Pressure in a liquid - Higher
James Stewart explains how pressure acts within a fluid
The Force exerted over an area. The greater the pressure, the greater the force exerted over the same area. in a liquid is different at different depths. Pressure increases as the depth increases. The pressure in a liquid is due to the The force acting on an object due to the pull of gravity from a massive object like a planet. The force acts towards the centre of the planet and is measured in newtons (N). of the column of water above. Since the particles in a liquid are tightly packed, this pressure acts in all directions. For example, the pressure acting on a dam at the bottom of a reservoir is greater than the pressure acting near the top. This is why dam walls are usually wedge-shaped.
Calculating pressure in a liquid
The pressure caused by a column of liquid can be calculated using the equation:
pressure = height of column × density of the liquid × gravitational field strength
\(p = h~\rho~g\)
This is when:
- pressure (p) is measured in pascals (Pa)
- height of column (h) is measured in metres (m)
- density (ρ) is measured in kilograms per metre cubed (kg/m3)
- gravitational field strength (g) is measured in newtons per kilogram (N/kg)
The symbol ρ is the Greek letter rho - it is pronounced ‘row’.
Example
The density of water is 1,000 kg/3. Calculate the pressure exerted by the water on the bottom of a 2.0 m deep swimming pool. (Gravitational field strength = 9.8 N/kg).
\(p = h~ρ~g\)
\(p = 2.0 \times 1,000 \times 9.8\)
\(p = 19,600~Pa\)
Question
A stone is dropped into a lake. Calculate the increase in pressure on the stone caused by the water when it sinks from 1 m deep to 6 m deep. (The density of water is 1,000 kg/m3 and gravitational field strength is 9.8 N/kg).
change in depth = 6 - 1 = 5 m
\(p = h~ρ~g\)
\(p = 5 \times 1,000 \times 9.8\)
\(p = 49,000~Pa\)
Question
The density of water is 1000 kg/m3. Calculate the pressure at the bottom of a dam 12 m deep. (Gravitational field strength = 9.8 N/kg).
\(p = h~ρ~g\)
\(p = 12 \times 1,000 \times 9.8\)
\(p = 117,600~Pa\)
Upthrust
An object that is partly, or completely, submerged experiences a greater pressure on its bottom surface than on its top surface. This causes a resultant force upwards. This force is called Upwards force exerted by a liquid or gas on an object floating in it..