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7/22/2019 8 pipe note 3.pdf
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Chapter 8 Pipe Flow
PIPE FLOW
Losses in Pipe
It is often necessary to determine the head loss, hL,
that occur in a pipe flow so that the energy equation,
can be used in the analysis of pipe flow problems.
The overall head loss for the pipe system consists of
the head loss due to viscous effects in the straightpipes, termed the major loss and denoted hL-major.
The head loss in various pipe components, termed the
minor loss and denoted hL-minor.
That is ;
hL= hL-major+ hL-minor
The head loss designations of major and minor
do not necessarily reflect the relative importance of
each type of loss.
For a pipe system that contains many components
and a relatively short length of pipe, the minor loss
may actually be larger than the major loss.
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Chapter 8 Pipe Flow
Major Losses
The head loss, hL-majoris given as ;
g
V
Dfh
majorL2
2l
=
where f is friction factor.
Above mention equation is called the
Darcy-Weisbach equation. It is valid for any fullydeveloped, steady, incompressible pipe flow, whether
the pipe is horizontal or on hill
Friction factor for laminar flow is ;
Re
64=f
Friction factor for turbulent flow is based on Moody
chart.
It is because, in turbulent flow, Reynolds number and
relative roughness influence the friction.
Reynolds number,
VD
=Re
Relative roughness D
=
(relative roughness is not present in the laminar flow)
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Chapter 8 Pipe Flow
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Chapter 8 Pipe Flow
The Moody chart is universally valid for all steady,
fully developed, incompressible pipe flows.
The following equation from Colebrook is valid forthe entire non-laminar range of theMoodychart. It is
called Colebrook formula.
+=
f
D
f Re
51.2
7.3log0.2
1
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Chapter 8 Pipe Flow
Minor Losses
The additional components such as valves and bend
add to the overall head loss of the system, which isturn alters the losses associated with the flow through
the valves.
Minor losses termed as ;
g
VKh LL 2
2
minor=
where KL is the loss coefficient.
Each geometry of pipe entrance has an associated
loss coefficient.
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Chapter 8 Pipe Flow
Entrance flow conditions and loss coefficient.
Condition: 02
1 =A
A or =
2
1
A
A
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Chapter 8 Pipe Flow
Exit flow conditions and loss coefficient.
Condition: 02
1 =A
A or =
2
1
A
A
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Chapter 8 Pipe Flow
Losses also occur because of a change in pipe
diameter
For sudden contraction:
22
2
2
1
2 1111
=
=
=
cc
LCA
A
A
AK
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Chapter 8 Pipe Flow
For sudden expansion
2
2
11
=
A
AKL
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Chapter 8 Pipe Flow
EXAMPLE 1
Figure 1
Water flows from the nozzle attached to the spraytank shown in Figure 1. Determine the flowrate if the
loss coefficient for the nozzle (based on upstream
conditions) is 0.75 and the friction factor for the
rough hose is 0.11.
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Chapter 8 Pipe Flow
EXAMPLE 2
Figure 2
Water at 10 degree Celsius is pumped from a lake
shown in Figure 2. If flowrate is 0.011m3/s, what is
the maximum length inlet pipe, l, that can be usedwithout cavitations occurring.
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Chapter 8 Pipe Flow
EXAMPLE 3
Figure 3
Water flows steadily through the 2.5cm diameter
galvanized iron pipe system shown in Figure 3 at rate
6x10-4m3/s. Your boss suggests that friction losses in
the straight pipe sections are negligible compared tolosses in the threaded elbows and fittings of the
system. Do you agree or disagree with your boss?
Support your answer with appropriate calculations.
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Chapter 8 Pipe Flow
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