Pressure in Fluids and Atmospheric Pressure

(Separate Physics only) All of pressure in fluids and atmospheric pressure is assessed in AQA GCSE Physics only, not in Combined Science.

A fluid is anything that can flow, which means both liquids and gases. The particles in a fluid are constantly moving and colliding with any surface they touch. Each collision exerts a tiny force, and together these collisions produce pressure.

The pressure in a fluid causes a force that acts at right angles (normal) to any surface in contact with the fluid.

This is why water pushes outwards on the walls of a container in every direction, and why air presses on every surface around you. Pressure is not a force in one direction: it acts perpendicular to whatever surface it meets, no matter how that surface is oriented.

Understanding pressure explains how submarines withstand deep water, why dams are built thicker at the bottom, and how objects float. The next slide gives the equation linking pressure, force and area.

Pressure tells you how concentrated a force is over a surface. The same force spread over a smaller area produces a higher pressure.

$p=\frac{F}{A}$

where $p$ is pressure in pascals (Pa), $F$ is the force normal to the surface in newtons (N), and $A$ is the area of that surface in square metres (m²).

You must recall and apply this equation. $p=F/A$ is not given on the equation sheet.

One pascal is one newton per square metre: 1 Pa = 1 N/m². The pascal is a small unit, so real pressures are often thousands of pascals.

Worked example — a box weighs 240 N and rests on a base of area 0.30 m². Find the pressure it exerts on the floor.

$p=\frac{F}{A}=\frac{240}{0.30}=800\text{ Pa}$

The box exerts 800 Pa on the floor. If it were tipped onto a smaller face, the same 240 N over a smaller area would give a higher pressure.

(Higher Tier only) The equation $p=h\rho g$ and the calculations in this slide are Higher Tier only.

Deeper in a liquid, there is more liquid above pushing down, so the pressure is greater. The pressure due to a column of liquid depends on the depth, the density of the liquid, and gravitational field strength.

$p=h\rho g$

where $p$ is pressure in pascals (Pa), $h$ is the height (depth) of the column in metres (m), $\rho$ is the density of the liquid in kg/m³, and $g$ is the gravitational field strength in N/kg.

This equation is given on the Physics equation sheet.

Pressure increases with depth because there is a greater weight of liquid above. It also increases with density, because a denser liquid has more mass in each column.

Worked example — find the pressure due to the water at a depth of 5.0 m. Take the density of water as 1000 kg/m³ and $g$ = 9.8 N/kg.

$p=h\rho g=5.0\times 1000\times 9.8=49000\text{ Pa}$

The pressure from the water alone is 49 000 Pa (49 kPa). This is why divers feel their ears pushed inwards as they descend, and why dam walls are built much thicker at their base.

(Higher Tier only) Explaining upthrust from the pressure difference is Higher Tier content.

A submerged object has liquid pressing on it from all sides. Because pressure increases with depth, the pressure on the lower surface is greater than the pressure on the upper surface. This pressure difference produces a resultant upward force called upthrust.

Upthrust is the resultant upward force on an object in a fluid, caused by greater pressure on its lower surface than on its upper surface.

Whether an object floats or sinks depends on how its weight compares with the upthrust:

Condition	Result
Weight greater than the maximum upthrust	the object sinks
Weight equal to the upthrust	the object floats, in equilibrium

An object floats when it can displace enough fluid for the upthrust to equal its weight. An object less dense than the fluid can always displace enough fluid to do this, so it floats; an object denser than the fluid cannot, so it sinks. A steel ship floats because its hollow shape displaces a large volume of water, giving a large upthrust that balances its weight.

The atmosphere is a thin layer of air surrounding the Earth. Air molecules are in constant motion, and when they collide with a surface they exert a force. The total effect of all these collisions is atmospheric pressure.

Atmospheric pressure is caused by air molecules colliding with a surface. It decreases as height above the ground increases.

The atmosphere gets less dense with increasing altitude. Near the ground the air is compressed by the weight of all the air above it, so molecules are packed closely together. Higher up, there is less air above pushing down, so the air is thinner.

Two linked reasons explain why atmospheric pressure falls with height:

• As height increases, there is less air above the surface, so there is less weight of air pressing down.
• The air is less dense higher up, so fewer molecules collide with the surface each second.

This is why aircraft cabins are pressurised, why mountaineers carry oxygen at altitude, and why a sealed packet of crisps taken up a mountain puffs outwards as the pressure around it drops.

1. Forgetting that fluid pressure acts normal to a surface

The force from fluid pressure acts at right angles to the surface, whatever the surface's orientation. Do not draw the force sideways along the surface or only downwards.

2. Using the wrong units in p = F/A

Area must be in square metres for the answer to come out in pascals. If an area is given in cm², convert it first (1 m² = 10 000 cm²), or the pressure will be wrong by a large factor.

3. Leaving depth in centimetres in p = hρg

In $p=h\rho g$, the height must be in metres and density in kg/m³. Convert any depth given in cm to metres before substituting.

4. Confusing weight and upthrust when explaining floating

An object floats when upthrust equals weight, not when there is no weight. Both forces still act; they are simply balanced. State that the upthrust equals the weight for a floating object.

5. Getting the altitude relationship backwards

Atmospheric pressure decreases with height because there is less air above. A common error is to say pressure increases with height. Higher up means thinner air and lower pressure.