# Pressure in liquids - Higher

in liquids are close together. They exert by colliding with each other and with objects and container walls. Liquid pressure is exerted equally, in all directions.

## Depth and density

The pressure in a liquid increases with the depth and density of the liquid.

### Depth

The deeper an object is submerged in a liquid, the greater the pressure it will experience. This is because the particles in any part of the liquid are being squashed by the of the liquid above them. The greater the depth, the greater the weight of liquid above.

This is why humans cannot safely dive beyond a certain depth in the ocean. The human body cannot withstand the extra pressure due to all the water above.

### Density

For a given volume of liquid, the greater the of the liquid, the greater its . This means that when comparing the pressure in liquids of different densities, the pressure is greater at the same height in the densest liquid. This is because there is a greater weight of liquid pushing down.

## Calculating pressure in a liquid

The pressure due to a column of liquid is calculated using:

pressure due to a column of liquid = height of column Ć density of liquid Ć gravitational field strength

This is when:

• pressure is in pascals (Pa)
• height of column is in metres (m)
• density of liquid is in kilograms per cubic metre (kg/m3)
• gravitational field strength is in newtons per kilogram (N/kg)

### Example

Calculate the pressure due to water on an object at a depth of 1.5 m. (The density of water is 1,000 kg/m3 and gravitational field strength is 10 N/kg.)

pressure due to a column of liquid = height of column Ć density of liquid Ć gravitational field strength

pressure = 1.5 Ć 1,000 Ć 10

= 15,000 Pa (15 kPa)

### Total pressure

The total pressure exerted on any submerged object will be the pressure due to the liquid plus the pressure due to the atmosphere. For example, the water pressure on an object at a depth of 1.5 m is 15 kPa. However, atmospheric pressure is 100 kPa:

total pressure on object = liquid pressure + atmospheric pressure

= 15 + 100

= 115 kPa

## Floating and sinking

An object that is partially submerged in a liquid experiences an upwards force, called . An object will:

• float, if upthrust equals the weight of the object
• sink, if upthrust is less than the weight of the object
The rubber duck exerts a downwards force on the water (its weight) and the water exerts an upwards force (upthrust) on the duck

Whether an object will float or not also depends on the area of the object. This is why a large oil tanker can float on the ocean but a smaller vessel with the same mass would sink. Objects of the same size but different densities will also float differently, as shown in the diagram below.

The cubes are all the same area, but the metal cube in the middle is much denser so it will sink in water
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