PhysicsRox Chapter 3 Pressure

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╞╡§¥Physics SPM 2015 Chapter 3: Forces and Pressure

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CHAPTER 3: FORCES AND PRESSURE

3.1 Pressure

Pressure is the perpendicular force per unit area.

A

F P

where P = pressure [Pa]

F = force [N]

A = area [m2]

3.2

Pressure in Liquids

Pressure in liquids does not depend on the size or shape of the container, or the volume of the liquid. It is

affected by factors in the following formula:

g h P

where P = pressure [Pa]

h = height of liquid [m]

ρ = density of liquid [kg m-3

]

g = gravitational acceleration [m s-2

]

3.3

Atmospheric and Gas Pressure

3.3.1 Atmospheric Pressure

Atmospheric pressure is measured by barometers.

Mercurybarometer Aneroidbarometer

Atmospheric pressure measured by a simple mercury barometer can be calculated using the formula P=hρg.

Units of pressure

Unit Note

Pa SIunit

N m-2

EquivalenttoPa

N cm-2

cm Hg

m water

atm 1 atm = 1 bar = atmospheric

pressureatsealevelbar

Atmospheric

pressure at sea

level:

76 cm Hg

10 m water

100 000 Pa

1 bar

1 atm





For example:

Given that h = 76 cm and the density of mercury is

13 600 kg m-3

:

Answer:

Atmospheric pressure = 76 cm Hg

State the answer in Pascal:

P=hρg=0.76(13 600)(10) = 1 3 36 Pa

3.3.2

Gas Pressure

• Gas pressure can be measured using manometers and Bourdon gauges.

Manometer Bourdongauge

In manometers, pressure can be calculated based on pressure equilibrium.

For example:

Pressure at point A = Pressure at point C

Gas pressure = Atmospheric pressure + hρg





3.4 Pascal’s Principle

Pascal’s Principle states that pressure which is exerted onto the surface of a fluid in a closed container will be

transferred uniformly throughout the entire fluid.

2

2

1

1

A F

A F

All hydraulic systems are built based on Pascal’s Principle.

3.4.1

Practical Applications

Hydraulic jack When the lever is pushed downwards, valve A closes while valve B

opens.

Pressure is transferred to the larger cylinder and creates a large

force to lift the car.

When the lever is pulled upwards, valve B closes while valve A

opens. The hydraulic oil flows out from the tank to fill the space in

the small cylinder. As every movement downwards by the lever creates a small

movement upwards for the large piston, the lever needs to be

pushed and pulled repeatedly before the car can be raised to a

certain height required.

The car can be lowered down by opening the release valve so that

the hydraulic oil can flow back into the tank.

Hydraulic brake When the driver steps on the brake pedal, the piston in the main

cylinder transfers pressure through the hydraulic oil in the

cylinders.

Pressure is transferred uniformly through the hydraulic oil.

The pistons in the slave cylinders are larger, therefore a largeamount of force is transferred to the brake pads.

The brake pads transfer the large amount of force onto the disc so

that the rotation of the tire is slowed down.

Hydraulic pump A hydraulic machine uses a hydraulic pump to transfer hydraulic

liquid from one vessel into a large cylinder to create a movement.

The diagram shows a hydraulic pump used to move the arm of a

crane.

2 1

F 2 F 1





3.5

Archimedes’ Principle

rchimedes’ principle states that when an object is partially or fully immersed in a fluid, the object

undergoes a buoyant force which is equal to the weight of the fluid displaced

Buoyant force = Weight of fluid displaced

= V ρg

where V = volume of fluid displaced [m3]

ρ = density of fluid [kg m-3

]


]

If the object is floating stationary:

Weight of object = Weight of fluid displaced

mg=Vρg

3.5.1

Hydrometer

A hydrometer is used to measure the relative density of a liquid.

When the hydrometer floats stationary on the surface of the liquid,

Weight of the hydrometer = Weight of the liquid displaced

mg =Vρg

where m = mass of the hydrometer [kg]

V = volume of liquid displaced [m3]

ρ = density of liquid [kg m-3

]


]

The higher the hydrometer floats, the denser the liquid.

The lower the hydrometer floats, the less dense the liquid.

Weight of object

Buoyant force





3.5.2

Practical applications

Submarine

The buoyant force acting on the submarine is always the same because the weight of fluid displaced is

always the same.

When water is pumped into the ballast tank, the

weight of the submarine increases. When the weight

of the submarine is greater than the buoyant force,

the submarine sinks.

When water is pumped out of the ballast tank and

replaced with air, the weight of the submarine

decreases. When the weight of the submarine is less

than the buoyant force, the submarine floats.

Hot air balloon

A hot air balloon displaces a large volume of air.

When the weight of the balloon is less than the

upward thrust, the hot air balloon will move

upwards.

Ships

Ships are marked

with Plimsoll lines

at the sides as a

guide on the

maximum load the

ship can bear indifferent

conditions.

TF = Tropical freshwater

F = Freshwater

T = Tropical ocean

S = Summer ocean

W = Winter ocean

WNA = Winter in NorthAtlantic Ocean





3.6 Bernoulli’s Principle

Bernoulli’s principle states that when the speed of a flowing fluid increases, the pressure at that point

decreases.

Uniform tube Venturi tube

Water flows from high pressure to low

pressure.

The cross-section at B is the smallest, therefore water travels at

the fastest speed.The pressure at B is the lowest.

Speed at A and C are sthe same because they have the same

cross-section area. However, the pressure gradient still

decreases from A to C.

3.6.1

Practical Applications

Aerofoil

As the aerofoil shape cuts through

the air, the air is forced to travel at

a higher speed on top of the

aerofoil compared to below the

aerofoil.

The high speed area causes the air

to have low pressure.

Therefore, the higher pressure

area pressures against the aerofoil

towards the lower pressure area

causing a lifting force.

Carburetor

Carburetor mixes petrol and air

for burning in the engine

cylinder.

When air flows through the

narrower part of the tube, the

speed increases thus the

pressure decreases. An area with

low pressure is formed at X.

The atmospheric pressure, which

is greater, pushes the petrol out

from the jet.

Bunsen Burner

Gas flows out through the

narrow jet at a very high

velocity.

A low-pressured area is formed

at X.

The air outside at atmospheric

pressure flows in and mixes with

gas to light it.

Oxygen supply which is enough

from the air will ensure a

complete burning to produce a

hotter flame and less luminous.

END OF CHAPTER

PhysicsRox Chapter 3 Pressure

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