![]() Here, $h$ is the height of the liquid which is the same for all the vessels. $$0 = - \frac + \rho g$$ $$\partial P = \rho g \partial y$$ ![]() If you write the Navier-Stokes equation in Cartesian (i.e., Descartes) coordinates and consider the projection on the vertical axis, you'll have that all the acceleration terms and viscous terms are zero and you're left with the following: ![]() It follows from the Navier-Stokes equation. Yes, it does, the pressure force acting on the bottoms of each container is the same. If the fluid exerts a force with a downward component on both walls, and neither the walls nor the fluid is in motion, we know that the walls exert a force with an upward component on the fluid, which must transmit this force as a reduction in apparent weight to the bottom of the container.Īrgue from Newton's Third Law and your knowledge of the pressure at some small volume for which there is a continuous column of water directly above the sample volume to prove that the fluid pressure at all points with the same height difference from the highest point of a static fluid exposed to air must be equal. If the fluid exerts a force with an upward component on both walls, and neither the walls nor the fluid is in motion, we know from Newton's Third Law that the walls exert a force with a downward component on the fluid, which must transmit this force as an increase in apparent weight to the bottom of the container. What can we infer about the direction of the net force on the side walls of each container caused by fluid pressure? Pressure at any given point points equally in all directions.
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