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A fluid in equilibrium is trapped inside a cube, outside the field of gravity. If a force F acts upon the centre of every seat of the cube via a piston of area A, what is the total pressure in the centre?

I think that the answer is $P=\dfrac{6F}{A}$ my textbook says it is $P=\dfrac{F}{A}$, why?

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    $\begingroup$ Well, this case is really the same as you have one piston and the other 5 walls are perfectly rigid. $\endgroup$
    – zeta-band
    Commented Jun 5, 2018 at 19:00
  • $\begingroup$ we have six pistons, one in the centre of every seat of the cube...why it is the same,please explain if you can. $\endgroup$
    – Anastasios
    Commented Jun 5, 2018 at 19:08
  • $\begingroup$ Why we cannot add the pressures? $\endgroup$
    – Anastasios
    Commented Jun 5, 2018 at 19:29
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    $\begingroup$ The key is that nothing is moving. If the fluid pushes out with F/A, then the walls must push in with F/A or something will start moving. $\endgroup$
    – zeta-band
    Commented Jun 5, 2018 at 20:22

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On each face of the cube the force is $F$ and the area is $A$ so the pressure exerted by this force is $\frac FA$.
To stop the face moving the fluid inside must also exert a pressure of $\frac FA$.
The pressure within all the fluid must be $\frac FA$ otherwise the fluid would start moving.
On the other faces there must also be forces of magnitude $F$ otherwise the faces would start moving.

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