Water Hammer Calculator (Joukowsky Equation)

How to use the water hammer calculator

Enter the liquid density, the pressure wave speed for your pipe material, the velocity change (usually the full flow velocity for a sudden stop) and the pipe length to the nearest reservoir or open end. You get the surge pressure, the surge head and the critical closure time.

Joukowsky equation

ΔP = ρ × a × Δv  ·  ΔH = a × Δv ÷ g  ·  t_c = 2L ÷ a

Surge for water in steel pipe (a = 1,200 m/s)

Velocity stopped	Surge pressure	Surge head
0.5 m/s	6.0 bar	61 m
1 m/s	12.0 bar	122 m
1.5 m/s	18.0 bar	184 m
2 m/s	24.0 bar	245 m
3 m/s	36.0 bar	367 m

Typical wave speeds (water)

Pipe	Wave speed
Steel	1,000–1,400 m/s
Ductile iron	1,000–1,300 m/s
Concrete	900–1,200 m/s
PVC	300–500 m/s
HDPE	200–400 m/s

Flexible plastic pipes have lower wave speeds, so surges are smaller.

Protecting instruments

Pressure gauges and transmitters on lines prone to surges need snubbers, liquid-filled gauges or pulsation dampers, and a pressure rating above the surge pressure.

Frequently asked questions

What is the Joukowsky equation?

ΔP = ρ × a × Δv — the pressure rise when flow velocity changes suddenly, where ρ is density, a the pressure wave speed and Δv the velocity change.

How big can water hammer be?

Stopping water flowing at 2 m/s in steel pipe causes a surge of about 24 bar — often more than the operating pressure.

What is the critical closure time?

2L ÷ a, the time for a pressure wave to travel to the reservoir and back. Closing faster than this gives the full Joukowsky surge; closing slower reduces it.

How is water hammer prevented?

Slow-closing valves, surge tanks, air vessels, surge relief valves, VFD ramp-down of pumps and lower design velocities.

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