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From Wikipedia:

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

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Suppose we apply 2 equal and opposite forces on a 2d plane with area 'A' perpendicular to it ($F_a$ & $F_b = F$)

Will we say that pressure is $0$ or $\frac{2F}{A}$

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Suppose we have static fluid in a container, then force applied by water on top of a cross-section (because of its weight) is equal the force being applied from the downside as it is a static fluid

Now as in the example of the plane if the answer is that pressure is 0 then the fluid at some depth also has equal and opposite forces then pressure even at some depth should be zero

And if it is $\frac{2F}{A}$ then the pressure should be multiplied by 2 which is not done in the derivation of "variation of pressure vertically with depth"

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id you excert a force in one direction , you always have the opposite force it is called actio= reaction, otherwise , with only one force you accelerate your plane in the direction of the force. as picture: you standing on the floor, exert a pressure of your weight divided by the area of your feet or shoes, but the floor presses against your feet.

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If you insert the plane into a container of gas at pressure P, the plane experiences equal pressure on both sides. That pressure is simple P. You are mixing up force and pressure. If pressure is only on one side of a plane, the net force on the plane is PxA (force per unit area, times area). Since the plane in this case is on both sides, and the area normal points in opposite directions on the two sides, the net force on the plane is PxA - PxA = 0.

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