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Force and Pressure - Pressure Exerted by Liquids and Gases

Grade 8CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Liquids exert pressure on the walls and the bottom of their container. The pressure exerted by a liquid column is directly proportional to its height (hh) and density (ρ\rho).

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Pressure in a liquid increases with depth. This is why the walls of dams are made thicker at the bottom than at the top.

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At the same depth, a liquid exerts equal pressure in all directions.

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Gases, like liquids, exert pressure on the walls of their container due to the constant motion and collision of gas molecules.

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The envelope of air surrounding the Earth is called the atmosphere. The pressure exerted by this air is known as Atmospheric Pressure.

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Atmospheric pressure decreases as altitude increases because the column of air above us becomes shorter and less dense.

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The reason we are not crushed by atmospheric pressure is that the pressure inside our bodies is also equal to the atmospheric pressure and cancels the pressure from outside.

📐Formulae

P=FAP = \frac{F}{A}

P=hρgP = h \rho g

1 Pascal (Pa)=1 Newton per square metre (N/m2)1 \text{ Pascal (Pa)} = 1 \text{ Newton per square metre (N/m}^2)

Ptotal=Patm+hρgP_{total} = P_{atm} + h \rho g

💡Examples

Problem 1:

Calculate the pressure exerted by a column of water of height 10 m10\text{ m} at its bottom. (Assume density of water ρ=1000 kg/m3\rho = 1000\text{ kg/m}^3 and g=9.8 m/s2g = 9.8\text{ m/s}^2)

Solution:

P=hρgP = h \rho g P=10 m×1000 kg/m3×9.8 m/s2P = 10\text{ m} \times 1000\text{ kg/m}^3 \times 9.8\text{ m/s}^2 P=98,000 PaP = 98,000\text{ Pa}

Explanation:

The pressure depends on the height of the liquid column. Here, 10 m10\text{ m} of water exerts a pressure of 98,000 Pascals98,000\text{ Pascals}.

Problem 2:

Why does a plastic bottle collapse inward when air is sucked out of it?

Solution:

When air is sucked out, the internal air pressure (PinP_{in}) decreases. The external atmospheric pressure (PatmP_{atm}) becomes much greater than the internal pressure, pushing the walls of the bottle inward.

Explanation:

This demonstrates that air (a gas) exerts pressure and that atmospheric pressure is strong enough to deform objects if not balanced by internal pressure.

Problem 3:

A deep-sea diver experiences more pressure at 50 m50\text{ m} below the sea surface than at 10 m10\text{ m}. Why?

Solution:

According to the formula P=hρgP = h \rho g, pressure is directly proportional to depth (hh). Since 50 m>10 m50\text{ m} > 10\text{ m}, the pressure is higher at the greater depth.

Explanation:

As the diver goes deeper, the weight of the water column above them increases, leading to an increase in pressure.