Pressure

Pressure of solid

Pressure is the force acting normally per unit area.

P = F / A

where F is the force acting, A is the area of the grey portion on which it rests.

If the weight of the block is 5 N and the area of the grey side of the block is 2.1 m², the pressure acting when it rests on that side is

P = F/A

F = 5 N

A = 2.1 m²

P = 5N x 2.1 m²

P = 10.5 Pa

Pressure due to a column of liquid

For a column of fluid, the pressure at any point is proportional to the height of the fluid above it and the density of the fluid. They are related to each other in the equation P = ρgh where P is pressure, g - acceleration due to gravity, h - height of the fluid, ρ- density of the fluid

Eg.

The density of liquid mercury is 13.5 x 10³ kg/m³. Calculate the liquid pressure at a point 0.50 m below the surface of a column of mercury.

P = ρgh

P = 13.5 x 10³ kg/m³ x 10 m/s² x 0.50 m

P = 67.5 x 10³ Pa

Atmospheric pressure acts all around and in all directions. The density of air at sea level is very high. This causes a large pressure to be exerted on anything at sea level.

Atmospheric pressure = 1 x 10⁵ Pa

Measuring Pressure using Manometer

We can use a U-tube manometer as a pressure gauge. Since P = ρgh, we can calculate the value for pressure at point B due to the height of the liquid in the right arm of the manometer..

Let the pressure at A = P₁

Pressure at B = pressure at surface, P₂ + liquid pressure due to h

P₁ = P₂ + ρgh

When P₂ is atmospheric pressure, ρgh gives the amount by which P₁ exceeds atmospheric pressure

If manometer was closed on the right hand side (so that there is a vacuum) then P₁ = ρgh