Page 383 - Civil Engineering Formulas

312 CHAPTER TWELVE

WATER HAMMER

Water hammer is a change in pressure, either above or below the normal pres-
sure, caused by a variation of the flow rate in a pipe.
The equation for the velocity of a wave in a pipe is
E 1
U (12.63)
B B1 ED/E p t
where U velocity of pressure wave along pipe, ft/s (m/s)
2
6
6
E modulus of elasticity of water, 43.2 10 lb/ft (2.07 10 kPa)
4
density of water, 1.94 lb s/ft (specific weight divided by accelera-
tion due to gravity)
D diameter of pipe, ft (m)
2
2
E modulus of elasticity of pipe material, lb/ft (kg/m )
p
t thickness of pipe wall, ft (m)
PIPE STRESSES PERPENDICULAR
TO THE LONGITUDINAL AXIS
The stresses acting perpendicular to the longitudinal axis of a pipe are caused
by either internal or external pressures on the pipe walls.
Internal pressure creates a stress commonly called hoop tension. It may be
calculated by taking a free-body diagram of a 1-in (25.4-mm)-long strip of
pipe cut by a vertical plane through the longitudinal axis (Fig. 12.11). The
forces in the vertical direction cancel out. The sum of the forces in the hori-
zontal direction is

pD 2F (12.64)

F F

D

F F
FIGURE 12.11 Internal pipe pressure produces
hoop tension.