1.8 Pressure

How Pressure Changes with Force and Area (Everyday Examples)

• Pressure increases Stand on the floor on one leg the pressure exerted on the one foot is greater than the pressure exerted when you stand on two feet. Stand on your toes the pressure exerted on your toes is greater than when standing on two feet. This mean that less area makes more pressure.
• Pressure decreases if the area increases. For example, if you wear snowshoes on soft snow, the large surface area stops you from sinking because the pressure is spread out.

Pressure is the concentration of a force:

1. If a force is spread over a large area it will result in a small pressure.
2. If it is spread over a small area it will result in a large pressure.

Pressure in Liquids

• Pressure increases as you go deeper in a liquid because there is more liquid above pushing down.
• Pressure also increases if the liquid is denser (heavier). For example, pressure is higher in saltwater (denser) than in freshwater.
• Think of when you’re swimming: the deeper you go, the more pressure you feel on your ears.

Change in Pressure in Liquids (Supplement)

• When you go deeper into a liquid, the change in pressure can be calculated using this formula:

Δp=ρgΔh

• Δp = change in pressure
• ρ (rho) = density of the liquid (how heavy it is)
• g = gravitational field strength (on Earth, this is 9.8 m/s²)
• Δh = change in depth (how deep you go)

This means that the deeper you go or the denser the liquid, the more the pressure increases.

Example 01:

A rectangular container has a base of dimensions 0.12 m × 0.16 m. The container is filled with a liquid. The mass of the liquid in the container is 4.8 kg.

a. Calculate

1. The weight of liquid in the container,

Weight = mg

Weight = 4..8 x 9.8

Weight  = 47N

2. The pressure due to the liquid on the base of the container.

$$P={{F}\over{A}}$$

$$P={{47}\over{0.12×0.16}}=\;2447Pa$$

b. Explain why the total pressure on the base of the container is greater than the value calculated in a. 2.

In addition to liquid pressure we need to add Atmospheric pressure as well.

c. The depth of liquid in the container is 0.32 m. Calculate the density of the liquid.

Δp=ρgΔh

2447Pa = ρ x 9.8m/s² x 0.32

Density (ρ) = 780Kg/ m³