1. ES 202 Fluid and Thermal Systems Lecture 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? V H Area = A 1 Area = A 2

8. The “Bent” Torricelli Experiment What will happen if a 90 o 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 Christmas and Happy New Year!!