Pascal Law: Pressure Increase in Symmetrical Container

[jonny23]

Homework Statement

a water filled symetrical container has four pistons , one on each side of area A to keep water in equilibrium

Now an additional force F is applied to all four pistons . then increase in pressure at the middle of container will be:

Homework Equations

pascal law: change is pressure is transmitted to whole fluid

The Attempt at a Solution

since F is applied from four sides so pressure should have been 4F/A but the solution says F/A

 

[Bystander]

What's the definition of pressure?

 

[jonny23]

Perpendicular force per unit area..

 

[Bystander]

Now apply that definition to the problem.

 

[jonny23]

but the force is from all sides so either vector sum should be 0
or if add as scalar it should be 4F/A...
but the answer is only F/A

 

[Bystander]

The force is being applied to a fluid, not a solid. What happens when you stand on a water balloon?

 

[jonny23]

can you give a more detailed reply to this question...

 

[Bystander]

Perpendicular force per unit area..

but the answer is only F/A

4F/4A is the same thing as F/A. If we're discussing pressure as a thermodynamic variable, it's what is called an intensive variable, independent of the size of a system. Mathematically, it's a scalar. Force has a direction, yes; force per unit area has no direction. Pressure times area has a direction. The scalar-vector conflict may be what's confusing you. Stick with it, and we'll sort it out for you.

 

[jonny23]

thanks @Bystander