# Pressure

## Defining Pressure

Pressure is the amount of force spread over a given area, and is measured in pascals (Pa).

If the same force is applied across a larger area then the pressure is reduced. Pressure is a way of thinking about how ‘concentrated’ a force is when it is acting on an object.

In both of these images the same force, F, is being applied to the surface by the object. The larger object spreads that force over a larger area, therefore the pressure is lower.

Pressure = Force ÷ Area or _P = F A _

P is the pressure in pascals (Pa)

F is the force in newtons (N)

A is the area in square meters (*m*²)

Solids, liquids and gases can exert a pressure on an object. Pressure requires a surface area over which the force can act. In the case of two solids this is the point of contact between the objects, as illustrated above. For both a liquid and a gas the force is produced by the collisions of the moving particles with a solid surface, creating a net force at right angles to the surface.

## Calculating Pressure

If an empty suitcase has a base measuring 0.5 m x 0.2 m and when empty has a mass of 2 kg, what pressure does it exert on the floor?

Area of the base 0.5 x 0.2 = 0.1*m*². Force (weight) = mass x gravity 2 x10 = 20N

If the suitcase is filled and has a new mass of 10 kg, the pressure on the base will increase as the force has increased but the base area is unchanged.

The pressure that a person exerts on the ground depends upon their mass and the area of the shoes in contact with the ground. On a soft surface, like snow, the pressure from normal shoes can make a person sink into the snow. Snowshoes, skies and snowboards are all designed to increase the surface area, thus reducing the pressure on the snow.

Large surfaces reduce the pressure on the surface.

## Atmospheric Pressure

Atmospheric pressure is caused by the accumulation of the air that extends upwards from the surface of the earth to around 480 Km. The particles of gas in the air collide with any surface producing a force. At sea-level the average atmospheric pressure in 101,000 Pascals (101 KPa), at this point the air is at its highest density. This means there are more particles to produce the pressure than there are at altitude.

The atmosphere is not a uniform body of gas, the air gets less dense as altitude increases, the majority of the mass of the atmosphere is in the lowest 16 Km. This thinning of the air at altitude results in a drop in the atmospheric pressure with height. This is due to the lower density of air particles able to collide with a surface to produce the force needed for pressure to exist. This change in pressure with height is used by all aeroplanes to calculate their altitude.

The drop in density and the pressure is not linear, there is only a small change in the first 1,000m but as altitude increase the rate of decrease of pressure accelerates.

## Pressure in Fluids

## Pressure and Depth in Liquids

As with all fluids the pressure caused by a column water is a result of the constant collisions between the particles of the water and a surface. The greater the number of particles the greater the number of collision and, therefore, the greater the force produced. This increase in force also increases the pressure.

Two factors affect the number of particles in water, the depth of the water column and the amount of other materials dissolved in the water. These two affect the density of the water, and in turn this affects the water pressure.

Dissolved chemical, such as salt make water more dense. This means that the sea is more dense than freshwater. This also means that pressure increases faster in sea water than in freshwater.

**Depth and Pressure**

The density of water increases as the depth increases, leading to a rapid increase in the water pressure with depth. Due to the very high density of water, 10 m of water has the same pressure as the whole atmosphere. As the scuba diver in the picture descends they experience an increase of 101 KPa of pressure for every 10 m of extra depth.

The exact pressure of a liquid at depth can be calculated from knowing, the height of the column of liquid (depth), the density of the liquid and gravity.

Pressure = Depth (m) x Density of liquid (kg/*m*^{3}) x gravity (9.8 N/kg)

*P =h ρ g*

Example

What is the pressure exerted by sea water at 25 m? Density of seawater = 1002 kg/*m*^{3}

P =h *ρ* g

P = 25 x 1002 x 9.8 =245,490 Pa approx 245.5 KPa

This is the pressure from the water, anyone diving at this depth would actual experience 346.5KPa, as the atmosphere above the water adds an additional 101 KPa of pressure.

What is the pressure exerted by fresh water at 25m? Fresh water density = 1000 kg/*m*^{3}

P =h *ρ* g

P = 25 x 1000 x 9.8 =245,000 Pa approx 245.0 KPa

The pressure is slightly lower due to the lower density of the water.

- A diver is at 55 m in the Red Sea, assuming the water has a density of 1004 Kg/m3 and that the atmospheric pressure is 0.998 KPa at the dive site. What is the total pressure experienced by the diver?
- Your answer should include: 542.154KPa / 542.154

Explanation:*P =h ρ g P = 55 x 1004 x 9.8 =541.156 KPa of water pressure Total pressure = water pressure + atmospheric pressure Total pressure = 541.156 + 0.998 = 542.154 KPa* - Explain why someone would feel less pressure at the top of a mountain at an altitude of 5000m than at a sea-level.
- Your answer should include: lower / density / atmospheric pressure

Explanation:*Pressure in the atmosphere is caused by the collision of air particles with the person. The density of the air is lower at 5,000m than it is at sea-level. The lower density, therefore, results in a lower atmospheric pressure at altitude.* - A force of 850 N is applied by a person standing in both feet. What happens to the pressure on the ground if they stand on one leg?
- Your answer should include: double / twice

Explanation:*As the force will remain the same, but the area over which the force is applied is roughly halved, the pressure would double.*