Pressure 10

Pressure





















❑ Introduction to pressure


❑ Pascal’s law and its application


❑ Archimede’s principle and its application


❑ Law of flotation and its application


❑ Simple numerical problems related to Pascal’s law and Archimede’s

principle


❑ Introduce atmospheric pressure and explain its application

• Pressure: The force applied perpendicular to the

surface per unit area is called pressure.



• Pressure(P) = ( )

( )

2
• SI unit of pressure is Pascal( N/m ).






• The formula shows that pressure is directly


proportional to the force applied and inversely

proportional to the area.






• Factors affecting pressure are :


❑ Force applied


❑ Surface Area

To Prove P = F/A



Proof: Let us consider ‘F’ be the force applied in per unit area of a surface A . Then
according to definition,

Pressure is directly proportional to the force applied.


i.e. p α F ………….(i)

And Pressure is inversely proportional to the surface area.

i.e. p α 1/A ………….(ii)


Combining relation (i) and (ii) we get,



P α F/A



Or, P = K F/A, where K is a proportionality constant.



When , F= 1 N, A= 1 m , then the pressure exerts is 1pa and k= 1.
2




There fore, =


•1 Pascal pressure: when one newton force is applied


2
on an object to travel 1 m surface area then it is

2
called 1 Pascal pressure.(1 Pa = 1 N/1 m ).








•Pressure is scalar quantity, though it is the



perpendicular force per unit area. In the case of


liquid, the pressure is exerted equally in all


directions, which means that pressure has no



definite direction.

Force (Thrust) Pressure


•Force is a push or pull •Pressure is the force per


acting on a body. unit area of the surface .


•It is independent of the •It depends upon the area


area over which the on which the force is


force is applied. applied.



•It is measured in •It is measured in pascal


newton(N). (Pa).


•It is vector quantity. •It is scalar quantity.



some application of pressure


Nails or needles are made pointed.

➢ Pointed parts of nails or needles cover less area. when area


is less, it exerts more pressure and vice versa. Since

1
pressure is inversely proportional to area (i.e.. P∝ )


keeping force constant. With the increase in pressure of

needles or nails it becomes easier to penetrate on the wall


or to sew clothes, respectively. Hence, nails are made


pointed.

Foundation of building is made wider.


➢ when foundation of building is made wider it covers more

area. when area increases, pressure decreases. Since


1
pressure is inversely proportional to the area (i.e.. P∝ )

keeping force constant. With the less pressure the building


will stand steadily and do not get destroy. Hence

foundation of building is made wider.

Heavy loaded trucks are provided with paired wheels.

➢ Heavy loaded trucks are equipped with huge masses of loads


that puts huge pressure on the tyre of vehicles by which it


may burst. Pair wheels cover large area on the road. Increase

in area decrease pressure and vice-versa. Since, pressure is


inversely proportional to area keeping force constant. When


pressure is decreased then the heavy loaded truck can run

smoothly on road with less possibility of bursting of tyres by


more pressure.





Hermit sleep on bed of nail.


➢ Pointing nails facing upward is kept making a bed which

covers more area. When area increases, pressure decreases.

1
Since, pressure is inversely proportional to the area (i.e.. P∝


) keeping force constant. When pressure decreases hermit

can sleep easily on the bed of nails with no pain. Hence, it is


said that hermit can sleep on the bed of nails.

Tanks are provided with metallic belt over sharp toothed wheel.


➢ Tanks are used to move during the war. It carries heavy load

along with during the warfare. Heavy load in the tank


increases the forces that causes to increase pressure. Since,

pressure is directly proportional to the force keeping area


constant. Very high pressure developed on the wheel can


cause the tank to get descent on the land. In order to prevent

from possible descent, they are provided with wider metallic


chain which cover more area. Increase in area decreases the


pressure and prevents the tank from getting descent.





It is easier to swim in sea or ocean than in a Rara lake.

➢ Seas contains salt in it so it has comparatively greater density


than the Rara lake. Greater density in seas causes liquid


upthrust to be more than Rara lake with less density. Due to

more liquid upthrust, it is easier to swim in oceans.

Assignment







•What is pressure? Write its formula and SI unit.



