ES 202 Fluid and Thermal Systems Lecture 9: Application of Bernoulli’s Equation & Pipe Flow (12/19/2002)

# ES 202 Fluid and Thermal Systems Lecture 9: Application of Bernoulli’s Equation & Pipe Flow (12/19/2002)

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## ES 202 Fluid and Thermal Systems Lecture 9: Application of Bernoulli’s Equation & Pipe Flow (12/19/2002)

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1. ES 202Fluid and Thermal SystemsLecture 9:Application of Bernoulli’s Equation & Pipe Flow (12/19/2002)

2. 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

3. Road Map of Lecture 9 • Comments on Quiz 1 • Application of Bernoulli’s equation • lift on airfoil, tennis ball • The Torricelli experiment • Modified Bernoulli’s equation • Concept of viscosity

4. 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!!

5. Reinforce My Teaching Philosophy • Learning happens both inside and outside the classroom • Inside classroom: interactive participation • Outside classroom: office hours, review sessions

6. 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 Bernoulli’s 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

7. 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

8. 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

9. “Modified” Bernoulli’s Equation • What if fluid friction causes some losses in the system, can I still apply the Bernoulli’s equation? • Recall the “conservation of energy” concept from which we approach the Bernoulli’s equation • Remedy: introduce a “head loss” factor

10. 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

11. Merry ChristmasandHappy New Year!!