Updated 11/26/08
Energy Losses in Bends
Introduction
Energy losses in pipe flows are the result of friction between the fluid and the pipe walls
and internal friction between fluid particles.
Minor (secondary) head losses
occur at any
location in a pipe system where streamlines are not straight, such as at pipe junctions,
bends, valves, contractions, expansions, and reservoir inlets and outlets.
In this
experiment, you will measure minor head losses through a pipe section that has several
bends, transitions, and fittings as shown in Figure 1.
Figure 1.
Schematic drawing of the energyloss apparatus.
Objective
The objectives of this lab are to measure head losses through bends, transitions, and
fittings, and to use these measurements to estimate the loss coefficients for each transition
or fitting.
Theory
The energy balance between two points in a pipe can be described by the Bernoulli
equation, given by
L
h
g
V
z
p
g
V
z
p
+
+
+
=
+
+
2
2
2
2
2
2
2
1
1
1
γ
,
(1)
where
p
i
is static pressure (in Pa) at point
i
,
is specific weight of the fluid (in N/m
3
),
z
i
is
the elevation (in meters) of point
i
,
V
i
is the fluid velocity (in m/s) at point
i
,
g
is the
gravitational constant (in m/s
2
), and
h
L
is head loss (in meters).
The term
p
i
/
is referred
1
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to as the static head;
z
i
is the elevation head; and
V
i
/2g
is the dynamic (or velocity) head.
The summation of the static head and the elevation head,
p
i
/
γ
+
z
i
, is referred to as the
piezometric head.
The piezometric head is what is measured with the piezometer
(manometer) board on the apparatus for this experiment.
Head loss,
h
L
,
includes the sum of pipe friction losses,
h
f
, and all minor losses,
∑
=
+
=
n
1
i
i
f
L
h
h
h
,
(3)
where
h
i
is the minor head loss (in meters) for the
i
th
component and
n
is the number of
components (fittings, bends, etc.).
Pipe friction losses are expressed as the Darcy
Weisbach equation given by
g
V
D
L
f
h
f
2
2
=
,
(2)
where
f
is a friction factor,
L
is the pipe length, and
D
is the pipe diameter.
Pipe friction
losses are assumed to be negligible in this experiment.
Minor losses occur at any bend, transition, or fitting where the streamlines are not straight
and are proportional to the velocity head.
For all components, head loss is given by
g
V
K
h
i
i
2
2
=
,
(5)
where
K
i
is the loss coefficient (dimensionless) for the
i
th
component and
V
is the fluid
velocity as it travels through the pipe component.
For the expansion and contraction, the
V used in Equation (5) is the velocity of the fluid in the smallerdiameter pipe.
In this experiment, the loss coefficients for different pipe components will be
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 Spring '12
 AmmarAli
 Fluid Dynamics, Gate valve, Total dynamic head

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