speed for your pipe material and installation — this is the value you must confirm, not one this tool supplies.
- Enter how fast the valve closes, or how quickly the pump trips.
Governing formula
ΔP = ρ·a·ΔV (when t ≤ 2L/a) Where:
-
ΔP= Peak pressure rise, bar -
ρ= Liquid density, kg/m³ -
a= Pressure-wave speed, m/s -
ΔV= Velocity change, m/s -
L= Pipe length the wave travels, m
Derived Equations:
t_c = 2L/a ΔP = 2ρLΔV/t Worked example — 200 m of pipe closed in 0.2 s
The figures below were produced by running this page's own engine with the example inputs (Initial velocity (m/s), Final velocity (m/s), Pipe length the wave travels (m), Pressure-wave speed (m/s), Liquid density (kg/m³), Valve closure time (s)). If the calculator returns something different for the same numbers, that is a bug, not a rounding difference.
| Governing surge pressure | 20 bar |
|---|---|
| Regime that applies | rapid |
| Critical closure time (2L/a) | 0.4 s |
| Joukowsky ceiling (rapid closure) | 20 bar |
| Slow-closure peak (line momentum) | 40 bar |
- The wave round trip is 2 × 200 / 1000 = 0.40 s, and the valve closes in 0.20 s.
- The closure is faster than the round trip, so the full Joukowsky peak applies.
- ρ·a·ΔV = 1000 × 1000 × 2 = 20 bar of surge pressure.
Assumptions & limitations
Engineering calculation. Rapid-closure (Joukowsky) and slow-closure (line-momentum) surge regimes, selected by the closure time against the pressure-wave round trip.
- The wave speed is entered by you. It is material- and installation-dependent; this tool holds no pipe-property table and selects nothing.
- Rigid-conduit analysis of the classic two-regime case. Column separation, vapour cavity collapse, distributed networks, air-valve cavity action, trapped-air pockets and pump-trip reverse rotation are not modelled.
- A single straight run is assumed. Branches, elbows, tanks and a second wave path change the answer.
- The result is a peak pressure rise, not a full hydraulic transient simulation, and not a pipe-schedule or flange-rating selection.
This tool supports professional engineering work; it does not replace a sealed design. Confirm every result against the applicable standard and a licensed engineer before it is built.
References & standards
- Joukowsky’s water-hammer equation, the classical rapid-closure result.
- Michaud’s line-momentum form for a closure slower than the wave round trip.