Liquids - Higher
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/m3. Calculate the pressure exerted by the water on the bottom of a 2.0 m deep swimming pool. (Gravitational field strength = 10 N/kg).
\(p = h~ \rho ~g\)
\(p = 2.0 × 1,000 × 10\)
\(p = 20,000~Pa\)
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 10 N/kg).
change in depth = 6 - 1 = 5 m
\(p = h~ \rho ~g\)
\(p = 5 \times 1,000 \times 10\)
\(p = 50,000~Pa\)
Question
The density of water is 1,000 kg/m³. Calculate the pressure at the bottom of a dam 12 m deep. (Gravitational field strength = 10 N/kg).
\(p = h~ \rho ~g\)
\(p = 12 \times 1,000 \times 10\)
\(p = 120,000~Pa\)
Floating and sinking
When explaining whether an object floats or sinks, the densities of the object and the liquid need to be considered, and also the force exerted by the object on the water and the force of the water on the object.
The first is the density of the object - if the density of the object is greater than the density of the liquid then it will sink. If an object is less dense than the liquid it will float.
The weight of the object acts vertically downwards. The upthrust acts in the opposite direction to the weight and is caused by the pressure of the liquid acting over the area of the object in the liquid.
Upthrust is caused by a pressure that is larger on the bottom of an object than it is on the top of an object submerged in a liquid. This is why objects appear to weigh less when immersed in a liquid.
If the upthrust is greater than the weight of the object, the object will rise up through the liquid. If the upthrust is less than the weight of the object, the object will sink. If the upthrust is equal to the weight of the object, the object will float (not move).
Any object which is floating has balanced forces acting on it in the vertical direction.
