Pressure

1. Pressure Textbook Chp 7 Pg 123-142

2. Topics • Definition of Pressure • Hydraulic Press • Liquid Pressure • Atmospheric Pressure • Mercury Barometer • Manometer

3. Definition of Pressure • Pressure is define as the Force acting per unit area • Pressure = Force/Area • S.I. Units of Pressure: Pascal (Pa) • 1 Pascal = (1 Newton)/(1 m2)

4. Video • When you push a balloon into one nail the balloon pops. • What happens when you push a balloon into a bed of nails? • http://www.youtube.com/watch?v=vo2iE94iAoA • How do you explain why it is harder to pop the balloon with a bed of nail?

5. Common Mistakes!! • Sometimes we are concerned about the pressure caused by the weight of an object • Recall that weight = mg • Sometimes student just consider “m”, not “mg” • Also, remember to convert all units to S.I. units before you do calculations

6. Worked Example 1 • A cube has mass of 2 kg, and has the dimensions 10 cm by 10 cm by 10 cm. Determine how much pressure it exerts when it is placed on a flat surface. • Base Area = (0.1 m)(0.1 m) = 0.01 m2 • Weight = mg = (2)(10) = 20 N • Pressure = F/A = 20/(0.01) = 2000 Pa

7. Hydraulic Press • A hydraulic press is a machine which allows someone to lift a heavy object using less force. • There are two arms of a hydraulic press, one arm is used to exert force downwards, another arm is used to lift a heavy object Heavy Object Force Fluid

8. Hydraulic Press • The principle behind the hydraulic press is: • Pressure in left arm = Pressure in right arm • Since Pressure = Force / Area • (Forceleft/Arealeft) = (Forceright)/(Arearight) • Note: Area refers to the cross-sectional area of each arm

9. Extra Info: • (not in syllabus) • the brakes of a car work using a modified hydraulic press • for Alice only: what is a brake drum? • When the brake pedal is pressed by the driver, it pushes hydraulic fluid which in turns exerts a force on the brake drum (which is attached to the wheel). The friction caused by this force causes the wheel to slow down or stop spinning (i.e. to brake)

10. Worked Example 2 • A hydraulic press is used to lift up a car of mass 2000 kg. If the car is placed on a right piston of area 5 m2, and the left piston has an area of 0.01 m2, calculate the downward force on left piston required to lift the car. • (Forceleft/Arealeft) = (Forceright)/(Arearight) • F/(0.01) = mg/(5) • F/(0.01) = (2000)(10)/(5) • F = 40.0 N (3 sf)

11. Liquid Pressure • Why can’t you wear a normal wetsuit to go deep sea diving? • Where does this water pressure come from? • Pascal Vases demo Normal Diving Wetsuit up to 40 m underwater Atmospheric Diving Suit up to 600 m underwater

12. Liquid Pressure • Pascal Vases show that liquid pressure does NOT depend on the volume of liquid • but instead depends on the height (or depth) of liquid • Equation for liquid pressure • P = ρgh • Liquid pressure is dependent on 3 things: • density of the liquid (ρ) • gravitational field strength (g = 10 ms-2) • height/depth of the liquid (h)

13. Worked Example 3a • A measuring cylinder is filled with water (density = 1000 kgm-3) and is quickly turned upside down and placed on a table. If the height of the column of water is 10 cm, determine the liquid pressure at the bottom of the water. • P = ρgh • = (1000)(10)(0.10) • = 1000 Pa 10 cm X

14. Worked Example 3b • The same setup is repeated except that instead of water, liquid mercury (13 500 kgm-3)is used to fill the measuring cylinder. What is the pressure at the bottom of the mercury? • P = ρgh • = (13500)(10)(0.10) • = 13500 Pa 10 cm X

15. Video • 1) some water is placed inside a steel drum and is heated up – becomes steam • 2) steel drum is then sealed, and placed in ice water • What do you think happens to the steel drum? • http://www.youtube.com/watch?v=nNXuk2RdULY • What was the force responsible for crushing the steel drum?

