# Water Hammer Effect

Water hammer is defined as the change in pressure, either above or below the normal pressure, caused by a variation of the flow rate in a pipe. The flow rate in the pipes can vary due to valve or pump operation either closure or opening. This results in pressure surges which are propagated along the pipeline from the source (valve). The velocity of the pressure wave is given by

where

C = velocity of pressure wave along pipe, ft /s (m/s)

E = modulus of elasticity of water, 43.2 x 106 lb/ft2 , (2.07 x 106 kPa)

If water is flowing with velocity V0 and the valve is closed suddenly then the adjacent layer to the valve stops. The previous layer exerts pressure on the first layer and compresses it similarly each layer is compressed by the following one.

The high pressure wave travels in the opposite direction of flow with velocity U or C and known as celerity generally for steel and iron pipes the celerity is 1300 m/s the high pressure also tries to expand the pipe.

The all kinetic energy is converted in to pressure head and the flow stops in the pipe. The pressure wave takes time “t = L/C” where L is the length of the pipe and C is the celerity of wave. When the pressure wave reaches at the reservoir causing imbalance of head the water from the pipe starts flowing backwards (fig d) and a low pressure wave travels to the valve the low pressure wave reaches the valve at time “t = 2L/C”. Due to negative pressure the pipe contracts and the water starts flowing towards valve. Low pressure wave reaches at reservoir at time “t = 3L/C”. The water again moves towards valve and high pressure develops at valve at “t = 4L/C”. The cycle repeats and the water finally comes to rest as the head loss due to frictional forces of the pipes.

The time “t = 2L/C” is known as reflection time i.e. time taken by a pressure wave to travel from the variant point (valve) to the reservoir and reflect back to the variant point OR the time taken by the water to flow in the pipe and back to the reservoir. If the opening or closing time of the valve is less than or equal to the reflection time then it is called rapid function of the valve. If the opening or closing time of the valve is more than reflection time then it is called gradual function of the valve. If the opening or closing time of the valve is much greater than reflection time then it is called slow function of the valve. If the opening or closing time of the valve is zero then it is called instantaneous function of the valve. Due to the water hammer pipe tries to expand when the pressure is positive in case of low elasticity and strength the pipe bursts (rupture) can occurs. On the contrary due to negative pressure the pipe sucks in and pitting (inside erosion of pipes) occurs and it is very common in hydro-electric power stations.

The rise in head due to instantaneous closure of the valve is given by
Where V0 is the initial velocity, C is celerity of pressure wave and ∆H is the rise in head. If V0 is 2 m/s the ∆H=(1300 x 3 / 9.81) = 265 m this can give he idea of potentially damaging effect of rapid closure of the valve. The pressure variation at the valve is as follows
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