1. AP Physics Chp 11

2. Density (mass density) • ρ=m/V • Solids and liquids are fairly constant at our range of temp/pressure but gases vary.

3. Pressure • P = F/A the force is perpendicular to the surface area but pressure is not a vector • 1 Pa = 1N/m 1 atm = 101,325 Pa • bar = 105 Pa • The english system used lb/sqin = psi

4. The pressure we experience now is due to the fluid above us being pulled down by gravity. • 14.7 lb/si or 101,325 Pa is the standard at sea level • The higher up you go the lower the pressure gets because of less fluid above you

5. Thus in a static fluid • P2 = P1 + ρgh • ρ is the density and h is the depth in m

6. We use this in constructing a barometer (measure air pressure).

7. As well as manometers which measure other fluid pressure.

8. Gauge pressure is the pressure compared to atmospheric pressure • Absolute pressure is the actual pressure

9. How high can a submersible pump raise water if it has a maximum pressure of 110 kPa?

10. P2 = P1 + ρgh • 110000 = 101325 Pa + (1000kg/m3)9.8m/s2(h) • h = 0.89 m

11. How much force would it have at the pump if the pipe was 2.3 cm in diameter? How much at the maximum height with the same size pipe?

12. At the pump • P = F/A • P = 110 kPa or 110000 Pa • A = πr2 r = 2.3cm/2 = 1.15cm = 0.0115m • A = π(0.0115m)2 = 0.00042m2 • F = PA = (110000 Pa)(0.00042m2) = 46 N

13. At the maximum hieght • P = F/A • P = 101325 Pa • A = πr2 r = 2.3cm/2 = 1.15cm = 0.0115m • A = π(0.0115m)2 = 0.00042m2 • F = PA = (101325 Pa)(0.00042m2) = 43 N

14. Why can’t a surface mounted pump pull water up out of a well that is 12 m deep?

15. P2 = P1 + ρgh • 101325 Pa = 0 Pa + (1000kg/m3)(9.8m/s2)(h) • h = 10 m

16. Pascal’s Principle • Any pressure applied to a completely enclosed fluid is transmitted undiminished to all parts of the fluid and enclosing walls. • P1 = P2 if the level of the fluid is equal at each point otherwise we add ρgh as needed

17. F1/A1 = F2/A2 useful in hydraulic jacks

18. Arcimedes’ Principle • Fluids apply a buoyant force on any object partially or totally submerged in it with a magnitude equal to the weight of the displaced fluid.

19. Fb = Wfluid • Fb = ρgV • Why do supertankers float?

20. The supertanker’s design displaces enough water/salt water such that Fg = Fb • Why will filling a ship to its limit in Boston create problems when it tries to go to Panama?

21. As fluid enters a tube that is open on both ends the mass of the fluid going in has to be equal to the mass coming out. • A1v1 = A2v2 continuity equation • How does this explain the effect on kinking a hose?

22. Bernoulli’s Equation • P1 + 1/2pv12 + pgh1 = P2 + 1/2pv22 + pgh2 • When the fluid isn’t moving this gives the pressure equation P = Po + pgh • This equation is used often to explain the affects of moving air like wind over a roof.

23. What is the pressure above the roof sheeting if the wind is blowing 32 m/s and there is no wind inside your attic space. Assume the height difference is negligible. Density of air is 1.29 kg/m3.

24. P1 + 1/2pv12 + pgh1 = P2 + 1/2pv22 + pgh2 • P1 + ½(1.29 kg/m3)(32m/s)2 = 101325 Pa • P1 = 100004 Pa