Waterhammer in A Composite Pipeline System

The relation between periodic time of pressure vibration and maximum pressure rise

Abstract

In a continuation of a previous paper, a waterhammer theory is developed from the viewpoint of the vibration model, in which waterhammer phenomena are treated as a phase of waterpressure vibration in pipeline systems. In this paper, the following equation is introduced in order to evaluate maximum pressure rise with vibration energy and periodic time.
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Where X_max is maximum pressure rise, V is initial mean velocity, g is gravity accelaration, ΔH ismean head loss from friction, and a_m is equivalent elastic wave velocity.
a_m of the composite pipeline system is represented by the following equation.
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or
a_m=4L/T
Where a_m is physical mean velocity, (f·f') is coefficient, L is pipeline length, and T is periodic time.
It is confirmed with numerical simulation that this equation is a better approximation than the, traditional theory based on elastic wave propagation.
In particular this relationship is very useful when we want to evaluate the maximum pressure rise in situ.