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Fluid Hammer Effect

Water hammer, a shock wave which is produced by the sudden stoppage or reduction of a fluid flow, can cause sudden rises in pressure which can damage instrumentation. In tank level measurement applications, surprisingly high pressures can be generated by the sudden closure of a valve on an outlet line.

Ignoring friction and pipe elasticity, the equation for the pressure change in a pipe due to a "sudden" valve closure is P=-pcV where p is the density of the fluid, c is the sonic velocity of the fluid, V is the change in pressure. For example, 25°C distilled water (p=1.937, c=4911) flowing in a pipe at 10ft/s can generate a hammer pressure of 661 psi if a valve is closed "suddenly". A valve is considered to be closed suddenly if the time of closure is less than the time it takes a pressure wave to travel the length of a pipe and return. That time constant Tc=2L/c where L is the length of the pipe and c is the sonic velocity of the fluid. In this example, if the pipe were 200 feet long, the time constant would be .082 seconds.

The above example describes the pressure change that can occur within the pipe. If that pipe were an outlet pipe for a tank, the tank itself would not see the same pressure change as the pipe. A rough estimate of the pressure of the pressure rise seen in the tank relative to the pressure rise in the pipe would be...

...the ratio of the pipe area to tank area:

Water hammer can also be affected by the installation of the valve. A valve closing against the direction of flow closes more slowly than a valve closing with the direction of flow, minimizing the water hammer effect.

A table of densities and sonic velocities of a variety of fluids (from CRC Handbook of Chemistry and Physics, 62nd Edition, 1981-1982) is provided below:

Fluids Density
(lbm/ft3)
Sonic velocity at
25°C (ft/sec)
Acetone 1.533 3852
Benzene 1.689 4249
Carbon disulfide 2.446 3770
Carbon tetrachloride 3.096 3038
Castor oil 1.881 4846
Chloroform 2.892 3238
Ethanol amide 1.976 5656
Ethyl ether 1.384 3232
Ethylene glycol 2.160 5440
Glycerol 2.446 6247
Kerosene 1.572 4344
Mercury 26.203 4757
Methanol 1.535 3619
Nitrobenzene 2.329 4800
Turpentine 1.708 4118
Water (distilled) 1.937 4911
Water (sea) 1.990 5023
Xylene hexaflouride 2.659 2884

   
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