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Physics 203 College Physics I Fall 2012

Physics 203 College Physics I Fall 2012. S. A. Yost. Chapter 10 - Part 3 Chapter 11 – Part 1. Fluid Dynamics Simple Harmonic Motion. Exam 3. Average: 32 High: 61.5. Announcements. Problem set 10B is due Thursday.

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Physics 203 College Physics I Fall 2012

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  1. Physics 203College Physics IFall 2012 S. A. Yost Chapter 10 - Part 3 Chapter 11 – Part 1 Fluid Dynamics Simple Harmonic Motion

  2. Exam 3 Average: 32 High: 61.5

  3. Announcements • Problem set 10B is due Thursday. • We will start discussing Ch. 11 late today or next time: Read sections 1 – 4 and 7 – 9 for next time. Topics: simple harmonic motion, intro to waves. • Next Tuesday: Ch. 11, sec. 11 – 13 and Ch. 12, sec. 1 – 4 & 7. If possible, we may finish Ch. 11 next time, leaving Ch. 12 for next week. • The end of Ch. 11 and Ch. 12 are related: waves and sound.

  4. Volume Rate of Flow • The volume rate of flow of an incompressible fluid is the same throughout a pipe. • Q = Av = constant v A

  5. v2 v1 P2 P1 Bernoulli Principle • Bernoulli’s Principle is an expression of energy conservation: • PV +½ m v2+ mgh= constant. • Work+kinetic energy • +potential energy = • constant. h

  6. v2 v1 P2 P1 Bernoulli Principle • P + ½ r v2 + rgh= constant. • This is a consequence of the work-energy theorem, assuming the only work is done by gravity and pressure. • This neglects friction in the fluid – viscosity. • It also assumes smooth “laminar” flow – no turbulance. h

  7. Question • 1. A fluid flows through the pipe shown. In which section is the flow velocity the greatest? • Selections: A B C D The same C A B

  8. Answer • The volume rate of flow Q = vAis constant for an incompressible fluid. The fluid moves fastest where the pipe is narrowest, sectionB. (It moves slowest in section C.) C A B

  9. Question • 2. In which section is the pressure of the fluid the greatest? • Selections: A B C D The same C A B

  10. Answer • This is Bernoulli’s principle: The pressure in a fluid decreases when the flow velocity increases. The fluid moves most slowly at C, so the pressure is highest there (and lowest atB). C A B

  11. Water Tower and Fountain • A water tower feeds a fountain, which shoots water straight up in the air. • How fast does the water leave the fountain? • Assume the top of the water is a height h = 55 m above the fountain. h v

  12. Water Tower and Fountain • We’ll assume the tank is big, so the top of the water stays fixed: • h1 = 55 m, • v1 = 0, • P1 = 0 1 h v gauge pressure

  13. Water Tower and Fountain • At the fountain, • h2 = 0 • v2 = v • What is P2? 1 h unknown v 2

  14. Water Tower and Fountain • Careful! • This isnothydrostatics. • If the fountain were turned off, the pressure would be • P2 = rgh = 1000 kg/m3 • x 9.8 m/s2 x 55 m • = 5.4 x 105 N/m2. 1 h no flow! 2

  15. Water Tower and Fountain • When the fountain is flowing, this changes! • The pressure just outside the pipe is P2 = 0, • normal atmospheric pressure. 1 h P2 v 2

  16. Water Tower and Fountain • The velocity is given by Bernoulli’s equation with • P1 = P2 = 0 • h1 = h, h2 = 0 • v2 = 0, v1 = v 1 h P2 v 2

  17. Water Tower and Fountain • The only terms remaining are • ½ r v2 =rgh • The result is the same as if the water had fallen from the top of the tower: • v = √ 2gh = 33 m/s. 1 h v 2

  18. Water Tower and Fountain • What is the volume rate of flow if the pipe has diameter 1 cm? • Q = Av • A = p (0.5 cm)2 • = 0.785 cm2 1 h v 2

  19. Water Tower and Fountain • Q = Av • A = 0.785 cm2 • v = 33 m/s = 3300 cm/s • Q = 2600 cm3 /s • = 2600 mL /s = 2.6 L/s 1 h v 2

  20. Water Tower and Fountain • How high does the water rise from the fountain? • Bernoulli’s equation between points 1 and 2: • P1 = P2 = 0, • v1 = v2 = 0 • implies rgh1 = rgh2. 1 2 h v

  21. Water Tower and Fountain • The water rises to the height of the tower. • This assumes energy conservation: • No friction (viscosity or air resistance) or turbulence is considered. 1 2 h v

  22. Hooke’s Law • From chapter 6: • Hooke’s Law describes a linear restoring force when a spring is displaced from its equilibrium position. • Elastic potential energy: U = ½ kx2 x F = -k x

  23. Simple Harmonic Motion When a mass oscillates under a linear restoring force F = -kx, the acceleration is always opposite the displacement from equilibrium, but proportional to it. a = F/m = -(k/m) x. This is called simple harmonic motion.

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