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Introduction to Fluid Mechanics
Chapter 8
Internal Incompressible Viscous Flow
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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
Internal Incompressible Viscous Flow
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.
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Turbulent flows in a duct
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Turbulent flows
Incompressible flow
Velocity profiles for fully developed pipe flow
Energy Consideration in Pipe Flow
Energy Consideration in Pipe Flow
Energy Consideration in Pipe Flow
Use the empirical power-law profile, Eq. 8.22.
Head losses
Head losses
Thermal energy converted from the mechanical energy from 1 to 2
Mechanical energies, pressure, kinetic, and potential energies.
Head losses
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.
Major losses
Google images of roughness of a pipe
Major losses
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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Calculation of Head losses
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Moody diagram
Calculation of friction factor
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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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Calculation of Head Loss
Minor Loss: Loss Coefficient, K
Minor Loss: Equivalent Length, Le
Calculation of Minor losses
TlhgZ
VPgZ
VP )
2()
2( 2
2
2
_
21
2
1
_
1
mT lll hhh
Mechanical energy change of the fluid across the pump
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!
Energy balance of a fluid system including a pump
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
.
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.
Noncircular Ducts
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