Consider a container of height $h$ filled completely with fluid of density $\rho$, Assume pressure at top is zero therefore pressure at the bottommost points will be $p_b=\rho gh$ and therefore force exerted by fluid at bottom surface will be $F=\rho ghA=mg$ where $m$ is mass of fluid.

The above equation implies that in a gravity free space force exerted by fluid at the bottom surface of container will be zero, but wouldn't fluid particles b colliding with the surface and exert some force on it, just like a gas does?

In short , are collisions of molecules with the surface ignored while calculating fluid pressure ?

In such a case if gravity only results in fluid pressure then why does two horizontal sections of fluid at same height push each other with force $PA$ where $P$ is pressure at that height?


1 Answer 1


They are not. Under gravity, the particles are held close to each other until the collisions between them are frequent enough to stop this compression reaching an equilibrium. It is precisely these collisions that exchange momentum with the wall and result in a pressure on the wall when coarse-grained.

Without gravity, initially there would be nonzero pressure on the wall too (assuming a certain mass of fluid begins in a configuration that is surrounded by walls on part of its boundary). But soon the particles would push each other apart and away from the surface, making the collisions less and less frequent and thus the pressure less and less intense. Here I am assuming there is a free boundary somewhere that applies zero traction to the fluid surface and a route for it to escape.

  • $\begingroup$ There would be some non zero pressure as you said in case gravity is not there but why does equation gives zero ? $\endgroup$ Mar 22, 2022 at 14:56
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    $\begingroup$ Because the equation assumes that the fluid has reached an equilibrium; that is, that is not in the middle of a transition to becoming less dense or moving at all. $\endgroup$ Mar 22, 2022 at 15:08
  • $\begingroup$ so what , even if it reaches equilibrium the liquid molecules cannot expand indefinitely like gas they will be bound by interatomic forces and hence they should execute some non zero pressure at equilibrium state also $\endgroup$ Mar 22, 2022 at 15:13
  • $\begingroup$ @LalitTolani Water will not stay as a liquid in space it will evaporate. $\endgroup$
    – Azzinoth
    Mar 22, 2022 at 15:21
  • $\begingroup$ Ok @Azzinoth but what will you say when I say I have a closed container? $\endgroup$ Mar 22, 2022 at 15:22

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