The total force applied per unit area is called pressure.

Mathematically,
Pressure (P) = Force (F) / Area (A)

Its SI unit is pascal (Pa).

One pascal pressure can be defined as the pressure exerted by applying 1 N force in a 1 m² area.

The pressure exerted by any liquid on the bottom and the wall of the container where it is kept is called liquid pressure.

Pascal's law states that pressure is transmitted equally in all directions when pressure is applied at a place on a liquid kept in a closed container.

Any two applications of it are:

1. Hydraulic jack
2. Hydraulic press

Let us consider a hydraulic machine of 2 vessels of CSA 'A1' and 'A2' respectively. These vessels are fitted with watertight frictionless pistons. The CSA of the small vessel is 'A1' and large vessel is 'A2'. So, 'A1' < 'A2'.

When a force 'F1' is applied on the small piston of area 'A1', a pressure 'P1' is exerted on the small piston. According to Pascal's law:

Pressure in small piston = Pressure in the large piston
i. e. P1 = P2
or, F1 / A1 = F2 / A2
or, F1.A2 = F2.A1

Since A2 > A1,F1 >...

The resultant upward thrust exerted by a fluid is called upthrust.

Its SI unit is kgm/s² and CGS unit is gmcm/s².

Let us consider a cylinder of height 'h' and uniform CSA 'A' is immersed in a liquid of density 'd'. If h₁ and h₂ are the depths of the upper and lower surface of the immersed cylinder then,

Force on the upper surface, F₁ = P₁ . A = h₁dgA

Force on the lower surface, F₂ = P₂ . A = h₂dgA

Here, g is the acceleration due to gravity.

Now, upthrust (U) = F₂ - F₁
= h₂dgA - h₁dgA
= (h₂ - h₁)dgA
= hdgA Since h₂ - h₁ = h
= Vdg Since Ah = V
...

Archimede's principle states that when a body is partially or wholly immersed in a liquid, it experiences an upthrust that is equal to the weight of the liquid displaced by it.

The law of flotation states that any body floats on a liquid if it can displace the liquid equal to its own weight.

The relation between the density and upthrust of a liquid is:

We have, upthrust = Vdg
So, upthrustd

The upthrust of any liquid depends on the following factors:

1. V: volume of the liquid
2. d: density of the liquid
3. g: acceleration due to gravity

A is water and B is air out of three media because in the water there is medium weight due to the medium upthrust exerted by water whereas in the air there is maximum weight because of the least upthrust exerted by air.

In air media, 10 N = 1 kg
So, 28 N = 28 / 10 = 2.8 kg

Therefore, the mass of stone is 2.8 kg.

As we all know that,P = F/Aso, P1/A

Usually, the bags are made to carry heavy loads. The handles should be able to handle the pressure exerted by the loads. Otherwise, the handles will break. So, to reduce the exerted pressure, and handle the bag easily, the handles of the bag are made broader to increase its area.

As we all know that,P = F/Aso, P1/A

We also know that rails are heavy vehicles with tons of loads. So, it exerts high pressure on its tracks while traveling and has chances to sink. Hence, to prevent sinking by reducing the pressure exerted by rail, the railway tracks are laid on large sleepers increasing its area.

As we all know that, P = F/A so, P1/A

In the graveled roads, there are many sharp-edged stones on the surface. While walking on it, more pressure is exerted by the sharp stones (due to less area) and it causes pain and difficulties while walking on the graveled roads.

We have, P = F/A so, P1/A

Usually, nails need more pressure to be inserted for different purposes in woods and metals. If it has a pointed end, the area of the edge is less and more pressure can be exerted with less force. So, it will be easy to work with nails. Hence, nails are made to have a pointed end.

We all know thatupthrust = Vdg so, upthrustd

The density of the concentrated salt solution is higher than that of pure water. So, more upthrust is exerted by the salt solution than by pure water. Hence, the egg floats in it but not in pure water.

We know that upthrust exerted by water is always greater than air. So, the bucket of water is uplifted by greater upthrust of water in water but the upthrust of air isn't much effective. So, it is easier to lift the bucket of water until it remains inside the water.

