Pressure in fluids

This part of the sub-topic comes in two halves, and it is worth knowing which is which before you start.

The first, for both tiers, is pressure at a surface — the force per unit area, wherever that force comes from. The second, Higher tier only, is pressure caused by the weight of a liquid above a point, which is what makes pressure increase with depth and what produces upthrust.

Both use the word pressure and both are measured in pascals, but they answer different questions: the first asks how a force is spread over an area, the second asks how deep you are.

A fluid can be either a liquid or a gas. That definition is worth noting at the start — everything in this sub-topic applies to gases as well as liquids.

The pressure in fluids causes a force normal, meaning at right angles, to any surface.

The pressure at the surface of a fluid can be calculated using the equation:

pressure = force normal to a surface / area of that surface p = F / A

pressure, p, in pascals, Pa; force, F, in newtons, N; area, A, in metres squared, m².

You should be able to recall and apply this equation.

The pressure due to a column of liquid can be calculated using the equation:

pressure = height of the column × density of the liquid × gravitational field strength p = h ρ g

pressure, p, in pascals, Pa; height of the column, h, in metres, m; density, ρ, in kilograms per metre cubed, kg/m³; gravitational field strength, g, in newtons per kilogram, N/kg. In any calculation the value of g will be given.

This equation is given on the Physics equation sheet.

You should be able to explain why, in a liquid, pressure at a point increases with the height of the column of liquid above that point, and with the density of the liquid.

Both follow from the same idea. The pressure at a point is caused by the weight of the liquid above it pressing down. A greater height of liquid above the point means more liquid, so a greater weight, so a greater pressure. A denser liquid means more mass in the same volume, so again a greater weight above the point and a greater pressure.

You should also be able to calculate the differences in pressure at different depths in a liquid — subtract the pressures found at the two depths, or use the difference in height directly.

A partially or totally submerged object experiences a greater pressure on the bottom surface than on the top surface. This creates a resultant force upwards, and this force is called the upthrust.

The reason follows directly from p = h ρ g: the bottom surface is deeper, so the pressure on it is greater, so the upward force on it exceeds the downward force on the top.

You should be able to describe the factors which influence floating and sinking. An object floats if the upthrust equals its weight, and sinks if its weight is greater than the largest upthrust it can generate. Because the upthrust depends on the volume of fluid displaced and the density of the fluid, an object whose overall density is less than that of the fluid will float, and one that is denser will sink. That is why a steel ship floats: it is shaped to enclose a large volume of air, so its overall density is less than that of water.

The atmosphere is a thin layer, relative to the size of the Earth, of air round the Earth. The atmosphere gets less dense with increasing altitude.

Air molecules colliding with a surface create atmospheric pressure.

The number of air molecules — and so the weight of air — above a surface decreases as the height of the surface above ground level increases. So as height increases there is always less air above a surface than there is at a lower height. So atmospheric pressure decreases with an increase in height.

You should be able to describe a simple model of the Earth's atmosphere and of atmospheric pressure, and explain why atmospheric pressure varies with height above a surface.

The explanation has a fixed shape, and the specification writes it out almost as a chain of consequences:

1. Atmospheric pressure is caused by air molecules colliding with a surface. 2. As height increases, there is less air above the surface. 3. So there are fewer molecules above to collide with it, and the weight of air above is smaller. 4. So the atmospheric pressure decreases as height increases.

Giving all four steps is what separates a full answer from a partial one.

An object in a fluid feels an upward force called upthrust, and where it comes from follows from something already known: pressure in a fluid increases with depth.

The bottom of a submerged object is deeper than its top, so the pressure on the bottom is greater than the pressure on the top. Pressure produces a force at right angles to each surface, so the upward force on the bottom is larger than the downward force on the top. The difference between them is the upthrust.

Its size is given by one statement, worth learning word for word: the upthrust is equal to the weight of the fluid displaced by the object. Push a beach ball under water and it pushes a large volume of water aside; that displaced water is heavy, so the upthrust is large, and the ball shoots back up.

Density is what all of this comes down to. A floating object displaces a volume of fluid whose weight equals its own weight; if the object is denser than the fluid, there is no volume it can displace that weighs enough, so it sinks. That is how a steel ship floats: the steel is far denser than water, but the hull encloses a large volume of air, and the average density of the whole ship is less than that of water.