Teaching Pascal’s Principle to a 10 year old

We will use the same method of Explore, Experiment, Experience and Express to learn the Pascal’s principle.

Assume there are four containers with water. They all have different shapes, but have the same base (area a) and height of water (h). As shown in the picture below. Say we call them C1, C2, C3 and C4.

What would the order of these containers be if we were to weight them (Of course the base is closed)

Most children would guess C3 > C2 > C4 > C1. Some could debate about C2 and C3. But, it’s quite obvious.

A little of bit of theory helps. Pressure is the force experienced per area.

In the class we do a small activity to experience the meaning of pressure. Have each kid push each other on one side. (Instruct them not to hurt each other !!)

Ask them if they felt the force on the other side? The answer is a lot of giggle and a clear NO.

No ask them to poke each other in the same place with a similar force. Now ask them when they felt more pain. The answer is when you poke, than when you push. That is the difference between low pressure and high pressure. When you push the force is distributed over a larger area. When you poke it is distributed over a smaller area.

This is the reason why a woman in high heels weighting just 100 pounds (~ 45 kg) exerts 15 times more pressure than an elephant weighting 12,000 pounds (~5,400 kg) does with one foot. (Source LSNED)

 

One last thing. The unit of pressure if Pascals. Let’s get back to the original problem.

Now imagine the bases are open and we check the pressure of water at the base (using some pressure gauge). The pressure is obviously caused by the force of water trying to jut out of the base.

What would the order of pressure be among the containers?

Most children will say it will probably be the same as the order of weight. I thought so too the first time. C3 > C2 > C4 > C1.

Pascal discovered that fluids behave in a very counter intuitive manner. The pressure would be the same across the containers.

C3 = C2 = C4 = C1.

Holy molly !! How unusual.

My friend Rajeev who attended the seesion asked if that would be the case if it was sand instead of a fluid. The answer is NO. This would happen only for a fluid.

This is the basis of what is called the Pascal’s vases. If we open all the bases and connect them, the water levels will remain the same. See the picture below.

 

Why do we see this counter-intuitive behaviour?

It is to do with the basic characteristic of fluids, like water. They are incompressible. So pressure change at any part is transmitted (almost instantaneously) to all parts of the fluid. The pressure at a certain point only depends on the depth of the fluid.

Pascal’s law (also Pascal’s principle or the principle of transmission of fluid-pressure) is a principle in fluid mechanics that states that a pressure change occurring anywhere in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere (Source Wikipedia)

The genius of Blaise Pascal (a 17th century physicist and mathematician) was not just in observing this phenomenon, but translating this into a very interesting application – the hydraulic press.

When a small force is applied on the left side, given the same pressure if transmitted everywhere, the force is multiplied on the right side (in this case by 10 times). This mechanism is used  in many places, including at your car garage and airplane brakes.

There is a lot more one can talk about the applications, but I’ll stop here for now.

In another blog I will also share a very interesting conversation I had with my friend and fluid mechanics guru Roopesh Mathur. He explained the deeper thinking behind this behaviour of fluids.