Pressure

Hello dear we have studied about buoyancy and thrust in std 9th. When we exert force on any surface, thrust act on the surface causes pressure. The basis of pressure due to fluid (liquid and gas) lies in the concept of buoyancy, which was explained by Archimedes principle. Also according to molecular theory, we know that the molecules of gas and liquid exerts force normally to given surface of container, due to which pressure is acts on the walls of container.

Let’s discuss the pressure in details……………!

Consider the following examples

  1. When we visit to doctor due to any illness and doctor advised you to take an injection, just look at the needle attached to syringe. It should be very sharp to get injected painlessly.
  2. The edges of instruments like knife, chopper should be sharp enough so as to utilise them effortlessly.

In above examples the pressure acting on the given surface plays very important role to decide the impact of efforts that we applied by the means of force.

Pressure is defined as the force or thrust acting normally to given surface area.

Hence by definition,

Pressure = Force/Area

∴ P = F/A

SI unit of pressure is N/m2 or pascal.

Dimension of pressure are [M1L-1T-2]

We know that the every fluid exerts the pressure on the wall of container. To find the pressure exerted by liquid, let’s consider that the liquid of mass ‘m’ is filled in vessel to height ‘h’ as shown in fig below.

 

 

 

Let, ρ= density of liquid

M= mass of liquid in container

g=acceleration due to gravity at the point

h= height of liquid column

And , A= area of bottom of container

Then the force exerted by liquid column on the bottom of container is nothing but the weight of liquid in the column.

∴Pressure = weight of liquid column/surface area at bottom of vessel

∴ P = Mg/A

But the density of liquid column can be written as,

∴ ρ =Mass/volume

∴ mass, M = density × volume

∴ M =ρ × V = ρAh

Then the equation of pressure can be,

 

∴P = ρAhg/A

∴P = ρhg

This is the formula for pressure exerted by liquid column.

If Pa is the atmospheric pressure above the free surface of liquid, then the total pressure can be written as,

∴ P = Pa + ρhg

Or

∴ P – Pa = ρhg

The quantiy P – Pa  is known as gauge pressure

Some important points……..!

  1. At sea level atmospheric pressure is 1.013 × 105 Pa (1 atm).
  2. Pressure of the atmosphere at any point is taken as the weight of a column of air per unit cross sectional area.
  3. The device named as “mercury barometer” is used for measuring atmospheric pressure, which was discovered by Torricelli’s.
  4. For 1 atm pressure, height of mercury column is 76 cm.

Let’s solve the numerical to understand the pressure in detail….!

Ex: Find the pressure below the depth of 550 m of liquid of density 1200 kg/m3. Take atmospheric pressure, Pa= 1 atm.

Solution:

Here, h = 550 m, ρ = 1200 kg/m3, Pa = 1.013 × 105 Pa

∴P =1.013 × 105  + 1200 × 550 × 9.8

∴P = (1.013 × 105  ) + (64.68 × 105)

∴P = 65.69 × 105  Pa


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