Water Hammer & Surge Tanks Notes

Last reviewed 16 Sept 2026 · 5 min read

What water hammer is

When a valve at the end of a long pipe is closed suddenly, the moving column of water is brought to rest. Its momentum is converted into a large pressure rise, which travels back up the pipe as a pressure wave, reflects at the reservoir and oscillates until damped by friction. The resulting knocking and pressure surge is called water hammer.

Water hammer also occurs on sudden pump stoppage (power failure) and on rapid load changes in hydropower penstocks.

Because the pressure rise can be many times the working pressure, it can burst pipes, damage valves and joints, and cause column separation (vapour cavities) on the negative-pressure phase.

Velocity of the pressure wave

FormulaCelerity of the pressure wave

Rigid pipe:

C = \frac{K}{ρ}

For water ( $K \approx 2.0$ – $2.2 \times 1 0^{9}$ N/m²): $C$ ≈ 1400–1480 m/s.

Elastic pipe (diameter $D$ , wall thickness $t$ , Young's modulus $E$ ):

C = \frac{K ^{'}}{ρ}, \frac{1}{K ^{'}} = \frac{1}{K} + \frac{D}{E t}

Pipe elasticity reduces the wave speed and hence the pressure rise.

Critical time of closure

The wave travels to the reservoir and back in

T_{c} = \frac{2 L}{C}

Gradual (slow) closure: closing time $t > 2 L / C$ — the reflected (relief) wave arrives before closure ends, limiting the rise.
Sudden (rapid) closure: $t \leq 2 L / C$ — full pressure rise develops.

Pressure rise

FormulaWater hammer pressure

Gradual closure (valve closed uniformly in time $t$ , incompressible column):

p = \frac{ρ L V}{t}

Sudden closure, rigid pipe (Joukowsky):

p = ρ V C = V K ρ

Head rise $h = \frac{C V}{g}$

Sudden closure, elastic pipe:

p = V \frac{ρ}{\frac{1}{K} + \frac{D}{E t}}

The sudden-closure pressure is independent of pipe length (as long as closure is faster than $2 L / C$ ).
Every 1 m/s of velocity destroyed suddenly causes roughly 140–150 m of head rise in a rigid water pipe — which is why valves in long mains close slowly.

Hoop stress in the wall from the total pressure (working + surge):

σ = \frac{p D}{2 t}

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Water Hammer & Surge Tanks