Wave celerity is the speed of the pressure wave that passes along the pipe following a flow disturbance. Typically it is in the order of 1000 m/sec for water in steel or iron pipe. It may be down to 400 n/sec for water in plastic pipe.
It is a function of the elasticity of the fluid and the pipe material.
For simplicity think of stopping the flow of water at the downstream end of a pipe. The water brought to rest compresses under the force of the water flowing behind it. This gives an increase in pressure causing the pipe to elastically expand. This pressure increase travels up the pipeline at the "wave celerity".
The analogy often used is that of a railway train coming to a stop against the buffers. The carriages come to rest one after another. The kinetic energy of the carriages is stored as potential energy in the buffers between each carriage. The carriages come to rest one after the other and the speed at which they come to rest is the "wave celerity". Once all the carriages are stopped then the potential energy stored in the buffers is released and transferred back to kinetic energy. Release of this energy causes the carriages to travel backwards (the same as releasing compression from a spring). This wave travels back along the train at the "wave celerity". The process repeats and waves of compression and tension can be observed moving up and down the train. The connections between the carriages go from alternative compression in the buffers to tension in the couplings. In time the as a result of friction the whole train comes to rest.
The wave celerity is important because if the fluid is stopped sufficiently slowly so that the negative (tension in the couplings) waves begin to return while the compression (compression in the buffers) waves are still being generated then the waterhammer pressures will be reduced.
Thanks for your reply. Is it then the "return" wave going upstream from the disturbance? Can the wave celerity be found on a table, if not, must it be calculated? Is it a factor of pipe size? Is it a factor of pressure?
Suggest you to consult "Fluid Transient" by Wylie and Streeter. The first chapter has a good write up on wave speed.
Wave speed or wave celerity has to be caculated because it depends on the support condition as well. Bris's information is pretty accurate.
I supplement the idea of wave celerity further by that it is equivalent to the speed of sound in the fluid. In water it is about 1km/s with variations according to the pipe wall material, thickness and restraint condition. In air, concrete and steel it is about 0.33, 4 and 6 km/s respectively.
The wave speed is the speed of the pressure surge which travels forward and backward many times before it is attenuated by the friction and the boundary conditions. Therefore the wave goes upstream as well as downstream in split seconds.
Last point to watch is that a small percentage of air in the fluid can greatly reduce the wave celerity. I rarely attain the theoretical wave speed with experiments. Higher wave speed should give you a high water hammer.
When you do get results from a water hammer analysis you can check the wave speed with the time between any two oscillations. That time between any two repetitive oscillation is the time the pressure wave doing one complete round in your piping system.
The wave speed is a factor of the elasticity of the fluid (bulk modulus) and the pipe material (elastic modulus and Poisson's ratio). Providing everything remains elastic and there is no air the speed (celerity) is independent of pressure but is dependent on pipe diameter and wall thickness and pipe shape. The speed in a square section is much less than in a circular section. It is also affected by the type of joint - welded, bell and socket etc. Most text books will give you the basic equation for wave speed.
As noted by Bbird a small percentage of air will reduce the speed and the speed will also become pressure dependent. (0.1% air at 10 bar pressure typically reduces the wave speed by about 30%).
For first approximate calculations for water in pipes you will be n the right order using about 1000 to 1200 m/sec for ductile iron and steel. 800 to 900 m/sec for cast iron, 700 m/sec for GRP and concrete, 200 to 400 m/sec for uPVC.
The maximum water hammer pressure that occurs with instant valve closure can be calculated by the "Joukowasky equation" DH= c x Dv/g (SI units).
DH is the pressure increase, DV is the change in pipe flow velocity, c is the wave speed (celerity), g is gravity acceleration (9.81 m/sec.sec).
The valve closure time is classified as instant if the valve closes in less time then it takes the wave to travel from the valve to the end of the pipe and back again (T = 2 * L/c) . If the valve takes longer to close than time T then the reflected waves will start arriving back at the valve while the valve is still closing and generating positive waves. The result be that the pressure is usually less than calculated by "Joukowasky equation".
(But this is not always the case - it depends on the upstream boundary conditions - in some cases such as where the pipeline is supplied through an automatic pressure regulating valve reflected waves can be positive and in these cases it is possible to generate escalating locked in pressure - and eventual pipe failure).