•Differentiate force and pressure. Any 4



•Prove that P= F/A.


•What are the factors that affect pressure?



•What is the relation between pressure with force


applied and surface area?



•What is one pascal pressure?


•Why are studs made in football players shoe?



•Tyres of a tractor are made wider, why?



•It is easy to cut a knife with sharp edge than the blunt


one, why?

The pressure exerted by a liquid per unit area of the surface in its contact is

called liquid pressure.

▪ Formula to calculate liquid pressure is ,

Liquid pressure(P) = Height of liquid(h)x Density of liquid(d)x Accel. due to
gravity (g)
▪ i.e.. P = hdg





▪Factors affecting liquid pressure are;

i. Height of liquid(h)


ii. Density of liquid (d)
iii. Acceleration due to gravity (g)




Properties of liquid pressure;


• Liquid applies pressure in all directions.

• Liquid pressure increases with depth.

• Liquid pressure does not depend upon the shape of the vessel.
• Liquid pressure depends on density of liquid.

“Liquid pressure is transmitted equally and perpendicularly in


all direction when pressure is applied at a point on a liquid kept

closed container.”.





Verification of Pascal’s Law

Application of Pascal’s Law














1. Hydraulic press

2. Hydraulic jack


3. Hydraulic brake


4. Hydraulic lift

These devices are commonly

known as Hydraulic


machines.

Q. Why is liquid used in hydraulic machines?

Ans : Liquid is used in hydraulic machines because of following reasons;


i. Liquids are incompressible.

ii. Liquid transmits pressure equally and perpendicularly in all directions.


Principle of hydraulic Machine:

The principle of hydraulic machine states that, “ A large force is developed on a larger piston
when a small effort is applied on the smaller piston.

Hydraulic Machine







Definition




Hydraulic machines are the devices based on the pascal’s law


which use liquid to multiply the applied force .









Multiplied
Small applied
force
force

Derivation


Prove that hydraulic machine is a force multiplier.


Let us consider a hydraulic machine as in figure below. It consists of two pistons

A and B of unequal are A and A such that A < A . Let, applied force on a
1 2 1 2
piston A be F and that developed in piston be F .
2
1
Developed force =
Applied force F 2

= F
1





Area = A 1




Area = A 2

Since hydraulic machine is constructed on pascal’s principle ,

Whenever force is applied on first piston, liquid transmits equal


pressure on all the sides so ,






Pressure exerted on piston A = Pressure Developed on piston B




Or, =


, =





∴ F = ×
2


Since A > A , the expression shows F > F . Hence hydraulic machine
2
1
2
1
is a force multiplier .

Hydraulic machines









Hydraulic machines are the devices which multiply force on the basis of

Pascal’s Law.


i. Hydraulic Jack: Hydraulic jack is a device based on the pascal’s law which
helps to raise heavy loads by applying a small efforts.






ii. Hydraulic brakes: Hydraulic brakes is a device based on the pascal’s law

which helps to stop heavy automobiles by applying a small effort.





iii. Hydraulic Press: Hydraulic press is a device based on the pascal’s law

which is uses for compressing cotton bales, extracting oil from seeds, giving
specific shapes to metal sheets, etc..


iv. Hydraulic lift:

Hydraulic Brake

Some Numerical based on




Pascal’s law



Numerical;









Q. The ratio of the area of cross-section of the two pistons in a hydraulic machine
is 1:15. calculate the force that should be applied on the narrow piston to
overcome a force of 1200N on the larger cross-section piston.

Assignment







❑State pascal’s Law and verify it experimentally.


❑Write any two devices based on pascal’s law.



❑Define hydraulic machine with a labelled diagram.



❑Hydraulic machines use liquid in it . Write two


reasons.


❑ Prove that, the hydraulic machine is a force



multiplier .



❑How does hydraulic brake work ? Write.

Density; Mass per unit volume of a substance is called density.

3
SI Unit : Kg/ m ( Kilogram per cubic meter)
3
CGS Unit : g/ cm ( Centimeter per cubic meter)
Formula ; Density (d) = Mass of a substance (m)/ Volume of s substance(v)

i.e. d = m/v

0
Relative Density; The ratio of density of a substance to the density of water at 4 C is called relative density
or specific gravity. It has no unit. (Since it is the ratio of two densities.)

