ES 202
Fluid and Thermal Systems
Lecture 12:
Pipe Flow Overview
(1/9/2003)
Assignments
• Homework:
– 11-105 in Cengel & Turner
• Study for Exam 1
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Announcements
• Lab 2 this week in Olin 110 from 7th to 9th period
– Section 6 meets on tomorrow
– post lab group assignment for Section 6
• Comments on Lab 2 write-up
• Homework assigned on Monday and Tuesday will be due on
tomorrow by 5 pm
• Review session on Saturday from 4 pm to 6 pm in GM Room
• What can you bring to the exam?
• What is covered on the exam?
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Road Map of Lecture 12
• Recap from Lecture 11
– major losses
• friction factor (functional dependency, Moody diagram, Haaland formula)
– notion of kinematic viscosity
• Major losses
– relationship between friction factor, viscous stress and head loss
– categorization of design problems
• Minor losses
– flow visualization
– empirical expressions
• Total loss
– schematic summary
• Pipe system
– in series
– in parallel
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Revisit an Example
• 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?
 density (r) decreases
 dynamics viscosity (m) increases
 Reynolds number decreases significantly!
• Notion of kinematic viscosity
m

r
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Re 
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VD

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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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Head Loss, Pressure Loss, Mechanical Energy Loss
• Relationship between various losses
– just representation of the same measure in different
dimensions
• Pressure loss
P  r g hloss
• Mechanical energy loss
Emech,loss  m g hloss
or
E mech,loss  m g hloss
• Head loss is likely to be the easiest one to visualize
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Categorization of Design Problems
1)
Given the flow rate at design condition, what is the required pump power
to drive the flow?
  V  Re  f  P
m
2)
Given a design pressure difference between inlet and outlet of a pipe,
what is the flow rate?
- requires iteration
?
Vguess  Re  f  P  Pgiven
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Introducing Minor Losses
• Clarification: “minor” does NOT imply “small”
• Flow is NOT always “well-behaved” and attached especially at
–
–
–
–
entrance
exit
connection
turn (elbow)
• Visualizations from Multi-Media Fluid Mechanics
– flow separation over a step
– flow separation in a diffuser
• Results in losses due to viscous effects (minor losses)
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Quantification of Minor Losses
• Similar to the concept of friction factor in major losses, a
dimensionless parameter, KL , is introduced to quantify minor
losses so that:
2
Pminor  K L
rV
2
• Show empirical expressions for various configurations
• Relatively “localized” event, NO L/D dependence as in major
losses
– notion of equivalent length used in text
KL  f
Lequiv
D
KL
Lequiv 
D
f
– interpreted as a hypothetical addition of pipe length
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Total Loss in a Pipe System
• Total loss includes both
– major losses
– minor losses
• Adopt a “divide and conquer” approach
– identify the individual sources of loss (major and/or minor)
– formulate pressure drop across individual sources
– integrate results to give total loss
• Pressure losses are additive in a series configuration, i.e.
Ptotal  Pmajor  Pminor
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Schematic Summary
Total Loss
Major Losses
Minor Losses
Li rVi
Pi  f i
Di 2
2
Pi  K L, i
rVi
2
2
Subscript i stands for individual source of loss
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Pipe Systems
• Integration of knowledge you have learned so far
• Two typical configurations:
– in series
• mass (volumetric) flow rate remains constant
– what does it mean by velocity?
– in parallel
• pressure drop across each section is the same
• Analogy to electrical circuit system
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