Environmental Engineering Reference
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V
1
2
/2
g
H
1
V
2
2
/2
g
P
1
/
g
P
2
/
g
Point 1
Q
Point 2
Z
1
Z
2
Datum
Figure 9.2
Schematic illustrating energy equation components (excluding
H
t
and
H
p
com-
ponents)
relationship. For a pipe system that conveys flow between two large reservoirs,
the driving head is the difference between the upstream and downstream reservoir
elevations plus any additional head added by pumps (
H
p
) if present. System
energy losses (
H
L
) include friction loss (
H
f
) caused by boundary shear stresses
and minor losses (
H
m
) resulting from the dissipation of turbulent eddies created
by flow passing through pipe fittings (e.g., elbows, tees, expansion, contractions,
etc.), valves, and pipe inlets and outlets.
H
L
=
H
f
+
H
m
(6)
2 FLUID FRICTION
The energy loss associated with boundary shear forces on incompressible flow
in closed conduits is referred to as
friction loss
. The following discussion is
developed for circular pipe; however, the results can be applied to noncircular
pipe by replacing the pipe diameter with four times the hydraulic radius (4
R
h
).
R
h
is the conduit cross-sectional area (
A
) divided by the conduit circumference.
The analysis in this section can also be applied to gases and vapors, provided that
the Mach number in the duct does not exceed 0.3. For Mach numbers greater than
0.3, the compressibility effect becomes significant and additional considerations
are required.
H
f
is dependent upon pipe diameter (
D
), pipe length (
L
), pipe wall material
roughness (
k
s
), fluid density (
ρ
) or specific weight (
γ
), fluid kinematic viscosity
(υ)
, and mean flow velocity (
V
). Dimensional analysis can be used to provide
a functional relationship between the
H
f
, pipe dimensions, fluid properties, and
flow parameters. The resulting equations are called the Darcy-Weisbach equation
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