16. Atmospheric Pressure • When you are surrounded by liquid (e.g. underwater) you will be under liquid pressure • Similarly, when you are surrounded by air, you are under air pressure • Right now, air is pushing against you and your skin!! • Atmospheric air pressure is approximately 105 Pa, sometimes referred to as “1 atm” • Air pressure varies with height (at the top of Mount Everest, air pressure is only 30 000 Pa)

17. What happened to the steel drum? • Water is heated until it boils and turns to steam • Steam pushes out the original cold air in the drum and replaces it with hot steam • When the drum is sealed, the gas in the drum is primarily hot steam • When placed in ice water, the hot steam in drum condenses to form water • Since water takes up much less volume than steam, when steam condenses the pressure inside the drum drops significantly • Atmospheric pressure outside the drum is much higher than pressure inside the drum, crushing it

18. Previously… • Demo 1: Drinking water from a straw • When you “suck”, you are lowering the air pressure inside your lungs to below atmospheric pressure • Because atmospheric pressure is now greater than the air pressure in your lungs, air exerts a force on the exposed part of the water, pushing it up the straw

19. Previously… • Demo 2: hole at bottom of water bottle • When the cap of the water bottle is open, atmospheric pressure pushes down on the water surface (in addition to liquid pressure), pushing water out through the hole at the bottom of the water bottle • When the cap of the water bottle is closed, atmospheric pressure is no longer pushing down on the water surface. • Instead, it is pushing the water through the hole, preventing water from coming out.

20. Previously • Demo 3: Cup of water turned upside down • air pressure pushing the card upwards is greater than the liquid pressure pushing the water downwards

21. Previously… • Demo 4: removing water from fish tank • Hose is filled with water (no air inside). When one end of the hose is removed from the tap and allowed to drain, the liquid pressure (i.e. ρgh) pushes the water out of the low end of the hose • When the water starts to drain from the hose, atmospheric pressure pushes on the exposed surface of the water in the fish tank, pushing it up the hose (similar to how water is pushed up the straw in Demo 1)

22. Mercury Barometer • A device which measures air pressure is called a barometer • For your syllabus, you are required to know how a very low-tech barometer works – the mercury barometer • [not in syllabus] because of the poisonous nature of mercury, mercury barometers are no longer produced since 2007 Modern weather barometer Mercury Barometer

23. Mercury Barometer • works using the principle of liquid pressure, P = ρgh • Atmospheric pressure is calculated using ρgh where h is the height of the column of mercury in the glass • Note that the space in the tube above the mercury is compete vacuum (i.e. absolutely nothing, no air) • Atmospheric pressure is around 760 mm (76 cm) of height of mercury

24. Did You Know? • (not in syllabus) • When you take an aeroplane, just after take-off, the aeroplane intentionally lowers the air pressure in the cabin (from 100 kPa to 65 kPa). This drop in pressure is what causes ears to “pop” sometimes. • The air pressure outside the plane is even lower (around 20 kPa) • When the plane lands, the air pressure in the cabin increases back (from 65 kPa to 100 kPa).

25. Manometer • A manometer is a measuring instrument which measures the pressure of an enclosed gas • It is made of a U-shaped tube with some liquid inside • It has two arms – one attached to the enclosed gas and another left exposed (to atmospheric pressure)

26. Manometer • If pressure of gas is same as atmospheric pressure, the liquid level in left arm = liquid level in right arm • If pressure of gas is higher than atmospheric pressure, the liquid level in left arm is lower than liquid level in right arm • If pressure of gas is lower than atmospheric pressure, the liquid level in left arm is higher than liquid level in left arm

27. Manometer • Principle of manometer – at the same height, total pressure in left arm is same as total pressure in right arm • Total pressure of left arm = pressure of enclosed gas + ρgh(if any) • Total pressure of right arm = atmospheric pressure + ρgh(if any) • The difference in pressure between enclosed gas and atmospheric pressure = ρgh

29. Important Note • Even though the SI units of pressure is Pa, because the barometer and manometer measure pressure in terms of height, • Sometimes, you may be asked to give pressure in terms of height as well (e.g. the pressure is 760 mm of Mercury, the pressure is 4 cm of water, etc.)

30. Worked Example 4a • Mercury level in left arm = 300 mm • Mercury level in right arm = 400 mm • Px >Pair • Difference in pressure = ρgh • Px - Pair = ρgh • Px= Pair+ ρgh • Px = 760 mmHg + 100 mmHg • Px = 860 mmHg

31. Worked Example 4a • If atmospheric pressure is 760 mm Hg, what is the pressure of gas X in terms of mm Hg? Gas X

32. Worked Example 4b • If the density of mercury is 13 500 kgm-3, calculate the pressure of gas X in terms of Pascals. • Answer to 4(a): 860 mm Hg • h = 860 mm = 0.86 m • ρgh= (13500)(10)(0.86) = 116 000 Pa (3 sf)

33. Summary • Pressure is Force per unit Area; P = F/A • In a hydraulic press, • pressure in left arm = pressure in right arm • FL/AL = FR/AR • Liquid Pressure; P = ρgh • Atmospheric Pressure • Mercury Barometer • Manometer • Difference in pressure (btn left arm and right arm) = ρgh

34. 10 min pop quiz! Again! MUAHAHAHAHA