Page 384 - Civil Engineering Formulas

HYDRAULICS AND WATERWORKS FORMULAS 313

2
where p internal pressure, lb/in (MPa)
D outside diameter of pipe, in (mm)
F force acting on each cut of edge of pipe, lb (N)
2
Hence, the stress, lb/in (MPa) on the pipe material is
F pD
f (12.65)
A 2t
2
2
where A area of cut edge of pipe, ft (m ); and t thickness of pipe wall,
in (mm).

TEMPERATURE EXPANSION OF PIPE

2
If a pipe is subject to a wide range of temperatures, the stress, lb/in (MPa), due
to a temperature change is
f cE T (12.66)

2
where E modulus of elasticity of pipe material, lb/in (MPa)
T temperature change from installation temperature
c coefficient of thermal expansion of pipe material
The movement that should be allowed for, if expansion joints are to be used, is

L Lc T (12.67)
where L movement in length L of pipe, and L length between expansion
joints.

FORCES DUE TO PIPE BENDS

It is a common practice to use thrust blocks in pipe bends to take the forces on
the pipe caused by the momentum change and the unbalanced internal pressure
of the water.
The force diagram in Fig. 12.12 is a convenient method for finding the resul-
tant force on a bend. The forces can be resolved into X and Y components to find
the magnitude and direction of the resultant force on the pipe. In Fig. 12.12,
V velocity before change in size of pipe, ft/s (m/s)
1
V velocity after change in size of pipe, ft/s (m/s)
2
2
p pressure before bend or size change in pipe, lb/ft (kPa)
1
2
p pressure after bend or size change in pipe, lb/ft (kPa)
2