Pressure

Introduction

What happens when you walk on soft snow or dry sand? Your feet sink into the snow or sand and walking can be difficult. If you ride a bicycle with narrow tyres over these surfaces, the tyres will sink even deeper than your feet. How deep you sink depends on your weight as well as the area over which you make contact with the sand or snow. For example, when you stand on snow with your normal shoes, you may sink deep into the soft snow [see figure (a)]. However, if you use special kinds of supports (or snow boards) having larger area than your shoes [see figure (b)], you can stand on the snow very easily.

In both cases, your weight exerted a downward force on the snow. What changed was the area of contact between you and the snow. By changing the area of contact, you changed the ‘pressure’ you exerted on the snow due to your weight. When you stood with supports
(or snow shoes), the area of contact increased, so that the same force was applied over a larger area. As a result, the pressure that was exerted on the snow decreased and you didn’t sink as deep.

1.0Pressure

Thrust

The force acting on an object perpendicular to the surface is called thrust.

Pressure

The thrust on unit area is called pressure.

$Pressure=\frac{Thrust}{Area}=\frac{Force}{Area}$

SI Unit of Pressure

N/m² or N m^–2. In honour of scientist Blaise Pascal, the SI unit of pressure is called "pascal", denoted as Pa.

1 Pascal = 1 Newton/(meter)²

or  1 Pa = 1 N/m² = 1 N m^–2

Definition of 1 Pascal

If 1 newton force acts perpendicular to a surface of area 1m², then the pressure acting on the surface is 1 pascal.

Pressure is a scalar quantity. Always remember it is the component of the force normal (perpendicular) to the area under consideration for calculating pressure, not the force vector.

A common unit of pressure is the atmosphere (atm), i.e. the pressure exerted by the atmosphere at sea level, 1 atm = 1.013 × 10⁵ Pa

Another unit of pressure is bar, 1 Bar = 10⁵ Pa

For a given force, pressure is inversely proportional to the area. Thus, the same force acting on a smaller area exerts a larger pressure, and a smaller pressure on a larger area.

The weight of a hundred rupee note resting completely flat on a table exerts a pressure of about 1 Pa on the table. Since 1 Pa is a very small unit of pressure, pressure sometimes is expressed in units of kPa (kilo pascal), which is 1,000 Pa.

Some more examples related to pressure

(1) You cannot cut vegetables with a blunt knife. But, if you use a sharp knife, it is quite easy to cut the vegetables. This is because the area of sharp edge of the knife is quite small and thus, pressure is large enough to cut the vegetables.

(2) The straps of shoulder bags are made wide (broad). This is because the wide straps have larger area so that the pressure exerted on the shoulder becomes quite small. Thus, it becomes quite comfortable to carry such shoulder bags.

(3) Porters (coolies) place on their heads a round piece of cloth, when they have to carry heavy load. By this they increase the area of contact of the load with their head. So, the pressure on their head is reduced and they find it easier to carry the load.

(4) Buildings have wide foundations so that they exert less pressure on the earth.

Solved Example

A block of wood is kept on a table top. The mass of the wooden block is 5 kg and its dimensions are 40 cm × 20 cm × 10 cm. Find the pressure exerted by the wooden block on the table top if it is made to lie on the table top with its sides of dimensions 

(a) 20 cm × 10 cm and (b) 40 cm × 20 cm (see figure, take g = 9.8 m/s²).

Solution

Given, mass of the wooden block, m = 5 kg

Thrust, F = weight of the wooden block = m × g = 5 × 9.8 = 49 N

(a) Area, A = 20 cm × 10 cm = 200 cm² = 200 × 10^–4 m² = 0.02 m² 

Now, pressure, P = = = 2450 N m^–2 

Now, pressure, P =$\frac{F}{A}=\frac{49}{0.02}$ = 2450 N m^–2 

(b) Area, A = 40 cm × 20 cm = 800 cm² = 800 × 10^–4 m² = 0.08 m²

Now, pressure,$P=\frac{F}{A}=\frac{49}{0.08}$ = 612.5 N m^–2 

Thus, the pressure exerted by the face 20 cm × 10 cm is 2450 Nm^–2 and by the face 40 cm × 20 cm is 612.5 Nm^–2.

Pressure in a fluid

A fluid is any substance that has no definite shape and has the ability to flow. You might think of a fluid as being a liquid, such as water or motor oil, but gases are also fluids. When you are outside on a windy day, you can feel the air flowing past you because air can flow and has no definite shape, air is a fluid. Gases, liquids, and the state of matter called plasma, which is found in the Sun and other stars, are fluids and can flow. Fluids can exert pressure on the base and walls of the container in which they are enclosed.