Physics-Fluids-Pascal's Principle Concept

[Dr. To Be]

Hello.


For the pistons system example, EK states since the area for Piston 2 is larger than the area for Piston 1 , then the force for Piston 2 would be greater. Why is that? Thanks

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[sapientnarwhal]

Pressure = F/A. The pressure exerted by the fluid is the same, so P1 = F1/A1 = P2 = F2/A2. Therefore if A2>A1, F2 must be proportionally larger to maintain the same pressure. However, the larger force is exerted over a smaller distance (work is the same).

 

[esob]

Well, we know from Boyle's law that PV = constant. That is, the product of pressure times volume is always the same, so if one goes up, the other goes down.

So in any given system then, P1V1 = P2V2. Think about if you push a certain volume of fluid from a syringe out of the tip. The product (PV) in the fat part of tube is equal to the product of (PV) coming out of the end.

Now, in a closed system, such as a typical bottle jack, the volume remains constant, so we know then that P1 = P2

Pressure, is a force per unit area, F/A

So if P1 = P2, then F1/A1 must equal F2/A2

Now if you think of these as ratios, it is easy to see that if A2 goes up, F2 must also go up to keep the ratio the same.

Specifically, if we plug in numbers for F1/A1, such as 10/10, we see that P1 = 1

If A2 = 20, the only way for the equation to remain balanced is for F2 to equal 20 as well.

The whole thing is easier to see if you write it out as fractions