# Investigating the pressure of a water column

#### Class practical

Observing water emerging from holes in a tin can.

#### Apparatus and materials

For each student group

Beaker or jug, 600 ml (approx)

Small beakers or disposable cups, 3

Tin cans, 2 (see Technical note 1)

Hammer

Bell jar (OPTIONAL)

#### Health & Safety and Technical notes

Wear eye protection when using the hammer to batter the cans.

1 The tin cans should preferably be about 0.5-litre size and can be obtained from home.

2 It is helpful to have a supply of sponges available for this experiment.

#### Procedure

a Take a tin can and make holes in it, near the bottom, with a bradawl. A block of wood, placed as an anvil inside the can, is a considerable help. The holes should be made at different places round the can all at the same level. With care, the bradawl will make the holes all the same size.

b Fill the cans with water over a sink and watch how the water spouts out.

c Take a second can and make three holes – one near the top, one part way down, one near the bottom. It is most convenient if the holes are slightly staggered around the can.

d Fill the cans with water over a sink and watch how the water spouts out. By pouring replenishing water into the can from the 600 ml beaker, the level of water in it can be kept constant. Collect the water spouting from the three holes in three separate beakers or cups and observe what happens.

e Take the first can and batter it into an irregular shape with a hammer. (Wear eye protection.) The aim is that the surface of the can at the three holes should be orientated in three different directions. Fill the can with water and observe the direction in which the water comes out and collect each stream in a separate beaker.

#### Teaching notes

1 These experiments are intended to be rough simple ones that can be repeated at home, to show students that simple experiments with common equipment can lead to useful knowledge. Therefore, it is essential to use ordinary things for the apparatus, such as tin cans and plastic or paper cups, and to make the holes with a bradawl. You may feel tempted to prepare special apparatus for this, which can have identical holes drilled so that it works well and can be stored away. That would miss the point of the present experiment, so rough apparatus should be used and students encouraged to make the holes for themselves using a bradawl.

2 It is difficult to twist a mercury barometer around to show that the atmosphere pushes in all directions, always perpendicular to any surface that it is offered; but we can show it with water.

3 With the holes all at the same level, and of the same size, then the water will spout out equally well from all the holes. The water from each of the holes could be caught in beakers and measured, so that a judgement on the equality of the hole size can be made.

4 With holes of the same size at three different levels in the can, the result is not what most people expect. Asked to sketch the jets of water from those three holes, you may predict a progression of ranges. The jet from the top hole can reach the table nearest the can, the jet from the middle will arrive further out and the jet from the lowest hole, with the biggest pressure will arrive farthest out.

A thought experiment warns that this must be wrong. If the can rests on the ground, water from the hole at the very top (the free surface) will dribble down the side and arrive at the very edge of the can. Water from the bottom, however fast it travels, will also hit the ground immediately, just at the bottom of the can. Yet water from some intermediate level will spout out and arrive some distance away.

5 To calculate the velocity v with which water emerges from a hole at depth h below the surface of the water, use:

mv2/2 = mgh
v2 = 2gh

where g is the gravitational field strength. Then the water can be treated as a projectile moving under gravity.

6 The third can has holes near to the bottom and is battered into an irregular shape so that the surfaces of the metal point in different directions. It will be found that the water leaves the can at right angles to the surface showing that pressure acts in all directions.

7 As an optional home experiment, students could fill a balloon with water and pierce it with a pin. First put a hole near the top, next halfway down, finally in the lower half, to see the direction of the pressure. This experiment does not always give consistent results and it is probably best to do it in the bath!

This experiment was safety-checked in July 2007