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Chapter 4
Flow in pressurized conduits
4.1 FUNDAMENTALS OF PIPE FLOW
In hydraulics, pipe flow is commonly considered as a full-pipe pressuredriven flow occurring in closed conduits of a circular cross-section. The
two basic equations that describe pipe flow are the continuity (or mass
conservation) equation and the energy equation. Assuming incompressible
fluid and considering a pipe with varying cross-sectional area, the continuity equation can be written as
Q = u 1 A 1 = u 2 A 2 = constant
(4.1)
Q u
D
u
D
=
=
=
1
1
2
2
2
2
4
4
π
π
constant
(4.2)
where Q is the volumetric discharge, u i is the uniform cross-sectional velocity, and A i and D i are the cross-sectional area and pipe diameter, respectively, at point (i). However, in the majority of the applications the pipe
cross-section is constant. Only in special cases (e.g. transitional sections
connecting pipes of different diameter) does the pipe vary in diameter.
The energy equation is comprised of the kinetic part and the potential
part (including the piezometric and the elevation energy). Written in terms
of ‘head’, the energy equation reads
u
g
p z
u
g
p z h e
1
2
1
1
2
2
2
2
2
2
+ + =
+
+ +
γ
γ
(4.3)
where p i (= γy i ) is the hydrostatic pressure at point (i), z i is the elevation of
the pipe from some reference datum, and h e is the energy loss (head loss)
between the two sections (Figure 4.1).