Beneath the waves diaries
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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.
The pressure experienced by a diver
One of the main problems confronting a diver is the rapid increase in pressure that occurs with increasing depth. This is noticeable even for shallow dives, such as those to the bottom of a swimming pool. A serious problem arises because the human body is not completely solid: internal spaces like the lungs are filled with air, so deep diving introduces the danger of being crushed by the pressure of the surrounding water, like an empty aluminium can being crushed underfoot. Breathing special mixtures of high-pressure gases, scuba divers have dived to 300 metres; but unfortunately, air becomes toxic at very high pressures, so special diving suits or submarines become essential beyond this depth.
In order to learn about the increase of pressure with depth, we will consider a fluid that is at rest, with no currents flowing. We will also assume that the fluid is incompressible, so that it has a fixed density, independent of the pressure. Both these assumptions are reasonable because currents have almost no effect on the pressure experienced by a diver, and water is practically incompressible.
Suppose a cube of water is at rest somewhere within a lake. If you like, you can imagine the cube to be surrounded by a thin plastic membrane, so that it is clearly separated from the rest of the water, although this is not really necessary. What are the forces acting on the cube? There is the weight of the cube acting downwards and there are inward forces acting on each face of the cube due to the pressure of the surrounding water.
First, consider the forces acting along the horizontal x-axis. These are due solely to the external pressure on the two shaded faces in shown here.
Forces on an imaginary cube of water in a lake.
Suppose the area of one face of the cube is A, the pressure on the left-hand face is PL, and the pressure on the right-hand face is PR. Then the x-component of the total external force on the cube is
Fx = PLA1-1PRA1.
Notice how the signs appear here: the force on the left-hand face is positive because it acts along the x-axis, while that on the right-hand face is negative because it acts in the opposite direction. Finally, remember that the cube is supposed to be at rest so Fx must be zero, leading to the conclusion that PL = PR. More generally, we can say that any two points at the same depth in a static fluid must be at the same pressure — if they were not, currents would flow, driven by the pressure difference.
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Content last updated: 01/02/2005
