Fluids and Pressure

1. Fluids and Pressure PHYS 1090 Unit 5

2. Balloon Mash • Greater force makes larger contact area

3. Pressure • Force applied per unit area p = F/A • If pressure is constant, force and area change together

4. Pressure within Fluids • Pascal’s Principle: fluids exert pressure evenly in all directions

5. Balloon Mash • Upward force (pressure  area) on plate exactly cancelled plate’s weight • As weight increased, contact area did too • (pressure may have increased as well)

6. Fountain • Water shoots farther from lower holes • Streams weaken as water drains

7. Supports weight above Static Fluids • Pressure counteracts weight of fluid above (Pascal’s principle) • Pressure increases with depth

8. h Liquid Pressure Formula p= rhg • p = pressure • r = density of liquid • h = depth under top of liquid p = pressure here

9. Pressure within a Liquid • Shape of the container does not matter! • All that matters are depth h, fluid density r, and gravitational field g. p = rhg

10. Fountain • Stream velocity depends on pressure • Pressure depends on depth • Rocks in the can have no effect

11. Sinking and Floating • Objects displace a volume of water equal to their submerged volume • A floating boat displaces an additional volume of air

12. What forces are present?

13. What forces are present?

14. What forces are present?

15. What forces are present?

16. Pressure in a fluid • Pressure increases with depth • Greater pressure at bottom than top of an immersed object • Results in upwardbuoyancy forcethat is the (vector) sum of all pA forces

17. Buoyancy Force • Buoyancyforce=weight of fluid displaced(Principle of Archimedes) F = rVg • r = density of fluid • V = volume of fluid displaced = volume of object submerged • g = 9.8 N/kg

18. Sinking and Floating • All objects are lighter under water • Difference is buoyancy force • If buoyancy > weight, object rises to surface and floats (so buoyancy = weight) • if buoyancy < weight, object sinks

19. Clay Lump • Weight of the lump was constant • Making a boat increased the volume of water displaced • That increased the buoyancy force • A great enough buoyancy floated the boat

20. Expanding and Contracting • The same amount of gas occupies more volume at a higher temperature.

21. Convection • Warm fluids expand, becoming less dense • Circulation is driven by buoyancy forces • Much faster than conduction

22. “Ideal Gas” Law • p = pressure • V = volume • N = number of gas molecules • kB = 1.3806610–23 J/K • T = absolute (Kelvin) temperature pV = NkBT

23. p V Gas Pressure and Volume pV = NkBT • At a constant temperature, pV is constant • IncreasingpdecreasesV and vice versa

24. Balloon Mash • Pressure may have increased with greater force because air was compressed (volume became less)

25. Diver • Diver’s weight = weight of (glass + air) • Buoyancy = weight of excluded water • Increasing pressure decreases air volume • Buoyancy decreases • Weight is unchanged

26. Neutral Buoyancy • Air doesn’t weigh much • Glass weight doesn’t change • At neutral buoyancy SF = 0, buoyancy↑ = glass weight↓ • Neutral buoyancy air volume is the same for all initial bubble sizes