Pressure

PressureTextbook Chp 7 Pg 123-142TopicsDefinition of PressureHydraulic PressLiquid PressureAtmospheric PressureMercury BarometerManometerDefinition of PressurePressure is define as the Force acting per unit areaPressure = Force/AreaS.I. Units of Pressure: Pascal (Pa)1 Pascal = (1 Newton)/(1 m2)VideoWhen 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=vo2iE94iAoAHow do you explain why it is harder to pop the balloon with a bed of nail?Common Mistakes!!Sometimes we are concerned about the pressure caused by the weight of an objectRecall that weight = mgSometimes student just consider m, not mgAlso, remember to convert all units to S.I. units before you do calculations

Worked Example 1A 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 m2Weight = mg = (2)(10) = 20 NPressure = F/A = 20/(0.01) = 2000 Pa

Hydraulic PressA 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 objectFluidForceHeavy ObjectHydraulic PressThe principle behind the hydraulic press is:Pressure in left arm = Pressure in right armSince Pressure = Force / Area(Forceleft/Arealeft) = (Forceright)/(Arearight)Note: Area refers to the cross-sectional area of each armExtra Info:(not in syllabus)the brakes of a car work using a modified hydraulic pressfor 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)Worked Example 2A 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)Liquid PressureWhy cant 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 underwaterAtmospheric Diving Suit up to 600 m underwaterLiquid PressurePascal Vases show that liquid pressure does NOT depend on the volume of liquid but instead depends on the height (or depth) of liquidEquation for liquid pressureP = ghLiquid pressure is dependent on 3 things:density of the liquid ()gravitational field strength (g = 10 ms-2)height/depth of the liquid (h)Worked Example 3aA 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 = gh= (1000)(10)(0.10)= 1000 Pa

10 cmXWorked Example 3bThe 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 = gh= (13500)(10)(0.10)= 13500 Pa

10 cmXVideo1) some water is placed inside a steel drum and is heated up becomes steam2) steel drum is then sealed, and placed in ice waterWhat do you think happens to the steel drum? http://www.youtube.com/watch?v=nNXuk2RdULYWhat was the force responsible for crushing the steel drum?

Atmospheric PressureWhen you are surrounded by liquid (e.g. underwater) you will be under liquid pressureSimilarly, when you are surrounded by air, you are under air pressureRight now, air is pushing against you and your skin!!Atmospheric air pressure is approximately 105 Pa, sometimes referred to as 1 atmAir pressure varies with height (at the top of Mount Everest, air pressure is only 30 000 Pa)What happened to the steel drum?Water is heated until it boils and turns to steamSteam pushes out the original cold air in the drum and replaces it with hot steamWhen the drum is sealed, the gas in the drum is primarily hot steamWhen placed in ice water, the hot steam in drum condenses to form waterSince water takes up much less volume than steam, when steam condenses the pressure inside the drum drops significantlyAtmospheric pressure outside the drum is much higher than pressure inside the drum, crushing it

PreviouslyDemo 1: Drinking water from a strawWhen you suck, you are lowering the air pressure inside your lungs to below atmospheric pressureBecause 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

PreviouslyDemo 2: hole at bottom of water bottleWhen 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 bottleWhen 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.PreviouslyDemo 3: Cup of water turned upside downair pressure pushing the card upwards is greater than the liquid pressure pushing the water downwards

PreviouslyDemo 4: removing water from fish tankHose 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. gh) pushes the water out of the low end of the hoseWhen 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)

Mercury BarometerA device which measures air pressure is called a barometerFor 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 BarometerMercury Barometerworks using the principle of liquid pressure, P = ghAtmospheric pressure is calculated using gh where h is the height of the column of mercury in the glassNote 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

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).

ManometerA manometer is a measuring instrument which measures the pressure of an enclosed gasIt is made of a U-shaped tube with some liquid insideIt has two arms one attached to the enclosed gas and another left exposed (to atmospheric pressure)

ManometerIf pressure of gas is same as atmospheric pressure, the liquid level in left arm = liquid level in right armIf pressure of gas is higher than atmospheric pressure, the liquid level in left arm is lower than liquid level in right armIf pressure of gas is lower than atmospheric pressure, the liquid level in left arm is higher than liquid level in left armManometerPrinciple of manometer at the same height, total pressure in left arm is same as total pressure in right armTotal pressure of left arm = pressure of enclosed gas + gh (if any)Total pressure of right arm = atmospheric pressure + gh (if any)The difference in pressure between enclosed gas and atmospheric pressure = gh

Important NoteEven 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.)Worked Example 4aMercury level in left arm = 300 mmMercury level in right arm = 400 mmPx > PairDifference in pressure = gh Px - Pair = ghPx = Pair + gh Px = 760 mmHg + 100 mmHgPx = 860 mmHgWorked Example 4aIf atmospheric pressure is 760 mm Hg, what is the pressure of gas X in terms of mm Hg?

Gas XWorked Example 4bIf 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 Hgh = 860 mm = 0.86 mgh = (13500)(10)(0.86) = 116 000 Pa (3 sf)SummaryPressure is Force per unit Area; P = F/AIn a hydraulic press, pressure in left arm = pressure in right armFL/AL = FR/ARLiquid Pressure; P = gh Atmospheric PressureMercury BarometerManometerDifference in pressure (btn left arm and right arm) = gh 10 min pop quiz!Again! MUAHAHAHAHA