Formula;
Relative Density(R.D) = Density of a substance

0
Density of water at 4 C
➢The relative density of aluminum is 2.7, it means the ratio of density of aluminum to the density of
0
pure water at 4 C is 2.7.


Difference between Density and Relative Density.

Density Relative Density



1. Mass per unit volume of a substance is 1. The ratio of density of a substance to the density of
0
called density. water at 4 C is called relative density


2. The SI unit of density is Kg/ m 3. 2. Relative density has no unit.

Upthrust(Buoyancy)








❑The resultant upward force acting on an object when partially or wholly immersed in a
liquid is called upthrust or buoyancy.

❑Formula to calculate Upthrust:

i. Upthrust = Weight of object in air – Weight

of object in liquid

ii. Upthrust ( U) = Volume of liquid(v) x

density of liquid(d) x a.d.g.(g)

i.e. (U) = v d g

This shows that,

i. Upthrust is directly proportional to volume of liquid(Uα v)

ii. Upthrust is directly proportional to density of liquid.(U α d)

iii. Upthrust is directly proportional to adg. ( U α g)

❑Factors Affecting Upthrust;

i. Volume of liquid(v) ii. Density of liquid(d) iii. Acceleration due
to gravity ( g)

Archimede’s Principle( Experimental study of upthrust)






Statement: Archimedes principle states “ When a body is completely or partially
immersed in a liquid, it experiences an upthrust which is equal to the liquid displaced by it.

i.e.. Upthrust (U) = Weight of the liquid displaced.






































Devices based on Archimede’s principle are
Ships and sub-marines, lactometer, hydrometer etc..



Verification of Archimede’s Principle



To verify Archimede's principle, a stone is hung with a hook of s spring balance using string.
A eureka can filled with water and empty beaker on a pan balance are set so that the
overflowed water pours in the beaker. When the stone sinks in water, the water is
displaced and collected in the beaker.
The following observations are recorded;

• Weight of stone in air = W1

• Weight of stone in water = W2

• Weight of empty beaker = W3

• Weight of beaker with displaced water = W4

• Weight lost by stone = W1 – W2

• Weight of displaced water = W4 – W3

From the experiment it can found that,

W1 – W2 = W4 – W3

i.e.. Weight lost by stone = Weight of displaced water

i.e.. Upthrust = Weight of the displaced water(liquid).
Or, Upthrust = Weight lost by a body.

Therefore the upthrust of water = the weight of the water displaced by the object.

In this way, the Archimede’s Principle is verified.6





Numerical based on Archimede's Principle




1.Observe the given diagram and answer the following questions;

a. Calculate upthrust experienced by the stone in water.


b. Find out the weight of water displaced by the stone.

c. Calculate the mass of water displaced if 1kg = 10N.


d. On which principle the given figure is based on? State that.

Solution: Given, Weight of the stone in air(W1) = 20N


Weight of stone in water (W2) = 15N

a. Upthrust (U) = W1 – W2 = 20N – 15N = 5N

b. Weight of water displaced = Upthrust = 5N.


c. Mass of water displaced( m) = ?

weight of water displaced = 5N


Then, according to question 10 N = 1 kg

or, 1N = 1/10 kg


or, 5N = 1/10 x 5 = ½ kg = 0.5 kg.

Therefore, mass of water displaced is 0.5kg.


d. This figure is based on Archimedes Principle’s . It states that…………

………………………..

Numerical based on Archimedes Principle




2. Observe the given figure and answer the following questions;

i. How much is the weight of the body in air?

ii. Find out the mass of the stone .

iii. How much is the upthrust exerted ?

iv. Calculate the mass of the water displaced.

Solution: Given, Weight of stone in water(W1) = 20N


Weight of water displaced (W2)= 5N

i. Weight of stone in air = W1 + W2 = 20N + 5N = 25N

ii. Mass of stone ( m) = ?

