ES 202 Fluid and Thermal Systems Lecture 9: Application of Bernoulli

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ES 202Fluid and Thermal SystemsLecture
9Application of Bernoullis Equation Pipe
Flow (12/19/2002)
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Assignments

• Reading
• Cengel Turner Section 12-3, 12-4
• Optional C T Section 11-5 (good stuff!)
• Homework
• 9-12, 12-4C, 12-9C in Cengel Turner
• Supplementary problem (dimensional analysis on
  pipe flow)
• Definition of Reynolds number
• 9 homework problems altogether due on Monday
  after Christmas holiday

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Road Map of Lecture 9

• Comments on Quiz 1
• Application of Bernoullis equation
• lift on airfoil, tennis ball
• The Torricelli experiment
• Modified Bernoullis equation
• Concept of viscosity

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Comments on Quiz 1

• What should you expect?
• Question 1
• perfect balance between pressure force and
  gravity (static equilibrium)
• Question 2
• The cause of buoyancy is the same regardless the
  density of the immersed object!
• Buoyancy is NOT due to difference in density, but
  difference in pressure!
• Honor code is strictly observed! I mean it!!

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Reinforce My Teaching Philosophy

• Learning happens both inside and outside the
  classroom
• Inside classroom interactive participation
• Outside classroom office hours, review sessions

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Lift on Airfoil and Tennis Ball

• Airfoil
• destroy the flow symmetry between the lower and
  upper surfaces
• show visualization
• which flow region can/cannot be analyzed by
  Bernoullis equation?
• Spin on a tennis ball
• what does the spin do to the tennis ball?
• the dimples on a golf ball are for a different
  purpose

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The Torricelli Experiment

• Schematic of experiment
• Describe the fluid motion
• What is the pressure at the exit?
• What is the maximum exit velocity?

Area A1
H
V
Area A2
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The Bent Torricelli Experiment

• What will happen if a 90o bend is added to the
  tank exit?
• How high can the water column go up?
• Do you expect the water column reaches the height
  you just found? Explain your answer.

V
H
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Modified Bernoullis Equation

• What if fluid friction causes some losses in the
  system, can I still apply the Bernoullis
  equation?
• Recall the conservation of energy concept from
  which we approach the Bernoullis equation
• Remedy introduce a head loss factor

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One Major Reason for the Losses

• Fluid friction
• also termed Viscosity
• basketball-tennis-ball demonstration
• exchange of momentum at the molecular scales
• no-slip conditions at the solid surface (imagine
  thin layers of fluid moving relative to one
  another)
• the two-train analogy
• stress-strain relation in a Newtonian fluid
• Description of supplementary homework

Stress viscosity X strain rate
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Merry Christmas and Happy New Year!!