Pressure:
Pressure is defined as the force acting per unit area of the surface.
mathematically,
from above equation we can say that pressure is inversely proportional to area provided when force is constant. That means, a given force (F) will exert more pressure if it acts on a smaller area, and less pressure if it acts on a bigger area.
i.e. 
Similarly, it follows that pressure is directly proportional to force provided the on the constant area. That means more pressure will create more force and vice versa.
i.e 
Unit: The SI unit of pressure is 
or pascal (Pa).
or pascal (Pa).
Though the force associated with the pressure at a point is a vector quantity, the pressure itself is a scalar i.e. pressure has no direction.
Atmospheric pressure:
The air that surrounds the earth is called atmosphere. It is extended about 9,600 km above the earth surface. The air has weight. Thus, it exerts pressure on the surface of the earth. The pressure exerted by the atmospheric air is called atmospheric pressure. At sea level, the air pressure is said to be one atmosphere. This is also termed as standard atmospheric pressure or normal pressure.
The normal pressure is the pressure exerted by 760 mm long column of mercury at 
C at sea level and at a altitude of 
. It is equal to 
. In short, we can write as, 1 atmosphere = 760 mm of Hg = 
or pascal.
C at sea level and at a altitude of . It is equal to . In short, we can write as, 1 atmosphere = 760 mm of Hg = or pascal.
1 torr = 1 mm Hg = 103.222 pa
Liquid pressure
A liquid substance in a container exerts pressure in all direction. For example liquid exerts pressure on the bottom and to the walls of the container. The pressure of the liquid is produced due to its weight.
liquid pressure
Derive the formula : P = dgh
Height ‘h’ and area ‘A’
Consider a liquid of density ‘d’ is contained in a beaker of cross — sectional area ‘A’. Let ‘h’ be the depth of the liquid column from its free surface as shown in the figure.
or, V = A * h
or, W = m* g
= ( v * d ) * g [ 
]
]![\therefore W = A * h * d * g [ \because V = A * h]](http://www.slcguru.com/wp-content/ql-cache/quicklatex.com-1da125e2761789de49fb4a607606c695_l3.svg "Rendered by QuickLaTeX.com")
Thus weight of the liquid column is the force acting on the area ‘A’, normally. Therefore,
[
]
P = dgh
Thus pressure exerted by a liquid of density ‘d’ on the base of the beaker is dgh. Therefore, the pressure exerted by liquid at rest depends on three factors:
a. depth or height of the liquid column (h)
b. density of the liquid (d) and
c. acceleration due to gravity (g)
For a given liquid at a given place, density of the liquid and acceleration due to gravity are constant. Hence, pressure exerted by a liquid is directly proportional to the depth of the liquid column from the free surface of the liquid
Pascal’s law
Blase Pascal, born in France in 1623 A.D. was a famous mathematician, physicist and philosopher. He was first to find out the behavior of liquid pressure and put forward a law which is popular as Pascal’s Law.
Pascal’s law stats that ” When pressure is applied on a liquid enclosed in a vessel, it is transmitted equally in all the directions.”
Application of pascal’s law
Pascal’s law tells that if pressure at any point in a liquid is changed, there will be equal change in pressure at any point in a liquid is changed, there will be equal change in pressure at other points in the liquid. This fact is used in hydraulic machines such as hydraulic press, hydraulic brake, hydraulic garage lift, hydraulic cranes etc.
Principle of hydraulic machine
If a force 
is applied at first piston of area 
, the pressure exerted at any point on it is given by 
is applied at first piston of area , the pressure exerted at any point on it is given by
This pressure is transmitted unchanged to second piston of area A_2. Therefore, the upward force F_2 exerted on second piston is given by 
From pascal’s law 
If 
, then 
. Thus a small force can be used to exert a much larger force. Thus, a hydraulic machine is a force multiplier.
, then . Thus a small force can be used to exert a much larger force. Thus, a hydraulic machine is a force multiplier.
The principle of hydraulic machine can be summed up as given below.
~ Any liquid cannot be compressed.
