# Is it possible to have no pressure gradient in a tank? [duplicate]

If a sealed container that is 20 miles high is filled to a pressure of 50psi gauge pressure, will it have a pressure gradient the same as the Earth or does the fact that it is filled to more than atmospheric make a difference. Is not 50psi 50psi? Are the molecules not pushing in all directions inside the tank at 50psi? Does that then mean that the pressure of 50PSI at the top of the container is the same as the pressure at the bottom of the container also at 50PSI? 50psi being well in excess of atmospheric pressure.

## marked as duplicate by BowlOfRed, Aaron Stevens, Thomas Fritsch, PM 2Ring, John RennieSep 3 at 19:18

The pressure gradient exists because the gas is in the presence of a gravitational field. This applies to all cases, regardless of the storage pressure of the gas. In addition, given that gases are compressible, you will find that the pressure gradient of the gas in question is $$dP=\rho g dh$$, where the density at 50 psig will be higher than the density of the atmosphere. An integration is required to get a function of height vs. pressure, but it should be noted that the pressure gradient in the 20 mile high container will be somewhat greater than in the outside atmosphere due to the higher density of the gas in that container.
At the top of the container, you can have a $$50 \ psi$$ pressure, as you mention. At that point, the force acting in every direction is 50 pounds per every square inch of surface area of the container. This keeps the fluid in equilibrium with the container and with the rest of the fluid.
The fluid on top of the container is pushing with $$50 \ psi$$ downwards. A bit further down the container, the fluid is being pushed by the $$50 \ psi$$ plus the weight of the air which is above it. This is the primary mechanism which creates your pressure gradient. More dense fluids will have a steeper gradient because they push down more on the fluid below.