Water Hammer Calculator: Pressure Surge from Valve Closure

Find how much the pressure jumps when a valve closes or a pump stops, and how slowly the valve must close to keep the peak under the rating of the pipe.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

When a liquid moving in a pipe is stopped suddenly, its momentum turns into a pressure wave that runs along the pipe. The pressure jump is the density times the wave speed times the change in speed (the Joukowsky equation).

The wave speed depends on the liquid and on how stiff the pipe is. It is about 1200 to 1400 m/s for water in steel pipe and far lower in plastic pipe. The wave runs to the end of the pipe and back in 2L over a, and a valve that closes in less than that time gives the full surge.

A slower closing lets the relief from the far end return before the valve is shut, so the surge is smaller. For a slow closing the surge is about twice the density times the length times the speed change, divided by the closing time.

Formulas used

  • a = \sqrt{\dfrac{K/\rho}{1 + KD/(Ee)}}
  • \Delta p = \rho\,a\,\Delta V
  • T_c = \dfrac{2L}{a}
  • \Delta p \approx \dfrac{2\rho L\Delta V}{t_c}

Worked example

With the default numbers in the calculator above:

  1. Speed of the pressure wave in this pipe: 1344.21 m/s (1484.73 m/s in the liquid alone)
  2. Time for the wave to run to the end of the pipe and back: 0.30 s
  3. Is the closure fast or slow?: rapid: the full surge develops
  4. Full (Joukowsky) surge for an instant stop: 26.83 bar (2683.04 kPa)
  5. Surge as a head of liquid: 274.14 m
  6. Peak pressure in the pipe: 32.83 bar
  7. Hoop stress in the pipe wall at the peak: 32.83 MPa
  8. Closing time needed to keep the peak under the rating: 0.80 s

Change the numbers in the calculator to see the full working, every step, for your own case.

A second worked example

A different case, with these numbers: Time the valve takes to close 1.5 s.

  1. Speed of the pressure wave in this pipe: 1344.21 m/s (1484.73 m/s in the liquid alone)
  2. Time for the wave to run to the end of the pipe and back: 0.30 s
  3. Is the closure fast or slow?: slow: the surge is reduced
  4. Full (Joukowsky) surge for an instant stop: 26.83 bar (2683.04 kPa)
  5. Surge for a slow closing of this time: 5.32 bar
  6. Surge as a head of liquid: 54.38 m
  7. Peak pressure in the pipe: 11.32 bar
  8. Hoop stress in the pipe wall at the peak: 11.32 MPa
  9. Closing time needed to keep the peak under the rating: 0.80 s

Common questions

Why should a valve be opened slowly?

Opening or closing quickly changes the flow quickly, which gives a pressure surge. A slow movement spreads the change over more time and gives a much smaller surge.

How do I reduce water hammer?

Close valves slowly, keep the liquid speed low, fit a surge vessel or a relief valve, use pump flywheels or soft-start drives, and avoid air pockets.

Does plastic pipe have less water hammer?

The surge is lower because the wave is slower, but plastic pipe is also weaker, so the margin is not always better.

Related calculators

Got a question about this? Ask an engineering question and get a plain-language answer with references.

Further reading: Standard fluid mechanics and pipeline texts (Joukowsky and Allievi surge). A surge analysis for a large or critical line should be done by a qualified engineer.

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