physics notes_ pressure

7/24/2019 Physics Notes_ Pressure

1/11

1

Pressure, p

Definition: Pressure is defined as theforce acting normallyper unitsurface area.

NB: Normally means: force must be perpendicular (at right angle) to the area of contact.

NB: The pressure depends on the force and the area.

(surface area) The unit is Pascal Pa

p=F

A

Where 1 Pascal is equal to Neton per meter square (N

m2 ) or Nm!"

#f there is a change in pressure of a liquid or gas it causes it to mo$e (to balance out the

difference in pressure).

Pressure is dependent on the $olume of the substance.

When a can is normal% the pressure inside is equal to the pressure outside.

1Pa=1N

m2

#f e rearrange the formula for pressure e get a useful formula for calculating force:

force=pressure area

F=pA

There are many other units of pressure in e$eryday use% for e&ample:

'tmospheres of pressure number of times a pressure is greater than atmospheric

pressure.

mm of mercury gas pressure read on a mercury barometer

Pounds per square inch% is an old unit still used for stating pressure for car tyres etc.

Prepared by: Mr. L. Adams G.H.S. Physics Notes: Pressure

AP


2/11

2



3/11

3Pressure in Solids

Pascal Pressure hen a force of 1N is acting on a surface area of 1 m"

Pressure and *orce is not the same term.

Pressure is directly proportional to the force but in$ersely proportional to the area

p F directly proportional

p 1

A in$erse proportionality

+maller area the greater the force

E.g.: ' bo& ith dimension , & - & " ith a mass of -/g. What is the least pressure the bo&

ill e&ert on the ground0

p=F

A

F=mg

48kg 10N kg1

480N

To get the least pressureP

1

A therefore you need the greatest area to get the smallest

pressure. Therefore% 64=24 largest force

480N

24 " Pa 23

480N

62 480

12 - Pa 23

480N

24 480N

8 , Pa



4/11

! Therefore% the loest pressure e&erted ould be " Pa at , & -side

The Pressure e&erted by solids depends on the surface area. #t is an in$erse relationship.



5/11

"Pressure in Fluids

*luids also e&ert pressure.

*luid pressure depends on the folloing factors:

4epth 5elo surface

4ensity of the fluid

The pressure in a liquid at a certain le$el is proportional to the height of liquid abo$e that le$el.

NB:The pressure in a liquid increases ith the depth belo its surface.

Pressure and Depth

The pressure is caused by the eight of the liquid in the container% at particular depths.

Pressure and Direction:

NB: The pressure in a liquid is equal in all directions at the same depth.

Pressure and Liquid Density

#f the pressure is measured at the same depth belo the surface of different liquids e find that:

The pressure is proportional to the density of the liquid.

Liquid levels

The liquid pressure depends only on the height of the particular liquid and not on the

shape or width of the tube.

When a liquid is poured into a set of connected tubes of $arious shapes the liquid flos round the

tubes until all the liquid surfaces are all at the same le$el. The pressures at the open tops of the

tubes are all the same% being the air pressure. The liquid pressures at the bottom of each tube

must be equal otherise the liquid ould flo to equali6e the pressures.

7$en though the tubes ha$e different shapes and different cross!sectional areas% for pressures at

the bottom of the tubes to be equal% they require only the same $ertical height h of the same

liquid.



6/11

#

! Pressure does not depend on the shape of the container

! 'll points on the same hori6ontal le$el in a liquid at rest ha$e the

same pressure! Pressure acts in all directions

! Pressure increases ith depth

! Pressure is directly proportional to the density of a liquid

Calculating Pressure in a Liquid

The $olume 8 of the liquid in the column is gi$en by:

volume=base area height

V=A h

The mass m of the liquid of density 9 is gi$en by:

mass=density volume

m= V

The eight W of the liquid is gi$en by: W=mg

W=mg=(V)g=(Ah)g

The pressure at the base of the liquid column is found from:

Pressure=normal force

area =

W

A

p=AhgA

=hg

p=hg



7/11

$The pressure belo a liquid surface is proportional to the height h of liquid abo$e and the

density% 9 of the liquid.