~ Pressure applied on an enclosed liquid is transmitted at each part of it (Pascal’s law)
~ The ratio of cross-sectional area of big cylinder 
to that of smaller cylinder is equal to the ratio of load overcome 
to effort applied .
to that of smaller cylinder is equal to the ratio of load overcome to effort applied .
i.e. 
This principle is applicable in different hydraulic machines.
Density:
The density of a substance is defined as the mass per unit volume
Mathematically,
i.e. 
In SI system density is measured in kg/m^3 and in CGS system it is measure in 
The substance having lesser density is said to be lighter one while the substances having greater density so is said to be heavier one.
Relative Density:
When the density of any substance is compared with water at 
, it is called relative density of that substance. Therefore, When the mass of a particular volume of substance is divided with the mass of the same volume of water at , it is called relative density of that substance.
, it is called relative density of that substance. Therefore, When the mass of a particular volume of substance is divided with the mass of the same volume of water at , it is called relative density of that substance.
Mathematically
Relative density is a simple ratio that’s why it does not have any unit.
Achimedes
Other Important Questions
1. The bottom of dam is wider and stronger than upper part.
OR
Walls of a dam are made thicker at the bottom. Why?
Liquid pressure is directly proportional to the depth of liquid from free surface. At the bottom of dam, there is high water pressure. To protect the dam from the high water pressure, the bottom is made wide and stronger than the upper part.
2. The pressure exerted by water at the bottom of the drum decreases slightly at the Himalayan region than that in the Terai region.
Since pressure of a liquid is directly proportional to the value of g and the value of g is more at Terai region than that in the Himalayan region. So, the pressure exerted by water at the bottom of the drum decreases slightly at the Himalayan region than that in the Terai region.
3. The bucket filled faster in the downstairs tap than in upstairs tap.
Pressure of a liquid is directly proportional to its depth or height from the free surface. The tap at the downstairs is at greater height than the tap at the upstairs. Water comes out with greater pressure from the downstairs tap. So, bucket is filled faster in the downstairs tap than in upstairs tap.
4. The speed of flow of water out of a tap of upper floor is less than that of the down floor.
Since pressure of a liquid is directly proportional to its depth or height from the free surface. The height of the liquid column on the down floor is more than that on the upper floor. So the speed flow of water out of a tap of upper floor is less than that of the down floor.
5. A deep sea-diver needs to wear diving suit.
The pressure of a liquid is directly proportional to the height of liquid column from free surface. When a person dives deep into sea, he or she has to bear high water pressure. To withstand with high water pressure, it is necessary to wear diving suit.
6.Weight of stone decreases in the salt solution.
When salt is dissolved in water, the upthrust increases due to the increases in the density of water. As a result, the weight of a stone decreases in the salt solution.
7. It is easier to lift a heavy stone inside the water.
The weight of the stone inside the water decreases due to the upthrust. So it is easier to lift a heavy stone inside the water.
8. The weight of a body is lighter in water than in air.
Upthrust due to water is greater than that of air. Upthrust decreases weight of body. Hence, the weight of a body is lighter in water than in air.
9. The weight of a body is more in vacuum than in air.
There is no upthrust in vacuum. Upthrust decreases the weight of body. Hence, the weight of body is less in air due to its upthrust.
10. It is easier to pull a bucket of water from the well until it is inside the water but difficult when it is out of water.
Upthrust due to water is greater than that of air. Upthrust exerted by water decreases weight of body. Hence, it is easier to pull a bucket of water from the well until it is inside the water but difficult when it is out of water.
11. Studs are made on the sole of football player’s boot.
Studs are made on the sole of football player’s boot to increase the pressure on the ground that prevents the player from falling or sliding during sudden run and turning.
12. It is easier to cut vegetables with the sharp-edged knife than the blunt one.
The area of the edge of sharp knife is less than that of the blunt one. So sharp-edged knife can exert more pressure while applying force than that of the blunt edged knife as the pressure is inversely proportional to the area. Due to more pressure, it is easier to cut vegetables with the sharp-edged knife than the blunt one.
