PRESSURE

pRESSURE Pressure is defined as the (perpendicular) force acting on per unit area. The unit of the pressure is Pascal (Pa). 1 Pascal is the pressure applied by 1 Newton of force pushing over an area of 1m2.

Example: A book weighing 18N has a 0.06m2 cover surface and lies on a table. What is the pressure of the book? If we place an encyclopedia of 52 N on the book, what will be final pressure be?

Example: A 400 N girl whose total shoes area is 0.05 m2 stands on the floor. What is the pressure exerted by the girl on the floor?

Example: Find the pressure exerted on the table by 48 N box for the two different positions shown in the figures.

Liquid pressure The solids transmit force in the same direction but the Liquids (in equilibrium) transmit pressure equally in all directions. The statement is known as Pascal principle.

HydraulIc LIFT The hydraulic lever takes advantage of Pascal’s principle to lift heavy objects with a small force. PA=PB

Example in order to lift the car, what must be weight of the object? Wcar=1200kgf

Gas pressure air pressure Like liquids, gases also exert pressure on the walls of a container. A gas can be compressed easily into a small volume, causing an increase in its pressure. air pressure The molecules in the air have weight. Therefore they exert force on the earth surface, the force exerted per unit area on a surface by the weight of air is called air pressure.

Measurement of pressure Manometers The open tube manometer is used to measure the pressure of a gas trapped in a closed container. The pressure at points A and B must be equal, PA=PB Pgas=Patm+PHg if, for example the open air pressure is 76 cm-Hg and the height of the mercury column on the right is measured to be h=10cm, then the pressure of the gas inside the balloon is 86 cm-Hg.

Pgas=P0 – h Pgas=P0 – h x ρliq x g If the liquid is different from mercury; Pgas=P0 – h x ρliq x g

Example: Calculate the pressure of the gas in the container.

Example: What is the pressure of the gas if h=14 cm.

Bernoulli’s principle If the speed of a fluid increases, its pressure decreases.

P1V1 P2V2 P1V1=P2V2=P3V3… Boyle’s law At a constant temperature, volume and pressure are inversely proportional. P1V1=P2V2=P3V3… P1V1 P2V2

Archimedes’ principle The magnitude of the lifting force applied by a liquid upon an object was first formulated by Archimedes more than 2000 years ago. The weight of an object in air is called its actual weight and in water, apparent weight. Archimedes Principle: A body sunk in a liquid is pushed up by a force equal to that of the weight of the liquid displaced. Fbuoyant= Vsunk.dliquid. g Fbuoyant=Weight of displaced liquid Fup=Actual Weight – Apparent Weight

example An object weighs 120 000 N in air and 80000 N (when completely immersed) in water. What is the density of the object? Ans:3000 kg/m3

example What percent of the total volume of a piece of ice will float on the surface of water? Density of ice and water are 900 kg/m3 and 1000 kg/m3, respectively. Ans: 10%

example An object weighs 45 N in air and 30 N in water. What is the volume and density of the object? Ans: dobject=3000kg/m3 Vobject=0.0015 m3

example 3.0 N An object of 3.6 N weighs, 3 N in water and 2.4 N in a liquid. What is the density of the liquid? Ans: dliquid=2000kg/m3