09Lesson - Pressure

St Josephs Institution

Physics Sec 3 Pressure

PressureSec-3Sec-3

Key ideas we will learn:

Define the term pressure, its formula, and SI unit

Pressure in liquid, its formula

Atmospheric pressure



Atmospheric pressure

Measuring pressure: barometer/manometer

Pressure transmitted through fluids



Definition: Pressure is defined as the force acting per unit area.

areaforcePressure =

m2)(inareaA

andN)in(forceF

pressurepwhere

AFp

=

=

=

=In symbols,

The SI unit of pressure is newton per square metre (N m-2) or pascal (Pa).



When we want pressure to be high



When we want pressure to be low



Example: A rectangular glass block of dimensions 30.0 cm by 50.0 cm by 10.0 cm

weighs 37.5 N. Calculate the least and the greatest pressure it can exert when

resting on a horizontal table.

50.0 cm10.0 cm

50.0 cm

30.0 cm10.0 cm

Greatest Pressure occurs

when the block is placed on

its smallest area.

Pmax = F / A

= 37.5 N / (0.10 m x 0.30 m)

= 1250 Pa

30.0 cm

Greatest Pressure occurs

when the block is placed on

its largest area.

Pmin = F / A

= 37.5 N / (0.30 m x 0.50 m)

= 250 Pa



Pressure in liquid



Liquids have weight (force) due

to the Earths gravitational pull.

Thus, a body of liquid exerts

pressure on an object placed in

it because of its weight.it because of its weight.

The deeper we go into the

liquid, the greater amount of

weight is above, hence the

greater the pressure.

Area, A

d1

d2

Area, A

WW



Consider a column of liquid of height h, base area A and density .

Volume, V = Ah

Mass of liquid, m = V

Weight of liquid, W = mg= (V)g= (Ah)g

Pressure, p = F

A=

(Ah)g

A

p = gh



Air is compressible.

Liquid is

incompressible.

Water rises into the

diver causes the

mass of diver to

increase.

Higher mass = Higher mass =

higher density

Hence diver sinks.



NOTE 1: The pressure of a fluid at a particular depth is independent of

the direction i.e. it is the same in all directions.

hp

pph

p

p

p

p

p

p

NOTE 2: The pressure acts perpendicular to the surface of the object.



NOTE 3: The pressure of a fluid at a particular depth does not depend

on the shape of the container, or the amount of fluid in the container.

For the 2 containers of different areas (A1 & A2),

the fluid pressure at depth h

= (A1h)g / A1 = (A2h)g / A2= gh h= gh

A1 A2

h

So the pressure at h for the same fluid is

exactly the same, regardless of the shape of

the container, or the volume of the container.

?4



h

1 2 3

?

5

A4A1 A2

For container 3, we only need to consider the column of fluid with cross-

sectional area A3. This will bring us back to the same pressure value as

containers 1 and 2.

A3

For container 4, we only consider column with area A4. Same rationale

for container 5.

A5



Final water levelWe start with a U-tube with

different water levels

Higher pressureLower pressure

Resultant force

Water from the right will rush

towards the left until pressure is

equalized.



This is why liquid, in whatever shape the container is, will

always settle at a common level.

Pascals vases



At equilibrium, pressures at A, B, C, and D are the same.

X X X X

A B C D



Atmospheric pressureAtmospheric pressure



Earths

atmosphere:

~100km (1.5% of

radius)

Atmospheric

Pressure

Radius of earth:

6,300 km



Source: http://www.stratosolar.com/

99% of air

is below

here



We have 30 km of air pressing on all of us on the surface

of the earth

Atmospheric Pressure

As a result, this layer of air exerts an atmospheric

pressure on us.

At sea level, this atmospheric pressure is

1.01325 x 105 N/m2 (or Pa), or about 100 kPa.

Thats about 10 N for every 1 cm2.

1.01325 x 105 Pa = 1 atmosphere

If ~100 kPa of pressure is acting on our

bodies, why dont we feel it?



Atmospheric Pressure example 1

Straw




Suction cup




Syringe



Example

Solution



Barotrauma

Volume of lung expands when

diver ascends from water

depths.

If volume in lung is not

equalized to pressure outside,

there will be rupture to the

lungs.



