Transcript ES 202 Lecture 1 - Rose

ES 202
Fluid and Thermal Systems
Lecture 11:
Pipe Flow (Major and Minor Losses)
(1/7/2003)
Assignments
• Reading:
– Cengel & Turner Section 12-6
• Homework:
– 12-72, 12-79 in Cengel & Turner
Lecture 11
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Road Map of Lecture 11
• Announcements
• Recap from Lecture 10
– “modified” Bernoulli’s equation
– concept of viscosity
• Major losses
–
–
–
–
friction factor
Moody diagram
flow chart to determine friction factor
non-circular ducts
• Minor losses
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Announcements
• Lab 2 this week in Olin 110 from 7th to 9th period
– Section 5 meets tomorrow
– Section 6 meets on Friday
• Post lab group schedule
– 2 lab sessions over the 3 hour period
– 1st session starts at 1:35 pm
– 2nd session starts at 2:55 pm
• Homework assigned on Monday and Tuesday will be due on
Friday by 5 pm
• Solutions to all homework sets are available at reserve library
under Mayhew
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Introducing the Friction Factor
• Recall results from dimensional analysis of pipe flow
 VD  l 
P
 g1 
, , 
2
V
D D
 
• From hindsight, cast the above equation as
 VD  
P
l
 g 2 
, 
2
V
D  
D


P  f
V 2 l
2 D
friction factor / 2
• The friction factor (as defined) only depends
– Reynolds number
– relative roughness
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How to find the friction factor?
• Since the friction factor only depends on two independent p
groups, it is simple to represent its variation with multiple
contour lines on a 2D plane
• Display and describe the Moody diagram
–
–
–
–
representation of two p groups
partition of different flow regimes
independent of surface roughness in laminar regime
insensitivity at high Reynolds number in turbulent regime
• The whole problem of finding the pressure drop across piping
system is reduced to finding the friction factor on the Moody
diagram
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Flow Chart
Find Reynolds number
• fluid properties (, )
• geometry (D)
• flow speed (V)
Laminar
(Re < 2300)
Re 
V D

Turbulent
(Re > 2300)
Find relative roughness
64
f 
Re
Look up Moody diagram
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Example on Moody Diagram
• Example: Water flows in a commercial steel pipe
pipe diameter = 10 cm
mean speed = 10 m/s
pipe length = 3 m
 Find the pressure drop between the entrance and exit of the pipe.
 What will be the difference if water is replaced by oil?
• What if the pipe/duct is not circular?
– needs a representative length measure of the duct cross-section
– notion of hydraulic diameter
• example with a rectangular duct
4 Ac
Dh 
perimeter
– extra factor of 4 recovers the diameter for a circular pipe
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Alternative Method
• The Moody Diagram is a handy way to represent data on friction
factor.
• If reading off the diagram does not seem appealing, the same
amount of data can be curve-fitted to give an explicit functional
relationship between friction factor, Reynolds number and
relative roughness.
• The Haaland formula offers another alternative
1.11

1
6.9   / D  
 1.8 log

 
f
 Re  3.7  
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Friction Factor, Viscous Stress and Head Loss
• Central question: is there a relationship between
– friction factor,
– viscous stress,
– head loss?
• Consider the following pipe flow problem:
1
–
–
–
–
2
Perform a mechanical energy balance for the above system
Perform a momentum balance for the above system
What can you conclude from the above analyses?
If the pipe is tilted at an angle of 30 deg with the horizontal, what will
be the difference in your analysis?
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