We know that , Weight (W) = m x g

or, 25 = m x 9.8


or, 25 / 9.8 = m

or, m = 2.55kg

Therefore, mass of the stone is 2.55kg.

iii. Upthrust (U) = Weight of water displaced = 5N

iv. Mass of water displaced(m) = ?

Weight of water displaced(w) = 5N

Then Weight( W) = m x g ( Same as previous)

3. Weight of a stone in air, water and salt solution is given in the table shown below. Answer the
following questions.
Medium Weight
a. Identify the mediums A, B and C.
A 20N
b. Calculate the upthrust of water.

c. Find the mass of the stone(use g=9.8m/s2) B 14N

d. Find the mass of water displaced. C 16N

e. Identify the mediums with the highest and lowest density. Give reason.

Solution : a. Medium A is Air, Medium B is Salt solution and Medium C is Water.

b. Upthrust (U) = Weight of stone in air – Weight of stone in water = 20N – 16N = 4N

c. Mass of stone ( m) = ? d. Mass of water displaced( m) = ?

we have, weight of stone in air ( W) = 20N. Ans; Weight of water displaced(W) =
U = 4N

Then ,We know that Weight (W ) = m x g Then , Weight ( W ) = m x g

or, 20 = m x 9.8 or,4 = m x 9.8

or, 20/9.8 = m or, 4/9.8 = m

Mass of stone is 2.04kg. Or, m = 0.408kg


Therefore, mass of water displaced is 0.408kg

e. Medium B has highest density and Medium A has lowest density, because body losses its more
weight on the liquid with more density and vice versa. As Upthrust is directly proportional to
the density of liquid. Due to more upthrust stone loses its more weight in salt solution and
less in air.

Some give reasons based on Upthrust





1. It is easier to swim in the sea water, why?

Ans; Upthrust is directly proportional to the density of the liquid. Sea water has a

greater density than river water. Thus, upthrust experienced by a swimmer in

sea water is comparatively more than in river water. So, it is much easier to

swim in the sea water.

2. The weight of an object in air is more than that in water. Why?


Ans; Upthrust is directly proportional to the density of the liquid. Density of air is

less than that of water. The upthrust due to air is negligible in comparison to
the upthrust due to water. S o, the weight of an object in air is more than that

in water.


3.An egg sinks in pure water but floats in salt solution, why?

Ans;. The density of water is less than the density of the


salt Solution. As, we know, upthrust is directly proportional


to the density of liquid.(i.e. Uα d ) so, salt solution exerts more


upthrust on the egg where as water exerts less upthrust on

the egg. Therefore, an egg floats in salts solution and sinks in pure water.

Some give reasons based on Upthrust





4. It is easier to pull a bucket of water from a well until it is

inside the water but difficult When it is out of water, why?


Ans; water exerts upthrust on the bucket which reduces weight of

the bucket. Outside water there is very less upthrust of air. Thus,


the force required to pull a bucket when immersed in water is

less than that required to pull when it is out of water.


5. An iron ball sinks in water but floats in mercury, why?


Ans; An iron ball has more density than water so it sinks in water


but it floats in mercury because it has less density than mercury.


6. What is the difference between a boat floating in fresh river water

and sea water?



Ans; A boat sinks more in fresh water to displace more amount of

water to float because fresh water has less density .But sea water

has more density due to the pressure of salt ,so the boat sinks less .

7. What happens when ship enters a river from the sea?


Ans; When a ship enters a river from the sea it will sink more then the sea . It

is because salty water of the sea has more density and provides more

upthrust. But fresh river water has less density and provides least

upthrust. So, a ship sinks more to push more weight of water to bloat.


8. When we press ball inside water it tries to come upwards, why?


Ans; A ball always tries to rise upward when pressed


inside the water because the upthrust acting in the ball


by water is greater than weight of the ball . Hence, the


ball can easily displace water equal to its weight.






9. One has difficulty breathing in deep well while cleaning it, why?


Ans ; We know that the density of carbon dioxide gas is more than


the density of air. Due to this, carbon dioxide accumulates at


bottom of a well. Hence, one has difficulty breathing in deep well while


cleaning it.

Law of floatation










❑Statement: It states that “ An object that floats on liquid displaces the liquid equal to its own
weight”


i.e. Weight of floating body = Weight of displaced liquid.

