1. PHY 231 1 PHYSICS 231 Lecture 22: Pressure Remco Zegers Walk-in hour: Thursday 11:30-13:30 am Helproom

2. PHY 231 2 Previously Solids: Young’s modulus Shear modulus Bulk modulus Also fluids P=F/A (N/m 2 =Pa)  =M/V (kg/m 3 ) General:

3. PHY 231 3 Force and pressure A P=0 Vacuum Air (P=1.0E+5 Pa) F What is the force needed to move the lit?

4. PHY 231 4 Magdeburg’s hemispheres Otto von Guericke (Mayor of Magdeburg, 17th century)

5. PHY 231 5 Pressure vs Depth Horizontal direction: P 1 =F 1 /A P 2 =F 2 /A F 1 =F 2 (no net force) So, P 1 =P 2 Vertical direction: F top =P atm A F bottom =P bottom A-Mg=P bottom A-  gAh Since the column of water is not moving: F top -F bottom =0 P atm A=P bottom A-  gAh P bottom =P atm +  gh

6. PHY 231 6 Pressure and Depth: P depth=h =P depth=0 +  gh Where: P depth=h : the pressure at depth h P depth=0 : the pressure at depth 0  =density of the liquid g=9.81 m/s 2 h=depth P depth=0 =P atmospheric =1.013x10 5 Pa = 1 atm =760 Torr Pascal’s principle: If P 0 changes then the pressures at all depths changes with the same value.

7. PHY 231 7 A submarine A submarine is built in such a way that it can stand pressures of up to 3x10 6 Pa (approx 30 times the atmospheric pressure). How deep can it go?

8. PHY 231 8 Does the shape of the container matter? NO!!

9. PHY 231 9 Your homemade pressure difference meter (PART I) P depth=h =P depth=0 +  gh Part 2 on Friday! h1h1 h2h2

10. PHY 231 10 Pascal’s principle In other words then before: a change in pressure applied to a fluid that is enclosed in transmitted to the whole fluid and all the walls of the container that hold the fluid. P=F 1 /A 1 =F 2 /A 2 If A 2 >>A 1 then F 2 >>F 1. So, if we apply a small force F 1, we can exert a very large Force F 2. Hydraulic press demo

11. PHY 231 11 Hydraulic brake 6.4cm 2 1.8 cm 2 F=44N R=0.34 m coef of friction: 0.5 What is the frictional torque about the axle exerted by the shoe on the wheel drum when a force of 44N is applied to the pedal?

12. PHY 231 12 Pressure measurement. The open-tube manometer. The pressure at A and B is the same: P=P 0 +  gh so h=(P-P 0 )/(  g)

13. PHY 231 13 Pressure Measurement: the mercury barometer P 0 =  mercury gh  mercury =13.6E+03 kg/m 3  mercury,specific =13.6

14. PHY 231 14 Pressure at different altitudes The pressure in the lecture room equals 1 atm (1.013E+05 Pa). What will the pressure on the 6th floor of the BPS building be (h=20m)? And at the top of mount Everest (h=8500 m)?