The pressure is independent of the area.

NB: the formula does not include any air pressure acting on the surface of a liquid. #t gi$es the

e&tra pressure in the liquid at a depth hbelo its surface.

The pressure due to the height of the fluid (liquid and gas) only also calledExcess Pressure is

calculated by:PF=PE=hg (h!height% 9!rho% g!gra$itational acceleration)

P& Patmospheric P7&

'lso called ;ydrostatic pressure because the fluid is at rest

Proof: P7& h 9 g

P=F

A

F=mg

=m

v sincem=v

andF=vg

ThenP=

v g

A

5ut 8olume is 'rea & h

v=Ah

P=

vg

A

P= Ahg

A +ubstitutev !ith Ah

P=hg

The pressure in a fluid is independent of 'rea (not needed).



8/11

%N5: Pressure is the same at the same hori6ontal

N5: Pressure is independent of the shape of the container% pro$ided that it is on the same plain.

ydraulic Brea!ing Syste"Pascals Law:

The pressure applied to any point of a fluid in a closed #essel is trans"itted equally

to e#ery point in the fluid.

The bra/es system of a car is an e&ample of the ;ydraulic iquids are uncompressible

! >iquid pressure acts equally in all directions at the same le$el

! #f pressure is applied to a trapped liquid% the pressure is transmitted to all parts of the liquid

'n ad$antage to this is the ability to magnify a force by using a piston of larger area.

Psmall piston=Plarge piston



9/11

&F1

A1=

F2

A2

F1=

F2A

1

A2

F2=

F1A

2

A1

A1=

F1A

2

F2

A2=

F2A

1

F1



10/11

1'Pressure due to gases

The pressure of solids and liquids can be attributed to their eightbut the eight of a gas is $ery

small to compare ith that of a solid or a liquid.

'tmosphere is a combination of many gases this causes a eight hich causes Atmospheric

Pressure.

#nstead e attribute the pressure of gases in a container e.g. 5alloon to the collision of the air

molecules ith the balloon alls. The molecules of a gas are at constant random motion. 's the

molecules mo$e around they stri/e the alls of the balloon and rebound from it. 't each

collision there is a change in momentum% this change in momentum per second results in a

normal forceon the inner alls of the balloon. This force actsper unit surface areahence

resulting in a Pressureon the alls of the balloon.

?ollisionmomentum per secondnormal force acting per unit surface area pressure

Ek=1

2mv

2

#f $elocity changes then momentum changes

P=mv

+econd la

F=ma

or

F=A P

t

there is a normal force acts per unit area

F

A

hich creates a pressure

%t"ospheric Pressure

The atmospheric pressure is as a result of the eightof all the gases in the atmosphere. 's you

go up air gets thinner% density decreases and pressure decreases because p=h g

+ince the pressure of the liquid inside the tube is equal to the pressure in the liquid in the through

hich is equal to the atmospheric pressure. Then the height of the liquid inside the tube can be

used to determine the atmospheric pressure.

&'( Tube $ano"eter



11/11

11@sed to measure the e&cess gas pressure .i.e. the pressure due to the height

Pressure of the ater is equal at the same le$els of height

%rchi"edes Principle

This principle states for a body fully or partially immersed in a liquid the up thrust experienced

by the body is equal and opposite to the weight of the fluid displaced by the obect!

The up thrust is the upard force acting on the submerged body caused by the difference in

pressure. 'rchimedes principle is used to e&plain hy obAects float.

The principle of floatation states that a floating body displaces its own weight in the fluid in

which it floats that is;

The eight of fluid displaced the eight of the obAect

@p thrust of force eight of fluid displaced

W>" sink

">W rising

The density of the fluid depends on hether the obAect floats or sin/s.

%rchi"edes Principal %nd )aw of Flotation

Archimedes Principle states that the upthrust on an object wholly or partially immersed in a

fluid is equal and opposite to the weight of the fluid displaced by the object

Law of !lotation states that a floating object displaces its own weight of the fluid in which it is

placed


physics notes_ pressure

Documents