Beneath the waves diaries
Discover Zanzibar
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In the Rough Science programme 'Beneath the Waves', Rough Scientists Jonathan and Kathy are given the task of building an air pump that presenter Kate can use to breathe underwater. It’s not just a question of pumping the air down to Kate – the air has to be at the same pressure as the water surrounding her so that her lungs aren’t crushed by the water pressure or over inflated by the pressure of the air pumped down to her.
This extract from the second level OU course The Physical World (S207) explains how pressure can be a problem for a diver.
In order to see how pressure depends on depth, we must consider the vertical forces acting on the cube.
Forces on an imaginary cube of water in a lake
It is convenient to choose a z-axis that points vertically downwards, with its origin at the surface of the water. Suppose the cube has mass M, the pressure on the upper face is P1 and the pressure on the lower face is P2. Then the z-component of the total external force on the cube is
Fz = Mg + P1A - P2A1.
Again, we can argue that Fz must be zero in order for the cube to remain at rest, so it follows that.
The pressure on the lower face is greater than the pressure on the upper face, allowing the weight of the cube to be supported. It is worth expressing this result in a slightly different way by noting that the mass of the cube is given by
where 
is the density of the water and V is the volume of the cube. Since V = A(z2 - z1), we have
This allows us to write
If we now place the cube with its upper face at the surface of the water, z1 will be zero and P1 will be equal to atmospheric pressure, PA. On the lower face of the cube, at depth z2, the pressure is then
Now there was nothing special about z2. It could have been any point below the surface, so the subscript 2 can be dropped, giving a simple formula for the pressure P at depth z below the surface:
The quantity 
, which is the contribution of the liquid to the total pressure, is known as the gauge pressure, since it is the pressure that would be registered on a diver’s pressure gauge, normally calibrated to read zero at the surface.
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Content last updated: 01/02/2005
