Push Water in a pair of Connected Syringes
This simple experiment is often taken as an example of Pascal's law of transmission of Pressure or a demonstration of \(F=PA\). However this popular belief does not pass the test of deeper analysis.
two syringes of different sizes connected by a small flexible plastic tube. Some water is filled in one of the syringes.
- Suppose you have water in the bigger syringe and the piston of the smaller syringe is staying against the end. Hold the bigger syringe between the two fingers and a thumb. The thumb is on the circular base of the piston while the fingers are on the two extrusions of the barrel.
- Push on the base by the thumb so that water goes from the bigger syringe to smaller one. Feel the amount of force.
- Now water is in the smaller syringe. Holding this syringe as usual between two fingers and one thumb, push the water back to bigger syringe. Feel the force you have to apply.
- In which case you had to apply a larger force?
As you are comparing forces in two different experiments (Step ii and iii above), you should not use Pascal's law which talks about increase in pressure everywhere in the liquid, but at the same instant. For the same reason you cannot equate pressure in two cases and make force proportional to the area of the base. Then what is it?