13. Buses and trucks have broad and double wheeled tyres.
The buses and trucks have to carry greater weight which exerts greater pressure on the tyres. The pressure on them is reduces by increasing the area of the tyres as the pressure is inversely proportional to the area.
14. Camel can walk easily on sand.
Camel has flat-soled feet which exert less pressure due to the body weight of camel. As there is less pressure exerted by flat-soled feet of camel, it can easily walk on the sand.
15. The wheel of tractor is wider than that of a car.
The rear wheels of a tractor are made large and flat to reduce the pressure and prevent the tyres from descending into the muddy land. As tractor is used for ploughing and threshing in crop fields, small and narrow real wheels may descent into the muddy and marshy load due to more pressure. (i.e.)
16. The water supply tanks are placed higher than any other building in a town.
The water supply tanks are placed higher than any other building in a town so that the pressure of water is more. Due to this, water can flow to the buildings located at higher level. As a result, water can be supplied easily on the taps of uppermost floors and houses built at higher level of ground.
17. The gravity bulb of hydrometer is made heavier.
The gravity bulb of hydrometer is made heavier so that its centre of gravity remains very low, when it is floating in denser liquids. It helps the hydrometer to float upright in stable equilibrium.
18. Hydrometer has a heavy bulb and narrow stem.
Hydrometer has a heavy bulb to float in a liquid vertically. The stem of hydrometer is made long and narrow to find the relative density of less dense liquid i.e. it increase its sensitivity.
19. The floatation bulb (buoyancy bulb) of hydrometer is made small.
The floatation bulb of hydrometer is made small because denser liquids provide more upthrust and hence the whole hydrometer does not float on the dense liquid.
20. An egg sinks in fresh water but floats in a strong solution of salt (or in a saturated salt solution).
Fresh water has less density than that of the egg so the egg cannot displace water equal to its weight and it sinks. But salt on mixing with water increases the density of water which increase upthrust and hence the egg can displace water equal to its weight and floats.
21. Iceberg made up of water floats in water.
The density of ice is less than that of water. Due to this, iceberg is able to displace the water equal to its weight. Hence, Iceberg made up of water floats in water.
22. An iron nail sinks in water but a ship made up of iron floats.
Since the density of iron is greater than that of water, the iron nail sinks as the weight of the nail is greater than the weight of the displaced water. But the ship made of up iron is designed in such a way that the relative density of ship becomes always less than that of water. Hence, the weight of water displaced becomes equal to the total weight of the ship and the ship floats.
23. It is easier for a man to swim in sea water than in river water.
The density of sea water is more than that of river water. Thus for the same volume, the sea water provides more upthrust as compared to the river water. So it is easier for a man to swim in sea water than in river water.
24. A hole at the bottom of a boat is more dangerous than that at the side.
The bottom of the boat exerts more pressure, as the force acts perpendicularly downwards, than that at the sides. If there is hole at the bottom of the boat, more water enters inside due to more upthrust and the boat may sink. So, a hole at the bottom of a boat is more dangerous than that at the side.
25. An iron nail sinks in water but floats in mercury.
The density of iron is more than that of the water. The iron nail cannot displace the eater equal to its weight and it sink. But the density of mercury is much more than that of the water. It gives more upthrust which helps the iron nail to float on mercury.
26. A girl with heeled shoe exerts a higher pressure on the ground than an elephant.
The area of the heels of the girl’s shoes is much smaller in comparison with the area covered by the flat feet of the elephant. As
27. A man exerts more pressure under his foot when he stands with one foot than when he stands on two feet.
The area of one foot is less than that of two feet. As
28. The base of the house is made wider than its wall.
The walls and roof of house exerts pressure on the base of a house. The pressure exerted by the building is reduced by making the base of the house wider as pressure is inversely proportional to the area.
29. The loaded ship sinks more than empty ship.
The loaded ship has larger mass. Hence, the weight (or volume) of displaced water is more for loaded ship. But the empty ship has lesser mass. Hence, the weight (or volume) of displaced water is less for empty ship. So the loaded ship sinks more than empty ship.
Thank you for sharing Pressure Chapter Notes
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