© Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow.
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Transcript of © Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow.
![Page 1: © Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow.](https://reader036.fdocuments.us/reader036/viewer/2022062313/56649f495503460f94c6b837/html5/thumbnails/1.jpg)
© Pritchard
Introduction to Fluid Mechanics
Chapter 8
Internal Incompressible Viscous Flow
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© Pritchard
Main TopicsEntrance RegionFully Developed Laminar Flow
Between Infinite Parallel PlatesFully Developed Laminar Flow in a PipeTurbulent Velocity Profiles in
Fully Developed Pipe FlowEnergy Considerations in Pipe FlowCalculation of Head LossSolution of Pipe Flow ProblemsFlow Measurement
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Internal Incompressible Viscous Flow
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Turbulent flows Fluid particles rapidly mix as they move along due to random
three-dimensional velocity fluctuations. Semi-empirical theories in conjunction with experimental data are the common approach for a turbulent flow. Computational solutions are also available through the use of some empirical parameters, however.
http://www.google.com/images
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Turbulent flows in a duct
http://www.google.com/images
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Turbulent flows
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Incompressible flow
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Velocity profiles for fully developed pipe flow
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Energy Consideration in Pipe Flow
![Page 10: © Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow.](https://reader036.fdocuments.us/reader036/viewer/2022062313/56649f495503460f94c6b837/html5/thumbnails/10.jpg)
Energy Consideration in Pipe Flow
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Energy Consideration in Pipe Flow
Use the empirical power-law profile, Eq. 8.22.
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Head losses
![Page 13: © Pritchard Introduction to Fluid Mechanics Chapter 8 Internal Incompressible Viscous Flow.](https://reader036.fdocuments.us/reader036/viewer/2022062313/56649f495503460f94c6b837/html5/thumbnails/13.jpg)
Head losses
Thermal energy converted from the mechanical energy from 1 to 2
Mechanical energies, pressure, kinetic, and potential energies.
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Head losses
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Calculation of Head Losses/Major Losses
The mechanical energy loss is primarily due to the friction along a pipe and may be divided into two parts: Frictional loss along a straight ,constant-flow-area pipe and frictional loss due to the change of flow area or path. The first part is called Major Loss and may be evaluated in terms of a horizontal pipe without the effect of elevation. The second part is called Minor Loss and will be discussed later.
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Major losses
Google images of roughness of a pipe
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Major losses
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Friction factor for turbulent flow
Wall roughness affects the friction loss of turbulent flow. Since the wall roughness is random, an effective roughness is determined.
sand size e
eroughnessRandom
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c08f014
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Calculation of Head losses
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© Pritchard
Moody diagram
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Calculation of friction factor
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© Pritchard
Heat losses due to flow area and pass changes/Minor Losses
Minor Losses• Examples: Inlets and Exits; Enlargements and Contractions;
Pipe Bends; Valves and Fittings
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© Pritchard
Calculation of Head Loss
Minor Loss: Loss Coefficient, K
Minor Loss: Equivalent Length, Le
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Calculation of Minor losses
TlhgZ
VPgZ
VP )
2()
2( 2
2
2
_
21
2
1
_
1
mT lll hhh
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Mechanical energy change of the fluid across the pump
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Mechanical energy change of the fluid across the pump
The above equation is only for Mechanical energy change of the fluid across the pump, not a general energy balance!
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Energy balance of a fluid system including a pump
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Energy balance of a fluid system including a pump
Tlinin
pumppipe hm
Wuu
m
Q
m
W
m
Quu
m
Q
)1()()()1()()()( 1212
The above equation may be rewritten as:
lT
pumphgZ
VpgZ
Vp
m
Wor )
2()
2( 1
2
1
_
11
2
2
2
_
22
.
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Thermal energy balance
Thermal energy balance:
Thermal energy due to the mechanical energy dissipation in the pipeline + thermal energy due to the mechanical energy dissipation in the pump per mass flow rate is equal to:
)( 12 uum
Q
m
Q pumppipe
However the mechanical energy dissipation in the pump = m
Win
)1(
Therefore
Tlinpumppipe h
m
Wuu
m
Q
m
Q
)-(1 )( 12
is the mechanical energy dissipation in the pipeline only, not including that in the pump.
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Noncircular Ducts
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c08u009
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c08u048
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