Water Hammer

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A) The sudden closure of valve at the end of a pipeline cause sudden change in the water velocity which in turn creates a phenomenon called water hammer. The water in motion is forced to stop or change direction suddenly (momentum change) and a pressure wave propagates in the pipe. It's also called hydraulic shock. The effect of this event can be effectively multiplied many times by the geometry of a piping system if the pressure wave is allowed to reflect, or bounce, back and forth within the system. A single valve closure can generate multiple positive and negative pressure surges, for seconds afterwards. This pressure wave can cause major problems, from noise and vibration to pipe collapse. It is possible to reduce the effects of the water hammer pulses with accumulators and other features.

Here is a brief description of the Pressure and velocity waves in a single-conduit, frictionless pipeline following its sudden closure. The areas of steady-state pressure head are shaded medium dark, those of increased pressure dark, and those of reduced pressure light. The expansion and contraction of the pipeline as a result of rising and falling pressure levels, respectively, are shown:

1. For t = 0, the pressure profile is steady, which is shown by the pressure head curve running horizontally because of the assumed lack of friction. Under steady-state conditions, the flow velocity is 0.

2. The sudden closure of the gate valve at the downstream end of the pipeline causes a pulse of high pressure _h; and the pipe wall is stretched. The pressure wave generated runs in the opposite direction to the steady-state direction of the flow at the speed of sound and is accompanied by a reduction of the flow velocity to v = 0 in the high pressure zone. The process takes place in a period of time 0 < t < 1/2 Tr, where Tr is the amount of time needed by the pressure wave to travel up and down the entire length of the pipeline. The important parameter Tr is the reflection time of the pipe. It has a value of 2L/a.

3. At t = 1/2Tr the pressure wave has arrived at the reservoir. As the reservoir pressure p = constant, there is an unbalanced condition at this point. With a change of sign, the pressure wave is reflected in the opposite direction. The flow velocity changes sign and is now headed in the direction of the reservoir.

4. A relief wave with a head of -Δh travels downstream towards the gate valve and reaches it at a time t = Tr. It is accompanied by a change of velocity to the value -V0.

5. Upon arrival at the closed gate valve, the velocity changes from -v0 to v = 0. This causes a sudden negative change in pressure of -_h.

6. The low pressure wave -Δh travels upstream to the reservoir in a time Tr < t < 3/2Tr, and at the same time, v adopts the value v = 0.

7. The reservoir is reached in a time t = 3/2Tr, and the pressure resumes the reservoir’s pressure head.

8. In a period of time 3/2Tr < t < 2Tr , the wave of increased pressure originating from the reservoir runs back to the gate valve and v once again adopts the value v0.

9. At t = 2Tr , conditions are exactly the same as at the instant of closure t = 0, and the whole process starts over again.

B) The sudden closure of a valve in a pipeline causes the mass inertia of the liquid column to exert a force on the valve’s shut-off element. This causes the pressure on the upstream side of the valve to increase; on the downstream side of the valve the pressure decreases. As an example: for a DN 200 pipe, L = 900 m, v = 3 m/s, the volume of water in the pipeline is calculated by:

This is more or less the same as the weight of a truck; v = 3 m/s corresponds to 11 km/h. In other words, if the flow is suddenly stopped, our truck – to put it in less abstract terms – runs into a wall (closed valve) at 11 km/h (water mass inside the pipe). In terms of our pipeline, this means that the sequence of...
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