# Pressure in liquids

If you dive down to the bottom of a deep swimming pool you can feel the water pressure pressing on you from all sides
Deep-sea divers must wear a reinforced diving suit if they are to work safely at great depths
If underwater survey vessels have any windows they must be made of very thick glass
If there is a leak in the skin of a submarine the water will be forced inside
Sometimes the water from a tap may come out slowly if the water supply tank is not much higher than the tap
Cars have hydraulic brakes
Dams are thicker at the bottom than they are at the top
A hydraulic jack can be used to lift cars or crush objects

All these effects are due to the pressure in liquids.

## The dam

You can see from the diagram that the dam is much thicker at the bottom than it is at the top. This is because the pressure of the water is much greater deeper down and the dam needs to be thick at the bottom so that it is strong enough to withstand this larger pressure.

## Experiments

You can investigate the pressure in liquids by the following simple experiments:
1. The pressure in a liquids increases with depth
Get a can or a large plastic bottle with a series of holes drilled in the side one above the other. Cover the holes with your fingers or a piece of sticky tape and then fill the container with water.
Now remove the tape. The water gushes out but comes out faster from the holes nearer the bottom where the water is deeper and so the pressure of the water is greater.
Just imagine doing the experiment with a high-density liquid. The pressure would be much greater.

2. The pressure in a liquids acts equally in all directions
Take a plastic bag and fill it with water. Make some holes in the bag and then squeeze it quickly. The water squirts out equally fast from all the holes, even the ones near the top of the bag.

These simple experiments show you three things:

1. Pressure in a liquid Increases with depth
2. Pressure in a liquid acts equally in all directions
3. The greater the density of the liquid, the greater the pressure at a certain depth.

The pressure at a depth in a liquid can be shown to be given by the formula:

Pressure at a depth h in a liquid = g x depth (h) x density of liquid (r)

where g is the acceleration due to gravity (10m/s2)

Example problem
What is the pressure in the water at the base of a 10 m high dam wall?
Pressure due to water = 10 x 10 x1000 = 100 000 N/m2

(This ignores the pressure of the air on top of the water).

The pressure of the air on the water surface is about 100 000 N/m2 so the total pressure is 200 000 N/m2. In other words the pressure 10 m below the water surface is twice what it is at the surface.

The pressure at a certain depth in the liquid is the same at all points at that depth.

Pressure at A = Pressure at B = Pressure at C = Pressure at D = Pressure at E

Notice that it is only the depth of the liquid that matters; not the angle of the tube, the cross sectional area of the liquid column or the area of the liquid surface.

Water finds its own level, if we open the tap in the tube shown in Figure 5 the levels will become equal.

Knowledge of water pressure is very important in the supply of water to our homes.

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