Chapter 5-22The friction factor chart 天大化工原理上册英文版课件

V a : average velocity in pipe leading to fitting
K f : loss factor for fitting (管件), which is found by experiment and differs for
each type of connection. A short list of
hfc
Kc
Vb2 2
(5.69)
K c is called the contraction loss coefficient
V b is the average velocity in the smaller, or downstream, section
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• By experiment,
• For laminar flow, Kc 0.1
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8
10. Nonisothermal flow
• Liquid is being cooled • f is increased. • Liquid is being heated • f is decreased.
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Байду номын сангаас
• f = f ’/ Ψ
•For Re>2,100:
w w00..1117
Note that flow rate, velocity and cross section area can’t be calculated by Deq .
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5.4 FRICTION FROM CHANGES IN VELOCITY OR DIRECTION
• 1. Friction loss from sudden expansion of cross section
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6. Separation from velocity decrease
• Boundary layer separation in no sudden change
cross section
sA :line of zero
tangential velocity
separation point
• 2. Friction loss from sudden contraction of cross section
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• 3. Effect of fittings and valves • 4. Form friction losses in the Bernoulli equation • 5. Velocity heads • 6. Separation from velocity decrease • 7. Minimizing expansion and contraction losses
Re.
1
Laminar flow
f 16 16 DV Re
Turbulent flow: for hydraulically smooth pipe
Coburn equation Blasius equation
f 0.04R 6 e0.2
f 0.07R 9e0.25
This applies over Re from about 50,000 to 1 x 106.
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11. Turbulent flow in noncircular channels
• Relationships for turbulent flow in pipes may be applied to noncircular channels by substituting the equivalent diameter Deq (or 4 times the hydraulic radius rH) for the diameter D in the relevant equations.
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5.5 Design of piping system
• 1. Compound pipes in series • Pipeline has the same diameter or consist of
sections of different diameters. 2. Compound pipes in parallel Pipeline branches off at a common point or has a bypass.
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9. Drag reduction in turbulent flow
• Dilute solutions of polymers in water or other solvents sometimes give the peculiar effect of a reduction in drag in turbulent flow.
For Re<2,100:
w w00..2338
fohr eating focrooling
fohr eating focr ooling
(5.60a) (5.60b)
(5.61a) (5.61b)
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Viscous dissipation
• Frictional or viscous dissipation of mechanical energy can result in heating a fluid, especially highly viscous liquids in small channels.
Zb)4f
D LKcKeKf V22
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5. Velocity heads
• velocity heads
2
V /2
the friction loss in a complicated flow system can be expressed as a number of velocity heads（速度 头）.
The skin friction loss in the straight tube is
4fL /D V 2/2
The contraction loss at the entrance to the tube is
2
KcV /2 2
The expansion loss at the exit of the tube is KeV /2
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1. Friction loss from sudden expansion of cross section
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• The friction loss from a sudden expansion of cross section
hfe
Ke
Va2 2
(5.63)
K e is a proportionality factor called the
expansion loss coefficient
V a is the average velocity in the smaller, or
upstream, conduit.
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• According to the steady-flow momentum-balance
equation (4.42), and the Bernoulli equation (4.62),
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7. Minimizing expansion and contraction losses
• Changing the cross section gradually rather than suddenly can minimize the friction loss.
• Such as using Conical reducer(trumpet-shape ) Conical expander
f 0.00140.125 Re0.3 2
Applicable over Re from 3,000 to 3 x 106
4
Turbulent flow: for rough pipe
f Re,k D
Complete turbulent flow:
f k D
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☆ 8. Reynolds numbers and friction factor for non-newtonian fluids
•the contraction loss is negligible
For turbulent flow,
Kc
0.41
Sb Sa
(5.70)
where Sa and Sb are the cross-sectional areas of the upstream and downstream conduits, respectively.
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The friction loss in the globe valve is Kf V /2
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The total friction is
hf 4fD LKcKeKfV22
(5.72)
To write the Bernoulli equation for this assembly
pa
pb
g(Za
VQcTpS
T pS
c
(5.62)
• For the flow of polymers the temperature rise is about 4°C for a pressure drop of 10 MPa; for hydrocarbons it is about 6°C per 10 MPa.
• (a) Calculate the pressure drop in lbf/in.2 per 100 ft of pipe.
• (b) If the pressure drop must be limited to 2 lbf/in.2 per 100 ft of pipe, what is the maximum allowable velocity of the water?