According to the law of floatation, a body floats on a liquid if it can displace the liquid equal to its weight. The body can displace the liquid equal to its volume. The volume of nails is less. So, it displaces less water and sinks. However, the ship displaces a large amount of water and floats due to the influence of high upthrust. Hence, an iron nail sinks in water but the ship made of iron floats.

We know that seawater is found as saline water (salt solution). So, seawater has a higher density than river water. Also, upthrustdensity. So, more upthrust is exerted in seawater than in river water. Hence, it is easier to swim in seawater than in river water.

We all know that the density of the iceberg is less than that of the water. So, it experiences more upthrust as it displaces the water more than its weight. Hence, it floats on water.

We all know that the density of mercury is greater than that of water. Also, densityupthrust. So, more upthrust is exerted by mercury than by water. So, an iron nail floats on mercury but sinks on water.

The pressure exerted by the atmosphere due to its weight is called atmospheric pressure.Its importance is:

1. Our blood pressure is balanced.
2. Helps to fill ink in the fountain pen.
3. Helps to fill medicine in a syringe.
4. Helps to fill the air in a tube.
5. Helps to drink liquid through a straw.

A barometer is a scientific instrument used to measure the atmospheric pressure of any place.

A syringe is a simple pump consisting of a plunger or piston that fits tightly in a tube that can take in and expel a liquid or gas. Its uses are as listed below:

1. Used in medical treatment.
2. Used to take out blood from the body.
3. Used to send different required drugs through the bloodstream.
4. Used in vaccination.

The syringe is made up of a plastic piston and barrel. The piston is fitted tightly in the barrel from the open end. The other end that is closed leaving a small tube to pass out is called a nozzle. When the piston or plunger is pulled, the vacuum is created inside the barrel and the air or liquid flows in through the nozzle. And when the piston is pushed in, the liquid or air inside flows out.

An air pump is a type of positive displacement pump specifically designed for inflating bicycle tires.

i. Force and pressure

Force	Pressure
It is the product of mass and acceleration.	It is the total force applied per unit area.
Force = m.a	Pressure = F/A
Its SI unit is Newton (N).	Its SI unit is Pascal (Pa).

ii. Archimede's principle and the law of flotation.

Archimede's principle	Law of flotation
It states that when a body is partially or totally immersed in a liquid, it experiences the upthrust equal to the weight of the liquid displaced by it.	It states that a body floats on...

P= F/A [definition of pressure]

or, P= m*g/A [since, F= mg]

or, P= d*v*g/A [since, d= m/v or, m= d*v]

or, P= d*A*h*g/A [since, V= A*h]

Therefore, P=d*h*g

The two factors which affect pressure due to the liquid contained in a vessel are as follows:

• The density of the liquid (p)
• The depth of the liquid (h)
• (Bonus) Acceleration due to gravity (g)

When a body is immersed partially or completely in a liquid, the resultant force on the body is called upthrust or buoyant force.

Pascal's law states that "when pressure is applied on a liquid enclosed in a vessel, it is transmitted equally in all directions." The two instruments based on Pascal's law are:

• Hydraulic garage lift
• Hydraulic brake

Archimedes principle states that"when a body is partially or wholly immersed in a liquid, it experiences an upthrust which is equal to the weight displaced by it."

The law of floatation states that the "weight of a floating body is equal to the weight of the fluid displaced by the body".

The weight of water displaced by the ship will be more than its own weight i.e., 5*10⁵because it is built in such a way that the weight of the water displaced by the ship is more than its weight itself. So that it will not sink in seawater

Most hand pumps used to inflate bike tires are reciprocating pumps. They have a piston inside and two one-way valves: one going to the bike tire and one to the outside air. When the pump is pulled up, the pressure inside decreases. This pulls in air from the outside but closes the valve to the bike tire. When the piston is pushed down again, it compresses the air inside. This closes the inlet valve and opens the valve to the tire, pushing air into the bike.

The downstroke of the piston is the condition in which the piston is pushed down when the handle of the water pump is lifted up.

When the handle of the water pump is pushed down, it lifts the piston up.

Water cannot be used as a barometric liquid because its density is lower than Mercury. Water's density is 1000 grams per cubic meter. hence it requires a barometer whose height is around 11 meters.