Beneath the waves diaries
Related programme
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.
It is interesting to calculate the rate of increase of pressure with depth. This can be done by rearranging Equation
to obtain
The left-hand side can be written as 
P / 
z so, taking the limit as 
z becomes very small.
The right-hand side of this equation, 
, is the force magnitude per unit volume due to gravity. The left-hand side of the equation is the pressure gradient, which can be interpreted as the force magnitude per unit volume due to pressure.
Notice that the pressure gradient, dP / dz, has the constant value 
. Inserting appropriate values for 
, the density of pure water, and g, the magnitude of the acceleration due to gravity close to the Earth’s surface, we obtain
Comparing this rate of increase of pressure with standard atmospheric pressure (1051Pa), we see that each metre of depth corresponds to about 10% of atmospheric pressure. So, if you dive to a depth of 10 metres, you will experience roughly twice the pressure as at the surface.
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Content last updated: 01/02/2005
