Hydraulics Laboratory - Water Hammer

Purpose

To demonstrate the behavior of elastic waves in a conduit and the use of the water hammer equations.

Investigation with very simple equipment is possible because the low modulus of elasticity of the polyethylene wall of the pipe cause the velocity of the elastic wave to be reduced to about 1/20^th of its value in pipes with metal walls.

Procedure

1) Each member of the group should observe the pressure oscillations by feeling the wave pulse in the wall of the plastic tube.

2) Running a test

1. Ensure that the upstream valve is opened 1 3/4 turns.
2. Fully open valve downstream and measure the flow at least three times carefully (time not less than 20 sec.). Calculate the flow rate.
3. Ensure the piezometer tube is closed.
4. Activate the computer program, then close the valve downstream within 1 sec. Ensure a soft end to closure (otherwise, you'll record vibration).
5. Display the graph on the computer. If the data looks good, then print. If not, try again. It may take some practice to obtain a decent plot.
6. Print the test data.
7. Repeat steps 4-6 to obtain a second set of data.
8. Repeat the experiment with the upstream valve at 1 1/2, 1 1/4, and 1 turns. Take two sets of data for each valve setting.

Reduction of Results

1) Speed of Pressure wave - From the graph or printed data, determine the time between the initial rise in pressure and the next rise: i.e. the wave has traveled 4 lengths of the pipe. The speed of the wave is thus 4L/t. The length of the pipe is 14.52 m.

The theoretical velocity of the elastic wave is given by:

a = 1/(r(1/K+Dc/Ee))^0.5 m/s

where
r = density of water (1000 kg/m³)
K = bulk modulus of water (2.07E9 Pa)
D = I.D. of pipe (23.8 mm)
e = wall thickness of pipe (3.8 mm)
E = modulus of elasticity of the pipe at the stress range encountered (1.015E7 Pa)
c = fixity factor for a pipe with fixed ends (1-m² where m is Poisson's ratio (0.45 for polyethylene))

2) Water Hammer Pressure Head - From the graph or printed data determine the rise in pressure due to water hammer. Beware of spikes caused by either too violent a closure of the valve, or electronic noise.

Comparison of Results

1) Calculate the water hammer pressure head rise using:

h = u(1+u/a)a/g m

where
u = velocity in the pipe (m/s)
a = theoretical velocity of the wave (calculated previously)

2) Compare the measured and calculated values for water hammer pressure rise. Calculate the percent deviation between them.

3) Compare the theoretical and measured speed of the pressure wave.

4) Comment on these results. In particular, if there seems to be any trend respecting the results with flow rate.

Figure 1: System Schematic

Figure 2: Idealized Variation of Pressure Head with Time at the Transducer (Frictionless)

Figure 3: Variation of Pressure Head with Time at the Transducer (with Friction)