Page 1 of 13

T2017

Unit 4 Pressure

Pressure depends on two things:

the Force (in Newtons) and

the Area it's pressing on (in square metres)

We work it out using: Pressure = Force ÷ Area

Pressure is measured in Pascals (Pa for short),

1 Pascal means 1 Newton per square metre Named after Blaise Pascal (1623- 1662), a French mathematician and physicist

Pressure in Liquids

Squeezing the top of a plastic bag with holes in

it causes the water to squirt out from all holes

Pressure acts equally in all directions

at a given depth.

If a can has holes at different levels, water

squirts out fastest from the bottom hole.

From above we can see that the

pressure in a liquid or gas, increases

with depth. Also the pressure depends

on the density of the fluid, the larger the density, the larger the pressure.

Pressure =Area

Force Force

Pressure x area

Pressure =Area

ForcePressure =

Area

Force Force

Pressure x area

Force

Pressure x area

Page 2 of 13

T2017

We can find the pressure due to a fluid using the relation……

Pressure = depth x density x gravity

or in short as

Pressure = hg

where h is the height (depth) and is measured in meters.

is the density and is measured in kg/m3.

g is the gravity and is measured in N/kg.

Fluid pressure on a surface is due to the force acting on a unit area by

the molecules of the fluid (liquid or gas) continuously hitting the surface.

The pressure does not depend on the shape of the container. The pressure at the bottom of each vessel is the

same even though the shape of the vessels is not the same.

Pressure in liquids, at the same level, is the same in all

directions.

The pressure done by a liquid increases if the density of the

liquid increases. Mercury whose density is 13600 kg /m3 does

more pressure than water which has a density of 1000 kg/m3.

liquid pressure depends on the density of the liquid and the height of the liquid.

Page 3 of 13

T2017

Using Pressure

1. Why do heavy loaded trucks have double wheels at

the back?

As the force done at the back of the truck is larger the double wheels produce a large area and so the force spreads and

produces less pressure on the ground.

2. Why do narrow stringed baskets hurt your hand?

The weight of the load in the basket pulling down will hurt your

hand as it acts over a small area. This produces a large

pressure that hurts your hand.

3. Why do football players wear slippers with studs?

The studs produce a very small contact area with the ground

producing a high pressure which increases the grip with the

grass, avoiding slipping.

4. Why a sharp knife is good at cutting things?

When the area is small, a moderate force can create a

very large pressure. When you push the very small area of

the sharp blade against something, it creates a really large

pressure.

5. Why do ice skates have sharp edges?

Sharp edges create a small area in contact with the ice, this

creates a very large pressure on the ice. Ice has an unusual

property: it can melt under pressure, even if it's below 0°C.

When you're ice skating, you're actually skating on a layer of

water that you've just melted, which quickly re-freezes when you move on .This means that there's very little friction as

you skate along.

Page 4 of 13

T2017

6. How can a thin supermodel damage wooden

parquet?

Even a slender supermodel can damage floors by walking on

then in high-heeled shoes. This is because the area of the heel is small, so you can easily create enough pressure to cause a

dent in the floor. The pressure can be greater than if an

elephant was standing there, even though the force is much

less. So you should be able to figure out why elephants and

camels have large feet.

7. Why do you feel ears hurting when you dive deep in

the sea?

As you dive deeper into a liquid, the pressure of the liquid increases. We need to remember this when designing the

walls of pools and dams: the wall must be thicker at the

bottom, to withstand the increased pressure down there.

8. Why do divers resurface gradually when deep

diving?

Divers which go at a very high depth down under the surface of

the water may suffer from pains called BENDS, if they quickly rise to the surface. The reason is that

in going up quickly, there is a rapid lowering of water pressure

on the body which will form nitrogen gas bubbles in the veins.

These gas bubbles, as the diver goes up increase in volume,

causing a lot of pain in the veins which may actually start

bursting, leading to death.

Page 5 of 13

T2017

Hydraulic machine We can use pressure in

liquids to move a piston

and do useful work. This

is how the hydraulic systems in diggers, car brakes and

fairground rides work: a pump creates pressure in an incompressible liquid, which acts on a piston. By adjusting

the area of the piston, we can adjust the force we get.

To understand how hydraulic machines work, it is important to

keep in mind these two things:

1. Liquids are almost incompressible.

2. Pressure is transmitted through the liquid.

Due to the liquid particles being quite

closely spaced, when applying a force

on a liquid, the liquid will not

compress (it will not decrease in

volume). The force applied will be

transferred from one place to

another. This means that pressure is

transferred in all directions in a liquid

equally.

A very important application which works on this fact is the

hydraulic machine. Examples where hydraulic machine is

used are the dentist’s chair, a hairdresser’s chair, hydraulic

jack to lift car and hydraulic brakes.

The simplest hydraulic machine is made up of:

A small area movable piston onto which you will do the

force. A large area piston from which the heavy load will be

lifted.

A connecting pipe between them filled with a liquid

(generally oil).

