 # WATER HAMMER

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Water hammer is a series of pressure pulsations, of varying magnitude, above and below the normal pressure of the liquid in the pipe. The amplitude and periodicity depends on the extinguished velocity of the liquid, as well as the size, length and material of the pipeline. Shock results from these pulsations when any liquid, flowing with a certain velocity, is stopped in a short period of time. The pressure increase, when flow is stopped, is independent of the working pressure of the system. The surge pressure in any pipeline occurs when the total discharge is stopped in a period of time, equal to or less than the time required for the induced pressure wave to travel from the point of valve closure to the inlet end of the line and return. This time is: Where:

t = Time for pressure wave to travel the length of the pipe and return (sec.)
L = Length of pipe line (m)
a = Velocity of pressure wave (m/sec)

When the liquid in the pipe is water, the velocity of the pressure wave a is determined by the following equation: Where:

a = Velocity of pressure wave (m/sec).
Kbulk = Bulk modulus of fluid (for example: 2,070 MPa for water at 20°C)
d = Inside diameter of pipe (mm)
e = Thickness of pipe wall (mm)
E = Instantaneous (short term) modulus of elasticity (MPa) for the pipe material (obtained from Tensile tests)

The surge pressure caused by water hammer is determined by the following equation: Where:

P = Surge pressure (bar)
ρ = fluid density (for example: 1 gr/cm3 for water at 20°C)
a = Velocity of pressure wave (m/sec)
V = Velocity of water stopped = line velocity (m/sec)
g = Acceleration caused by gravity (9.81 m/sec2)

Pressure caused by water hammer can be minimized by increasing closure times of valves to a value greater than 2L/a. For example, when the closure time is 10 times 2L/a, the pressure surge can be 10%–20% of the surge caused by closure in a time equal to or less than 2L/a.

The value of the short-term modulus of elasticity E for PEX pipes is much lower than the value of E for steel pipes, concrete pipes or HDPE pipes. Since the velocity a of the pressure wave is related to the short-term modulus of elasticity E, the velocity a decreases when the value of E is lower.

In order to determine the resistance of the pipe material to the water hammer phenomenon, the total occurring pressure (surge pressure + working pressure) should be calculated and compared to the maximum allowable total occurring pressure in each pipe material. The resistance of HDPE pipes depends on the nature of the water hammer.

In case of recurring water hammer shock waves, HDPE pipes are limited to a maximum total occasional pressure of only 1.5 times the working pressure. Because of the flexibility and resilience of Pexgol pipes, the surge pressures caused by the water hammer are much reduced. Furthermore, because of the cross-linked structure, Pexgol pipes can withstand a total transient pressure (recurring or occasional surge pressure + working pressure) at least 2.5 times the design pressure in the relevant temperature.

## Comparison calculations for other pipe materials

Surge pressures in Pexgol pipes

Pipes Class SDR E=465MPa E=350MPa E=228MPa
20ºC 30ºC 40ºC
a [m/sec] Surge pressure [bar] a [m/sec] Surge pressure [bar] a [m/sec] Surge pressure [bar]
6 26 139 1.4 bar 120 1.2 bar 97 1.0 bar
8 21 156 1.6 bar 135 1.4 bar 109 1.1 bar
10 16.2 180 1.8 bar 156 1.6 bar 126 1.3 bar
12 13.6 198 2 bar 173 1.8 bar 140 1.4 bar
15 11 225 2.3 bar 196 2.0 bar 158 1.6 bar
19 9 254 2.6 bar 221 2.3 bar 179 1.8 bar
24 7.4 288 2.9 bar 251 2.3 bar 204 2.1 bar
30 6 332 3.4 bar 290 3.0 bar 236 2.4 bar

The value of a = Velocity of pressure wave was calculated using the instantaneous Modulus of Elasticity. Please note the surge pressure P is in direct linear relation to the value of the line velocity V.
Therefore, values for different surge pressures for the same pipe class can be calculated by changing the values of the Line velocity V.

• Example: Calculating the surge pressure in paragraph 4. Pexgol 180 mm SDR 9 Class 19.
Above ground installation ambient temperature is 40°C.
Fluid temperature is 20°C
Design temperature is 40°C.
Design pressure of the pipe is 14.9 bar at 40°C.
Maximum allowable total transient pressure is 30 bar.

OD 180 mm | w.t. 20.1 mm | d = 139.8 mm | V = 2.7m/sec

From the table: “Low surge pressures in Pexgol pipes”, the surge pressure for class 19, velocity of 1 m/sec and design temperature of 40°C is 1.8 bar.
For the Pexgol 180 mm class 19 which has a velocity of 2.7 m/sec, the surge pressure will be: 1.6 x 2.7/1 = 4.9 bar

For water density higher than 1.0, divide the value of the Velocity of the pressure wave a (taken from the table: “Low surge pressures in Pexgol pipes”) by the square root of the actual water density.