Exploring the Pressure Change in a Cylinder w/ Piston

[rajumahtora]

Homework Statement

Given below is a cylinder with piston with same area at both the ends. The cylinder holds pure water in it. If force F is applied from both the ends, find the change in pressure at point B.Ignore Atmospheric Pressure

2. Diagram

The Attempt at a Solution

According to me, the answer is 2F/A coz we have to add pressure from both the sides.
∴ The change in pressure at Point P is 2F/A.
But the answer given in the solution is F/A. When I said to check the answer, they told that F/A is correct.
How is it possible? Please Explain.

 

[Chestermiller]

Imagine that you replace all the fluid (and piston) to the left of location B with a new piston, and imagine that you apply whatever force is necessary on that new piston to prevent the fluid to the right of the new piston from moving. Does the fluid on the right of B know that you have done this? No. So the force exerted by the fluid to the left of B and acting to the fluid to the right of B must be F.