The pressure waves created by hydraulic shock have characteristics similar to those of sound waves and travel at a similar velocity. The time required for a water hammer pressure wave to negotiate a length of pipe is simply the pipe length divided by the speed of sound in water (approximately 4,860 feet per second [ft/sec]). In water hammer 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. It takes the form of Tc = 2L/a (where L is the pipe length and a is the velocity of the wave, which is the speed of sound). In a 1,000 foot pipe, the wave can make a complete round trip in less than one half second.
P(additional) = aV / 2.31g
P = the additional pressure the shock wave creates
a = wave velocity
V = the velocity of the flowing water in the pipe in feet per second
g = the universal gravitational constant 32 ft/sec2
2.31= the pressure conversion constant.
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. Although Equation 1 does not take into account the effect of pipe length, diameter and elasticity, it will provide some insight as to the additional pressure created by a water hammer pressure wave.
At a pipeline velocity of 5 ft/sec, the additional pressure created by the shock wave is approximately 328 psi. Increasing that velocity to 10 ft/sec increases the additional pressure to about 657 psi. Obviously, systems that are not designed to accommodate such an increased pressure are often damaged or even destroyed.
Valve Closure & Opening
One of the primary causes of water hammer is the abrupt closure of a valve. Figure 2 shows a main pipeline with a branch circuit that is fed by a “Tee.” At the end of the branch is a valve. The black arrows show the flow direction in the primary and branch lines, and the purple arrow is the length of the branch line. As in the system in Figure 1, the valve acts as the primary barrier, but this time the secondary barrier is the “Tee.”
If water is flowing in the branch line and the valve is closed quickly, a shock wave will develop. Its inception follows the same sequence of events in our hypothetical example. One small difference is that some of the intensity of the waves will be lost in the “Tee” as it is open to the main pipeline on either side. Still, a significant portion will be reflected back toward the valve.
P = 0.07 (VL / t)
P = the additional pressure generated by the shock wave
V = the flow velocity in ft/sec
L = the pipe length between the barriers in feet
t = the valve closing time in seconds.
0.07 = a derived constant.
A difference in this example is that we have some control over the valve closure time. In our hypothetical example the valves closed at nearly the speed of light. Closure time has a significant effect on the inception and intensity of water hammer. Two other variables, flow velocity and pipeline length, are also major factors. Equation 2 shows the relationship of these three variables. The additional pressure created by the shock wave is directly proportional to flow velocity and pipeline length and inversely proportional to closure time. In other words, higher values of V or L will increase pressure while higher values of t will result in a decreased pressure. Table 1 shows the results from this equation when using differing velocities, pipe lengths and closure times. The V values are 5 and 10 ft/sec, L values are 100 and 1,000 feet, and t values are 1 and 2 seconds. Two of the variables are constant in each example.
Both columns of the table illustrate the proportional influence of velocity and length—pressure increases as they increase. The lower values in the right hand column illustrate the inverse relationship of time; these pressures are half those in the left hand column because the closure time has doubled. The value of L is often fixed and depends on the application, but we can exercise substantial control over the other two variables. By doing so, we can eliminate or greatly reduce water hammer’s effect.
Pipe diameter and the elasticity of its material also influence the pressure generated. Larger diameters and more elastic materials absorb some of the intensity of the shock waves and therefore reduce the pressure generated. Several pipe manufacturers publish curves or tables that show the potential water hammer pressure increase for various pipe diameters and materials.
Suppose that the branch line valve is closed. If it is opened quickly, the effect is similar to that of quick closing. When the valve is opened quickly, the branch line sees an immediate drop in pressure, and incoming water from the main line accelerates the previously static column. As friction and other factors restrict its flow, the forward portion of the column can act as the initial barrier and give rise to water hammer. Usually its effect is much smaller than that of valve closure and is often referred to as a “surge.” Still, under certain conditions, this surge can be damaging.