❑Devices based on Law of Floatation are lactometer, hydrometer ,etc.

❑Difference between Archimede’s principle and Law of Floatation;

Archimede’s Principle Law of Floatation


1. Archimedes principle states “ When a body is 1. Law of Floatation states “ An object that
wholly or partially immersed in a liquid, it floats on liquid displaces the liquid equal to its
experiences an upthrust which is equal to the own weight”
liquid displaced by it.


2. It is applicable for both sinking and floating 2. It is only applicable for floating bodies only.
bodies.



Force Acting on an immersed Body





➢When a body is immersed in a liquid, it is acted upon by two forces. They are;

I. The weight of the body ‘ W’ acting downwards.

II. The upthrust due to the liquid ‘U’ acting vertically upwards.

➢ Conditions for floatation of a body in liquid;


a) When the weight of the body is greater than upthrust; ( W > U) ; the body sinks in the liquid.

b) When the weight of the body is equal to the upthrust; W = U ; the body floats freely.

c) When the weight of the body is less than the upthrust; W < U ; the body floats in the
condition of being partially immersed.

An egg sinks in fresh water but floats in salty water.

➢Salty water has greater density than fresh water due to which


liquid upthrust increases in salty water. Since, liquid pressure is

directly proportional to the density of water keeping g, h and d


constant. Due to the high density of salty water it provides


more upthrust then floats and sinks in fresh water due to its

less upthrust.





It is easier to lift a bucket of water until it is inside the level of


water but difficult outside.


➢When a bucket is inside the water, if experiences more liquid

upthrust due to which the bucket can be easily lifted inside the


water. On separating it out from the water, if looses the

upthrust experiences by liquid and hence it becomes more


difficult to lift a bucket outside the water.

The blood pressure is more at the feet than at the head.

➢ Blood is fluid connective tissue which is found circulating


inside the cardio-vascular throughout our body. The height or

depth of blood is found to be minimum in our head but it is


found to be maximum at the feet. Greater height of blood in


cardiovascular system in feet causes to increase the liquid

pressure (blood pressure) at the feet than at the head. Since,


liquid pressure is directly proportional to the height or depth

of liquid keeping acceleration due to gravity and density of


water are constant.





An iron nail sinks in water but a ship made up of iron floats.


➢ Iron nails cover less area so that it experiences less upthrust in

water and it can’t displace the water equal to its own weight


and sinks. But ship made up of iron covers more area so that it


experiences more upthrust as a result it can float in water.

What difference is observed when a balloon filled with air and a balloon filled

with hydrogen gas released?

➢ A hydrogen filled balloon gradually rises up in the sky. It is because the weight of

hydrogen filled balloon is lesser than the weight of air displaced by the balloon.

Since hydrogen is lighter than air. An object that displaces the fluid more than its
own weight gets rises up in the given fluid medium.

But air filled balloon displaces the weight of air lesser than its weight . As a

result, if can’t satisfy the law of floatation and settles down in the ground.



A hydrogen filled balloon gradually rises up in the air and burst on reaching

certain height.

➢ A hydrogen filled balloon gradually rises up in the sky. It is because the

weight of hydrogen filled balloon is lesser than the weight of air displaced

by the balloon. Since hydrogen is lighter than air. An object that displaces

the fluid more than its own weight gets rises up in the given fluid medium.

As a balloon rises up, it reaches gradually to lower atmospheric

pressure region. As a result, hydrogen gas inside the balloon continuously

exerts outward pressure on the wall of balloon. As a result balloon gradually

gets inflated. And the elastic behavior of balloon ceases at a point of height.

As a result, the balloon get burst.

An iceberg made up of water floats in water, why?

3
3
Ans; The density of ice(0.917g/cm ) is less than that of water(1g/cm ).
Iceberg is able to displace water equal to its weight. Therefore,

iceberg floats in water.


A ship can carry more loads on sea water than on the river, why?


Ans; The density of salty water is more than that of fresh water. So,

sea water offers more upthrust to the ship than that of river

water. As a result, a ship can carry more loads on sea water than

on river water.





Why does an iron nail sink in water but ship made of iron floats?


