Upthrust in Fluids

When we dip ourselves in a swimming pool, we feel lighter. There is a force from the water pushing us up. This force is called the upthrust. A piece of wood floating on water, and a helium balloon floating in the air, are both effects of upthrust.

Here, we want to learn how to calculate this upthrust. The way is called the Archimedes principle. It states that: the upthrust is equal to the weight of the fluid displaced.

To see what this means, consider putting a rock in a bucket of water. Suppose that the rock has a mass of 300 g, and volume of 100 cm3. When this is put inside the water, it would have to push aside some water. (In this case, it would end up raising the water level in the bucket.) The volume of water that is pushed aside would be equal to its own volume, that is 100 cm3. We call this the displaced water. What the Archimedes principle says is that the weight of this displaced water is equal to the upthrust.

Lets work out what this upthrust force is. The density of water is 1 g/cm3. The volume of the water displaced is 100 cm3. So the mass = density x volume = 1 g/cm3 x 100 cm3 = 100 g = 0.1 kg. The weight = mass x acceleration of free fall = 0.1 kg x 9.81 m/s2 = 0.981 N. According to the Archimedes principle, this weight is the upthrust. So the upthrust is 0.981 N.

Where does this upthrust come from? The answer is water pressure. The pressure of water increases as you go deeper. On the top surface of the rock, the pressure ofwater there would be pushing down on the top. On the bottom surface, the pressure of water there would be pushing up at the bottom. Since this pressure is larger than the pressure on top, there would be a resultant upward force. This is the upthrust.

This idea applies to all types of fluids, whether they are liquids or gases. So a helium balloon floats upwards because the air pressure is higher on the bottom surface than on the top surface of the balloon. The resulting upthrust is again given by the Archimedes principle. So the upward force on the balloon is equal to the weight of the air displaced. This is the weight of air with the same volume as the balloon. If a hot air balloon were to be able to lift up a person, the weight of the air displaced must be more than the weight of the person. Since the density of air is very small, we need a very large volume. This explains why hot the air balloon has to be very large.


Copyright 2011 by Kai Hock. All rights reserved.
Last updated: 12 March 2011