Pressure in Liquid

Pressure in Liquid

If you ever go underwater in a swimming pool, you will feel the pressure of the water. This pressure comes from the weight of the water above you. However you would not just feel a downward pressure. The water presses against you from all directions - on you back, you chest, your ear drums, your eyes, your legs.

Pressure of water, and of any liquid, acts in all directions. This is obviously different from the pressure of a book on a table, which only acts downwards. It is a result of the water molecules moving randomly in all directions.

We can calculate the water pressure p at a certain depth h, if we know the density ρ. Think of water in a beaker. Start by finding the pressure of the water on the bottom of the beaker. Pressure on the bottom surface acts downwards. It is just the weight W of the water, divided by the area A of the bottom. So p = W/A.

Weight is W = mg, where m is the mass, and g the acceleration of free fall. Mass m is density times volume V, so m = ρV. Volume of the water is V = Ah, the base times the height.

Combining, W = mg = ρVg = ρAhg.

Therefore, p = W/A = ρAhg / A = ρgh.

This is the formula to calculate water pressure. It also works for other liquids, like oil or alcohol. It also works for any container, not just for a beaker with vertical edges. What if we have a bowl with the same area at the bottom, but a larger area on top? The same height of water now has a greater volume and weight. Does this mean a larger pressure at the bottom?

No. The pressure is the same, p = ρgh. It has to do with the slanted sides helping to support some of the weight.

Even though the formula, p = ρgh, is derived from pressure acting downwards at the bottom of a container, it also works for pressure on a body at the same depth. The reason is simply that we know pressure acts in all directions in a liquid.

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