Ans; According to law of floatation, the object which displaces liquid

equal to its own floats in liquid. In case of an iron nail, it has

surface are. Due to this , the weight of water displaced by an iron

nail is less than the weight of the needle. So, it sinks in water. In

case of ship, it has very wide surface area. Due to this the weight

of water displaced by the ship is equal to the weight of the ship.

So, the ship floats in water.



What happens when a load is removed from a ship which is floating

on water? Why?


Ans: When a load is removed from a ship, the ship floats more on

water. It is because when the load of the ship is decreased, it can

float by displacing less amounts of water. Thus the boat rises up

from its original position.





What is the effect of density of liquid on the floatation of an object?


Ans; The density of liquid is directly proportional to the upthrust.

Hence, an object floats easily if the density of liquid is high.






The loaded ship sinks more than the empty ship, why?


Ans; To float on water, the weight of ship should be equal to the

weight of water displaced by it. When weight is increased un the

ship it should displace more water to be floated. Therefore, the

loaded ship sinks more than the empty ship.

Atmospheric Pressure






Atmosphere; The thick layer of air covering entire earth’s surface

is called atmosphere.


Atmospheric Pressure: The force exerted by the weight of the

atmosphere per unit area on the earth’s surface is known as

atmospheric pressure. It is Maximum at sea level and Minimum

at top of mountain.


Units Of Atmospheric Pressure ; The SI unit of atmospheric

2
pressure is N/ m or Pascal(Pa).


Atmospheric Pressure is generally expressed in millimeter of

mercury column.


At sea level, 1 atm = 760 millimeter of mercury (mm of Hg)


5
= 1.013x 10 Pa.


Standard Atmospheric Pressure: The pressure exerted by

atmosphere at sea level is called standard atmospheric pressure.

It is equal to 760mmof Hg, taken as1 atmosphere(1 atm).

The device which is used to measure atmospheric pressure is

called barometer. The commonly used barometer is Mercury

barometer.


1. At high altitudes, nose bleeding is a common

experiences, why?



Ans; At high altitudes, the atmospheric pressure is lower than the

pressure within our body. This results bursting of the thin

capillaries in the nose and bleeding happens from the nose. So,

at high altitudes, it is a common experience to have nose

bleeding.



2.When a heated can is closed and allowed to cool, it gets

squashed. Why?



Ans; When a can is heated, hot air escape out. When we close the

lid, a vacuum is formed due to low pressure inside it. So, the

atmospheric pressure crushes the can when it is cooled.

Mercury barometer:





A barometer that measures the atmospheric pressure with the help of

mercury column is called a mercury barometer. It was invented by


Evangelista Torricelli(1608-1647)






Construction;

❖ Mercury barometer consists of mercury.

❖ A simple mercury barometer can be made

with clean, dry, thick-walled glass tube of

about one meter long.

❖ The tube is sealed at one end and filled

with mercury.

❖ The tube is inverted over a trough with

mercury. The tube is fixed with the help of

a scale.

❖ A graduated scale is made on the tube to

measure atmospheric pressure.

Working: When atmospheric



pressure increases the Mercury level in

the glass tube increases and when the


Atmospheric pressure decreases, the

mercury level also decreases. The


reading is taken with the help of scale in


the glass tube. In this way the barometer

works.


Torricelli Vacuum: The vacuum at the

top of the tube of mercury barometer is


called Torricelli Vacuum.


Note: The height of the mercury

column decreases with increase in


altitudes due to decrease in atmospheric

pressure.

Applications of the Atmospheric Pressure




There are some devices that works on the principle of atmospheric


pressure. They are;


1. Syringe


2. Hand pump ( Water pump)


3. Air pump ( Bicycle pump)

1. Syringe: A syringe is a medical instrument which is used to insert

drugs into the body and to take out blood from the body of patients.




























Construction;


❑A syringe has an air-tight piston, storage cylinder(barrel) and needle.



❑A hollow needle is attached to the storage cylinder.


❑Its piston is slides smoothly inside the cylinder.


❑When the plunger handle is pulled, fluids are drawn into the storage

cylinder.



❑This fluid is forced out through the needle when the handle is pushed.