Pressure in a fluid 2 (HT only) — AQA GCSE Physics

A pressure difference between two depths needs only the difference in height, because the density and the field strength are the same at both. A diver ten metres deeper than another is at a pressure about 101 kPa greater in sea water, which is roughly one extra atmosphere for every ten metres of depth. The same idea explains why a dam is built much thicker at its base than at the top, why a water tank in a roof space gives good pressure at a ground-floor tap, and why the lowest hole in a punctured bottle squirts furthest. If a question asks for the absolute pressure at a depth rather than the difference, add atmospheric pressure, normally taken as about 100 kPa, to the pressure due to the liquid.

Pressure in a liquid grows with depth, so the lower face of a submerged block sits deeper than the upper face and the liquid pushes harder on it. Both pushes are normal to their faces, up on the bottom and down on the top, and the difference between them depends on the vertical height of the block and the density of the liquid, not on how deep the block is overall. The side faces are pushed inwards equally from both directions, so those forces cancel. A brick a tenth of a metre tall lying on the floor of a pool has about one kilopascal more pressure on its underside than on its top, and multiplying that difference by the area of the face gives the extra upward force.

The downward push on the top face and the upward push on the bottom face do not cancel, because the bottom lies deeper and the pressure there is greater. Subtracting one from the other leaves a resultant that points straight up. Its size is the pressure difference multiplied by the area of the face, and that works out to be the weight of the fluid the object has pushed out of the way. This is why a stone feels lighter under water and why a boat with a large submerged volume can support a heavy load. The upward resultant does not depend on what the object is made of, only on the volume submerged and the density of the fluid, so a steel block and a wooden block of the same size receive exactly the same upward push.

Upthrust is the name for that upward resultant, and it is a contact force, so mark schemes accept it alongside tension and the normal contact force when examples are asked for. It always acts upwards through the submerged volume and is equal in size to the weight of the fluid displaced. Whether an object rises, sinks or stays put depends on how the upthrust compares with the weight. A brick resting on the floor of a pool is held still by three forces: its weight downwards, the upthrust upwards and the normal contact force from the floor upwards, so the weight equals the upthrust plus the contact force. A helium balloon rises because the upthrust from the air exceeds its weight, and a floating object has settled where upthrust and weight are equal.

An object floats when it can displace a weight of fluid equal to its own weight before it is fully under. Push a solid object right under and it displaces its own volume, so the upthrust is the weight of that volume of fluid: if the object's density is lower than the fluid's, that upthrust beats its weight and the object rises until only part of it is submerged; if its density is higher, the upthrust is too small and it sinks. The factors are therefore the density of the object, the density of the fluid and the volume submerged. Shape matters only because it changes the volume displaced - a steel sheet sinks, but the same steel formed into a hull encloses air, has a much lower average density and floats. Salt water is denser than fresh, so objects float higher in it.