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Water hammer, also known as hydraulic shock or surge, is a sudden pressure increase or shockwave that occurs within a fluid-carrying pipe system when there is a rapid change in flow velocity. It happens due to the inertia of the moving fluid and the compressibility of water. The phenomenon often results from abrupt valve closures (including check valves), pump starts and stops, or sudden changes in flow direction.

When a flow is suddenly halted or redirected, the kinetic energy of the moving water transforms into pressure energy, causing pressure spikes that can damage pipes, valves, and other system components. The resulting shockwave travels through the piping system, creating a distinct banging noise.
The pressure rise that will happen due to water hammer when there is a sudden stop of the flow (very quick valve or check valve closure for instance) can be calculated thanks to the following formula [Hall] :
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1. Pressure drop
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4. Churchill equation
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ΔPh = ρ * cs * u
With :
ΔPh = increase of pressure due to water hammer (Pa)
ρ = fluid density (kg/m3)
cs = velocity of sound in the fluid (m/s) = 1439 m/s for
water (change if another fluid)
u = fluid velocity (m/s)
It's important to note that water hammer can have serious consequences, including pipe bursts, equipment damage, and system failures.
Note the formula above assumes that the velocity of the fluid will go to 0 *(hence expressing with u), other sources are considering a difference in velocity (Δu) that could be useful for change of directions for instance.
Another formula is proposed when slow closure of a valve is happening :
P2 = 2 * ρ * L * u / t + P1
With :
P2 = pressure reached during water hammer phenomena (Pa)
P1 = inlet pressure when the closure happens (Pa)
ρ = fluid density (kg/m3)
u = fluid velocity (m/s)
L = upstream pipe length (m)
t = valve closure time (s)
This formula is approximate [Perry], apply safety factors.
The following designn considerations can help to prevent the water hammer to happen :
You can access to an Excel calculation tool in order to calculate
the pressure rise in a pipe when the phenomenon of water hammer
happens : Water
Hammer Pressure rise Excel calculation
tool (click here)
Warning : this calculator is provided to illustrate the concepts mentioned in this webpage, it is not intended for detail design. It is not a commercial product, no guarantee is given on the results. Please consult a reputable designer for all detail design you may need.