Page 6 of 13

T2017

Hydraulic Press

A multiplication of force can be achieved by the application of fluid

pressure according to Pascal's principle, which for the two pistons

implies

P1 = P2

This allows the lifting of a heavy load with a small force, as in an auto hydraulic lift, but of course there can be no

multiplication of work, so in an ideal case with no frictional

loss:

Winput = Woutput

Page 7 of 13

T2017

Automobile Hydraulic Lift

A hydraulic lift for automobiles is an example of a force

multiplied by hydraulic press, based on Pascal's principle.

The fluid in the small cylinder must be moved much further

than the distance the car is lifted.

For example, if the lift cylinder were 25 cm in diameter and the

small cylinder were 1.25 cm in diameter, then the ratio of the

areas is 400, so the hydraulic press arrangement gives a

multiplication of 400 times the force.

Page 8 of 13

T2017

Atmospheric Pressure

Air in the atmosphere above is exerting a pressure on us.

The atmospheric pressure at sea level is 101,000 Pa.

A person on a mountain has a small column of air above him

such that he feels a smaller pressure. On the other hand a

person at sea level will feel a larger pressure.

The atmospheric pressure varies with height. Just outside

the earth’s atmosphere the atmospheric pressure will be

zero.

The pressure of the atmosphere on you right now is around

101,000 Pa. OK, that's just a number, so think of it this way:

- you probably have a skin area of around 2 square metres,

- Pressure = force ÷ area, so force = pressure x area

thus the force on you = 100,000 x 2 = 200,000 Newtons.

That's about the same force as having over a dozen cars

piled on top of you! Why are you not feeling this force?

Page 9 of 13

T2017

Otto von Guericke, (1602-1686), a

German physicist, born in Magdeburg,

performed a famous experiment: the

"Magdeburg Hemispheres".

These were two halves of a large,

hollow metal ball. When all the air was

sucked out of the ball, two teams of

eight horses couldn't pull them apart,

because the pressure of the Earth's atmosphere created a very

large force on the ball.

Manometer is the instrument for measuring pressure in terms

of the difference in fluid levels between the vertical arms of a

glass U-tube.

Barometer is the instrument used to

measure atmospheric pressure.

The average atmospheric pressure at

sea level corresponds to 760 mm Hg

(which is the vertical height of mercury

in a barometer) or 10.336 m of vertical height of a water column. To correctly

measure the atmospheric pressure, the

space above the mercury level in a

barometer is essentially vacuum.

Page 10 of 13

T2017

Four States of Matter - Solid, Liquid, Gas, Plasma

Everything around us is made up of atoms.

Matter is defined as any material that has mass and occupies

volume.

A Solid has a rigid shape and constant volume . The forces

between molecules far outweigh the heat energy held by the

molecules, and so the molecules form a rigid structure (in

which they vibrate).

A Liquid has a constant volume but takes on the shape of it’s

container. The heat energy possessed by the molecules is more significant, but still not enough to allow them to completely

overcome the forces between them. As a result, the molecules

are free to move within the liquid, but only exceptionally fast

molecules can escape it.

A Gas fills any container it is placed in (no constant volume or

shape) . The heat energy between the molecules is greater

than the forces between the molecules, and so they move

randomly.

A Plasma forms when a gas is heated enough, then the

molecules lose their electrons, and the ions and atoms form

something similar to a gas, with random particle movement.

Most of the matter in the universe is plasma (that’s what you

make stars from) but most of the matter on earth is

solid/liquid/gas.

Page 11 of 13

T2017

Pressure in gases

Gases create a pressure on their containers, because of the gas

molecules colliding with the walls.

Increase in temperature = increase in pressure (volume

constant)

As a gas is heated its molecules gain kinetic energy, so they

increase in velocity and start hitting each other and the walls of

their container more frequently. This gives rise to an increase

in Pressure.

Decrease in volume = increase in pressure (

temperature constant)

When the volume of a fixed mass of gas is decreased the distance between the molecules of a gas and their container

decrease as well. Hence the rate of collision increases and so

does the pressure.

Pressure and the Weather

Regions where atmospheric pressure is lower then average are

called Cyclones while regions where atmospheric pressure are higher then average are called anticyclones. In these

anticyclones, winds circulate round the high pressure centre ,

spiralling outwards.

A decrease in pressure usually results in bad weather as winds

start blowing which move rain clouds.

Practical Effects of Pressure: RUBBER SUCKERS.

When the sucker is pressed into place, the air inside is forced out.The sucker is held in position by the high atmospheric pressure on the outside surface.

Page 12 of 13

T2017

THE COLLAPSING CAN.

When the air inside the can is cooled, its pressure decreases. The high atmospheric pressure outside exerts a great force on the can and causes it crashes.

SCUBA DIVING

Page 13 of 13

T2017

When the brake pedal is pressed, the piston of the master cylinder

applies a pressure on the brake fluid.This pressure is

transmitted uniformly to each cylinders at the wheel, cause the

pistons at the wheels to push the brake shoes to press against the

surface of the brake. The friction between the brakes and brake

shoes causes the vehicle to slow down and stop

Drinking straw: When you pull up water the pressure in the

straw will be reduced and the atmospheric pressure on the

water will be greater, pushing up the liquid.

Water bottle experiment: When a bottle is completely filled

with water and then put upside down in a container with water,

the water will not flow. This is because pressure of water inside

is equal to atmospheric pressure on the surface of the water.