“P” is the additional pressure created by the shock wave, “a” is wave velocity, “V” is the velocity of the flowing water in the pipe in feet per second, “g” is the universal gravitational constant 32 ft/sec2, and 2.31 is the pressure conversion constant. Although the equation below does not take into account the effect of pipe diameter and elasticity, it will provide some insight as to the additional pressure that is created by a waterhammer pressure wave. The pressure created by this shock wave is directly proportional to both the wave velocity and the velocity of the water flowing in the pipe. For a 1000 foot length of pipe it would require less than one half second for the wave to make a complete round trip. It takes the form of Tc = 2L/a (where “L” is the pipe length and “a” is the velocity of the wave (speed of sound)).

In waterhammer analysis, a time constant that is often used describes the progression of the wave from its inception to the secondary barrier and then back again. The time required for a waterhammer pressure wave to negotiate a length of pipe is simply the pipe length divided by the speed of sound in water (approximately 4860 ft/sec). The pressure waves created by the hydraulic shock has characteristics similar to those of sound waves and travel at a similar velocity. Water hammer in pipes has been known to pull pipe supports from their mounts, rupture piping, and cause pipe whip. The shock wave caused by water hammer can be of sufficient magnitude to cause physical damage to piping, equipment, and personnel. A shock wave results because of this rapid loss of kinetic energy. If it is closed quickly, the loss of kinetic energy is very rapid. If the valve is closed slowly, the loss of kinetic energy is gradual. The initial shock of suddenly stopped flow can induce transient pressure changes that exceed the static pressure. Normally, the entire hammer process takes place in under one second. These pressure waves will travel back and forth several times until the fluid friction dampens the alternating pressure waves to the static pressure of the source. This contraction is transmitted back to the source, which places the pressure in the piping below that of the static pressure of the source. When this shockwave reaches the valve, due to the momentum of the fluid, the pipe wall will begin to contract. This release of energy will form another pressure wave back to the valve.

The compressed liquid and stretched pipe walls will now start to release the liquid in the pipe back to the source and return to the static pressure of the source. When this wave reaches the source, the mass of fluid will be at rest, but under tremendous pressure. Elasticity of the fluid and pipe wall produces a wave of positive pressure back toward the fluids source. It is affected by the initial system pressure, the density of the fluid, the speed of sound in the fluid, the elasticity of the fluid and pipe, the change in velocity of the fluid, the diameter and thickness of the pipe, and the valve operating time.ĭuring the closing of a valve, kinetic energy of the moving fluid is converted into potential energy. Water hammer is a liquid shock wave resulting from the sudden starting or stopping of flow. Related: Water Hammer Pressure Spike Equations and Calculator Water Hammer (Waterhammer) Review and Equation

Speed of sound in water