Measuring pressureMeasuring pressure



A mercury barometer is used

The mercury level in the tube

drops until it is about 760mm

vertically above the mercury level

in the trough.

The atmospheric pressure is

Measuring atmospheric pressure

The atmospheric pressure is

measured in mm Hg (millimeters

mercury)



The height of the mercury column does not depend on the diameter

or the angle of the glass tube.

When the tube is tilted at different angles, the vertical height

remains at 760mm as long as mercury has not filled up totally

At equilibrium, the pressure on the surface (i.e. along line ABC)

is equal to the atmospheric pressure of 1.013 x 105 Pa



At sea level, the height of the mercury column

level is found to be about 760 mm from the

mercury surface in the trough.

Atmospheric

pressure

h

At point B, atmospheric pressure is acting on

the surface of the mercury

Pressure at point A is the same as B. (At the

x x

A B

Pressure at point A is the same as B. (At the

same depth, pressure experienced is the same

between 2 points)

Atmospheric pressure (B), 1.013 x 105 pa = pressure exerted by the

column of mercury h cm in height (A).

1.013 x 105 pa = x g x h = 13.6 kg/m3 x 9.8 N/kg x h

h = 0.760 m = 760 mm



Example (class to try)

If the barometer is filled with water (density = 1000 kg/m3), how

high will the column h be? Take g = 10 N/kg

Atmospheric

h

Atmospheric

pressure

x x

A B



Example

Find the pressure at A, B, C, and D

Solution

The space above the mercury column is a

vacuum hence there is no weight acting at

point A. P = 0 cm Hg

A

B

h1

h2

h3

96

cm

50

point A. PA = 0 cm Hg

First we calculate the values of hs:

h1 = 96 50 cm = 46 cm

h2 = 96 20 cm = 76 cm

h3 = 96 10 cm = 86 cm

Hence,

Pressure at B, PB = 46 cm Hg

Pressure at C, PC = 76 cm Hg

Pressure at D, PD = 86 cm Hg

CD

20

10

Metre

rule



Measuring gas pressure the manometer

The manometer is an instrument used to measure the differences in

pressure of gases or liquids.

It consists of a U-tube containing a column of liquid (usually

mercury, water or oil).

The height difference in the liquid levels in both arms of the U-tube

helps us measure the pressure difference between the two sides.



At equilibrium, pressure at B and C must be equal since they are at the same

horizontal level.

PB = atmospheric pressure + pressure due to liquid column AC

PB = Po + hg

left right



Example

Manometer contains mercury ( = 13,600

kg/m3). Calculate pressure of the gas supply.

Pressure at point C

= pressure at point B

cm Hg



Example (class to try)The pressure of a gas is pg. If

atmospheric pressure is 76 cmHg,

find the value of pg (express answer

in cmHg).pg

A B



Hydraulic system:Hydraulic system:

Transmitting pressure through fluid



Hydraulic system: Transmitting pressure through fluid

A hydraulic system uses 2 properties of fluid:

Liquids are incompressible

If pressure is applied to an enclosed liquid, the pressure is

transmitted to all parts of the liquid

Pascal's law states that pressure exerted anywhere in a confined incompressible

fluid is transmitted equally in all directions throughout the fluid such that the

pressure ratio (initial difference) remains the same.



If a force Fx is

applied at piston 1:

px =Fx

Ax

This pressure is transmitted to every part of the liquid.

piston-1piston-2

This pressure is transmitted to every part of the liquid.

= py =Fy

Ay

px =Fx

Ax

This pressures is felt at piston 2: Fy

Aypy =

Fx

Ax

=Fy

Ay



Fx

Ax

=Fy

Ay

FAx

=FyAy

FxAx

Since Ay > Ax, this means that Fy > Fx

This shows that a small force (Fx), applied at a small

piston, can lift a large load, on a bigger piston.

F



Remember that conservation of energy applies:

Work done at piston 1 = work done at piston 2

Fx x dx = Fy x dy



Example (class to try)

A force of 50N is applied to the small

piston, of area 0.01 m2. What is the

force experienced at the larger piston,

of area 0.20 m2?

F1

F2

If smaller piston moved by 10cm,

what would larger piston have moved?

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09Lesson - Pressure

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