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.

Pressure in a fluid
To measure the pressure inside a fluid, imagine introducing a sensor in the form of a tiny evacuated cylinder, with a piston at one end supported by a spring.

This is diagram of a sensor for measuring pressure inside a fluid. The fluid exerts a force of magnitude along the axis of the piston, causing it to compress. The ratio of to the area A of the piston defines the pressure.

The compression of the spring indicates the magnitude of the force exerted along the axis of the piston by the fluid. Then, if the cross-sectional area of the piston is A, and the force acting along the piston’s axis has magnitude , the pressure P is defined to be

It is assumed that the act of introducing the sensor has no significant effect on the pressure in the fluid. If the fluid is static this is a fair assumption, but if the fluid is flowing, like a river in spate, we should be more careful. It is essential for the sensor to drift with the fluid, so that it experiences exactly the same pressure as the fluid itself. We can imagine introducing a large number of sensors and letting them drift with the flow, allowing the pressure to be measured at different places and times throughout the fluid. The expense and practical difficulty of putting this plan into action need not concern us — the important point is simply that pressure at any point in the fluid can be given a precise definition.

Our definition of pressure is based on an important observation. In a fluid, the reading on a pressure sensor does not depend on the orientation of the sensor. If the sensor is turned around so that it points in a different direction, the same pressure will be recorded. In mathematical terms we can say that pressure is a scalar quantity, with no associated direction, in contrast to force which is a vector and acts in a definite direction. Both the magnitude of and the cross-sectional area are positive quantities, so pressure is itself a positive quantity. Zero pressure corresponds to a perfect vacuum.

In this section, we will consider the pressure inside a fluid that is at rest. Two rather different examples will be discussed: the pressure experienced by a diver and the pressure experienced by a mountaineer.

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