Day 155, Tuesday, 6 May, 2014

1. Day 155, Tuesday, 6 May, 2014 Fluid Mechanics Fluids Pressure Pascal’s Principle Archimedes's principle Pressure at depth

2. Fluids • Fluids have no shape of their own • Liquids have no shape but definite volume • Gases have no shape and variable volume

3. Pressure • P = F/A • Perpendicular to surface • In the metric (SI or mks) system the unit of pressure is the Pascal abbreviated Pa • 1 Pascal (Pa) = 1 newton/1 meter2

4. Atmospheric Pressure • 1 atmosphere (atm) = 101.325 Pa • 14.7 psi • 760 mm Hg • 1.01 bar • 1 bar = 100 kPa Atmospheric pressure drops by 4% upon 300 m rise

5. Pascal's Principle • Blaise Pascal 1623 – 1662 • French mathematician and physicist • Pressure is transmitted undiminished through a fluid. (shape has no effect) • Pressure is transmitted equally to every point in the fluid and to the walls of the container.

6. Hydraulic Press

7. Archimede's principle • Archimedes – Greek scientist 212 B.C. • Fb = ρVg • Density of a fluid is rho or ρ The magnitude of the buoyant force is equal to the weight of the displaced fluid

9. Pressure at depth P = F/A = mg/A d =m/v => m = dv P = dvg/A v =Ah P = dAhg/A P = dhg d = ρ P = ρgh

10. An aluminium scuba tank is rated to 3,000 psi. How deep can you dive with this tank? • P = ρg h  h = P/ ρg • P = 3,000 psi • lb/in2 (kg/lb)(in/m)(in/m) = kg/m2 • Kg/m2 (m/s2) = N/m2 = Pa • 3,000 (1/2.2)(39.4/1)(39.4/1) = 2.11 x 106 • 2.11 x 106 (9.81) = 2.077 x 107 Pa • ρ = 1,000 kg/m3 • g = 9.81 m/s2

11. h = 2.077x 107 /[(1,000)(9.81)] • H = 2117 m = 2000 m • Checks • At 10 m/atm that is 200 atm • 3,000 psi/(15 psi/atm) = 200 atm

12. What pressure must a typical submarine withstand? • 300 m typical submarine operating depth • P = ρg h = (1,000)(9.8)(300) = 2.9 x 106 Pa • 2.9 x 106 / 1.01 x 105 = 29 atm • (atm)(psi/atm) = psi • 29 (15) = 435 psi

13. Summary • P = F/A • Pascal’s principle: Pressure is transmitted undiminished through a fluid. (shape has no effect) • Archimedes's principle: Buoyant force = weight of displaced fluid • Pressure at depth: P = ρgh

14. Pascal's Principle • Pressure is transmitted equally to every point in the fluid and to the walls of the container.

15. Hydraulic Press

16. Equation of Continuity A1v1 = A2v2 In this case v is velocity (not volume) area 1 x speed in region 1 = area 2 x speed in region 2 Reduce the cross sectional area and the rate of flow increases.

17. Equation of continuity problem • Water pressure at 3.00 x 105 Pa flows through a horizontal pipe at a speed of 1.00 m/s. The pipe narrows to ¼ its original diameter. What is the speed of the flow in the narrow section?

18. Equation of continuity problem worked out A1v1 = A2v2 v2 = (A1v1) / A2 v2 = (r12)(v1) / (r22) v2 = (r12 v1) / r22 v2 = 12(1)/(1/4)2 = 1/(1/16) = 16 m/s

19. Bernoulli’s Principle • When the velocity of a fluid increases the pressure decreases

21. Fluid Equations 1. ρ = m/v 2. P = P0 + ρgh 3. Fbuoy = ρVg 4. A1 V1 = A2 V2 5. P + ρgy + ½ ρv2 = const.

22. Fluid Problems AP Physics, Chapter 9 # 47, 58, 67, 70

23. Credits • Hydraulic Press picture • hyperphysics.phy-astr.gsu.edu/.../hpress.gif • Archimedes's graphics • www.aeic.alaska.edu/.../index.html • Archimedes picture www.daviddarling.info/images/Archimedes_princ...

24. Credits II • Fluid graphic • www.physics-net.com/force/sf000.htm • Pressure cartoon • www.physics.utah.edu/~mohit/Physics_Cartoons.html

25. Credits III • Hydraulic Press picture • hyperphysics.phy-astr.gsu.edu/.../hpress.gif • Archimedes's graphics • www.aeic.alaska.edu/.../index.html

26. Credits IV • Physics problems • Physics: Principles and Problems published by Glencoe, 2002 ISBN 0-07-825934-7 • Barn door photo • http://www.wrh.noaa.gov/images/otx/photo_gallery/spokane_tornado/P5220353.JPG

27. Credits V • Physics problems • Physics: Principles and Problems published by Glencoe, 2002 ISBN 0-07-825934-7 • Hydraulic Press picture • hyperphysics.phy-astr.gsu.edu/.../hpress.gif

28. Credits VI • Wing stall • virtualskies.arc.nasa.gov