1. Physics 1B03summer-Lecture 12 1 Survey + $150 !!! The Faculty of Science is conducting an online survey to help us better understand your educational and career goals, and your views on how well your undergraduate program is helping you reach those goals. Faculty of Science students will find the survey at http://iserv.mcmaster.ca/science/survey.htm and it will be available until April 23rd. The survey will take about 5 minutes to complete, and the department will be awarding $150 Titles gift certificates to two students who complete the survey. Your input as a Science student will help us ensure that the quality of undergraduate education in the Faculty of Science is as high as we can make it.

2. Physics 1B03summer-Lecture 12 2 Fluid Mechanics Pressure Pascal’s Law Pressure and Gravity Buoyancy

3. Physics 1B03summer-Lecture 12 3 -Includes liquids and gases. No resistance to “shear” (changes in shape), in equilibrium. -To describe mechanics of a continous fluid (instead of a discrete object), we use density, pressure instead of mass and force. -Dynamics is approached from an energy perspective (Bernoulli’s equation—next lecture). Fluids

4. Physics 1B03summer-Lecture 12 4 Density,  (“rho”), is mass per unit volume (kg/m 3 ). Specific Gravity (“SG”) is the ratio: (density of substance)/(density of water), which is a pure number (no units). Density Substance  SG  water 1000 kg/m 3 1 mercury 13600 kg/m 3 13.6 air 1.29 kg/m 3 0.00129 helium 0.18 kg/m 3 0.00018

5. Physics 1B03summer-Lecture 12 5 P  force per unit area unit: 1 N/m 2 = 1 pascal (Pa) Also, 1 atmosphere (atm) = 101.3 kPa Pressure Pressure is a scalar property of the fluid; the force is always exerted perpendicular to the surface in contact with the fluid. Forces exerted by the fluid

6. Physics 1B03summer-Lecture 12 6 Pascal’s Law: Pressure in an enclosed fluid in equilibrium is the same everywhere, except for differences due to gravity. Or, pressure changes are transmitted throughout a fluid in equilibrium without loss; there is no static friction in fluids. push here Pressure increases here as well

7. Physics 1B03summer-Lecture 12 7 Example: How hard do you need to push to lift a cement truck (weight w = 200 kN)? F 1 = ? piston, radius 5mm piston, radius 100mm w

8. Physics 1B03summer-Lecture 12 8 Pressure variation with depth h P1P1 P2P2 Pressure increases with depth, by an amount P 2 – P 1  gh (if  and g are uniform). Proof: Consider forces on a cylinder of fluid

9. Physics 1B03summer-Lecture 12 9 “Gauge Pressure” : pressure difference between a fluid and the surrounding atmosphere. It is equal to P 2 –P 1. Example: a tire gauge measures gauge pressure, and reads zero when the air inside the tire is at atmospheric pressure. “Absolute Pressure” is the pressure compared to vacuum. Zero absolute pressure means a vacuum. Example: the pressure on the surface of the earth.

10. Physics 1B03summer-Lecture 12 10 Example At what depth in water is the pressure 1 atm higher than the pressure on the surface? That is, where is P=2atms ?

11. Physics 1B03summer-Lecture 12 11 Example What is the difference in air pressure between the floor and the ceiling?

12. Physics 1B03summer-Lecture 12 12 Example What is the total mass of air directly above a 1-metre square, from ground level all the way to outer space? Approximately how thick is the atmosphere, assuming (incorrectly) that the air density is uniform?