Rapid-change water-hammer estimate

Estimate the Joukowsky pressure rise from a velocity reduction and compare closure time with a wave round trip.

How this calculation works

Use this tool as a rapid-change reference rather than a complete pressure-transient prediction. Enter liquid density, wave speed for the actual liquid-and-pipe system, the magnitude of the velocity reduction, the distance to the relevant reflecting boundary and effective flow-change time. Density times wave speed times velocity change gives the Joukowsky pressure rise. Dividing the corresponding pressure by liquid weight per volume gives surge head. The separate round-trip time is twice the reflection length divided by wave speed. Comparing flow-change time with this travel time indicates whether the simple rapid-change assumption is applicable. A slower change requires a different transient analysis. Reflections, column separation, entrained gas and system interactions can change the outcome, so the calculated rise is not a guaranteed maximum or a pipe-rating check.

Inputs and units

Liquid density (kg/m³)
Pressure-wave speed (m/s): Wave speed in the actual liquid and elastic pipe system, not simply bulk-liquid sound speed.
Velocity-reduction magnitude (m/s)
Pipe length to reflecting boundary (m)
Effective flow-change time (s)

Method and formula

Rapid-change Δp = ρ a Δv; surge head = a Δv/g; wave round-trip time = 2L/a. Divide pressure in Pa by 1000 for kPa; g = 9.80665 m/s².

Worked example

Example inputs

Liquid density: 1000 kg/m³
Pressure-wave speed: 1000 m/s
Velocity-reduction magnitude: 1 m/s
Pipe length to reflecting boundary: 100 m
Effective flow-change time: 0.1 s

Calculation steps

Rapid-change reference rise = 1000 × 1000 × 1 = 1000000 Pa = 1000 kPa.
Equivalent surge head = 1000 × 1 / 9.80665 ≈ 101.971621 m.
Wave round-trip time = 2 × 100 / 1000 = 0.2 s. The entered 0.1 s flow-change time is shorter than this round trip.

Example results

Joukowsky rapid-change reference rise: 1000 kPa
Equivalent surge head: 101.9716213 m
Wave round-trip time: 0.2 s

Example notes

Flow-change time is within one wave round trip, consistent with the simple rapid-change assumption.
Wave reflections and system interactions can amplify or alter pressure; this is not a maximum-pressure guarantee.

Assumptions

One-dimensional elastic-wave estimate for a sudden specified velocity reduction.
User supplies system wave speed and the relevant reflection length.

Limitations

Not a full transient solver or a guaranteed upper bound; excludes friction history, complex reflections, column separation and entrained gas.
Does not determine pipe pressure rating, surge protection or safe operating speed.
For slow closure, actual valve motion and the full system require separate transient analysis.
Preliminary educational check; verify inputs and equipment data before design or operation.

Sources

KSB: Surge Pressure planning brochure: Pages 9–12: reflection time 2L/a, Joukowsky equations 1–2, validity and line-packing limitations