If a column of water flowing through a pipe has its momentum suddenly arrested by closing a valve, the momentum of the moving water will produce an impulse upon the valve, and also upon the sides of the pipe. This impulse is called water hammer.

If the water were inflexible and incompressible as a bar of steel, the force of the impact would equal the weight of the column of water times the square of the velocity divided by twice the acceleration due to the force of gravity and would affect only the gate of the valve. As the water is flexible and slightly compressible, it exerts a pressure of equal intensity upon the sides of the pipe as well, which yields to the pressure and thus absorbs some of the energy of the moving column. The water, too, yielding to the pressure, slightly compresses, so that a short interval of time elapses before all of the energy of the moving water is brought to bear upon the gate and the sides of the pipe. The pipe being slightly elastic yields to the pressure and thus absorbs some of the energy, but it returns to its normal size again, and thus causes a reflex pressure wave back from the valve. This pressure wave passes back and forth in the pipe until the energy is absorbed in the friction of the water and iron molecules among themselves and against each other. Thus, a high pressure wave may pass back and forth through a pipe a dozen or more times, the intensity of each wave becoming less until it finally fades away to the dead level of the initial static pressure.

Fig. 72

Fig. 73

Fig. 74

The intensity of a high-pressure wave caused by suddenly closing an ordinary 1/2-inch self-closing basin cock attached to the end of a 1 1/2-inch pipe, is graphically shown in the following diagrams.

In the diagrams, the line EF represents zero or atmospheric pressure, the line a the static pressure of water in the pipes, that portion of the diagram above the level of the line a indicates the increase of pressure due to water hammer, and that portion of the diagram below the level of the line a shows the drop of pressure below the static pressure due to the reflex pressure wave.

Diagrams 73 and 74 were obtained when no air chamber was on the water pipe. It will be noticed that in the diagram, Fig. 75, the wave is more uniform and symmetrical than in the others, and dies away gradually with a uniform intensity to the static pressure. It will be further observed that although there are the same number of pulsations in this as in the other diagrams, they are of less intensity both above and below the static pressure line. That was due to the fact that an air chamber was used in this experiment. The experiment from which diagram Fig. 76 was obtained was conducted with the air chamber filled with water. Such a condition would be equivalent to having no air chamber on the pipe, and the results obtained under those two conditions were very similar.

Fig. 75

Fig. 76

The conditions under which the experiments were made that produced the foregoing diagrams are given in Table XXIX, which shows intensity, duration and number of pressure waves produced in a 1 1/2-inch pipe by suddenly closing a 1/2-inch self-closing basin cock. Approximate time of closing cock 1/100 of a second.

The intensity of a high pressure wave caused by suddenly arresting the momentum of a column of water in a 2-inch pipe by shutting a quick-closing gate valve of the full size of the pipe, is graphically shown by the diagram Fig. 77. It will be noticed that this diagram records a vacuum of about 15 pounds due to the reflex wave. This is supposed by the experimenters* to be an error. It is believed by them that the momentum of the moving parts of the recording apparatus carried the line that much below the line of atmospheric pressure E F, and that likewise it recorded a maximum pressure of 15 pounds in excess of the pressure actually produced. Allowance should therefore be made for the error.

Fig. 77

Table XXIX - Intensity Of Water Hammer

Note

Table and diagrams from Transactions of American Institute of Mechanical Engineers, Vol. XV, page 510.

* Two students of Cornell College acting under the direction of Prof. Carpenter.

A number of experiments were made with the 2-inch pipe and quick-closing lever-handle gate valve, to determine the intensity of the water hammer under different velocities. Some of the experiments were made with an air chamber of 40 cubic inches capacity, attached to the water pipe near the valve. Some of them were made with an air chamber of 320 cubic inches capacity attached, and still others were made without an air chamber. From the results obtained by the experiments, the diagram Fig. 78 was plotted.

Fig. 78

In this diagram the curves all start at the point of static pressure in the pipe, as that is the initial pressure. The results of the experiments plotted on the diagrams show the high pressure that can be produced in a pipe by abruptly stopping the flow of water, even when the velocity and pressure are comparatively low. It also shows the value of air chambers on water supply pipes and the necessity for using slow-closing cocks in practice, particularly when the pressure of the water is high.

With a static pressure of 30 pounds per square inch and a velocity of 8 feet per second, the maximum pressure due to water hammer when no air chamber was used was 320 pounds to the square inch; an increase in pressure of 290 pounds or an ultimate pressure of almost eleven times the initial pressure. At a velocity of 4 feet per second with all of the other conditions unchanged, the maximum pressure was about 135 pounds per square inch, or an ultimate pressure of 4 1/2 times the initial pressure. With an air chamber of 40 cubic inches capacity and a velocity of 8 feet per second, the maximum pressure was about 230 pounds, or an increase of 200 pounds above static.