# Variation of pressure of a gas in any accelerating container

Like the picture shown above the container contains a liquid with density 'rho' and the container is given an acceleration towards right and so by considering that any liquid section is also having the same acceleration as that of the container we can find out the pressure variation by using Newton's laws of motin . But if there were a gas instead of liquid would its pressure also vary like that of the liquid? And if it varies then can we find out the variation of pressure inside the gas like the same way we have found out in case of the liquid? Since gas and liquids both are fluids and share a large number of common properties . And both the liquid and the gas in this context must be assumed as ideal . And the container in which the gas would be kept is totally closed.

• I'm not sure how you are intending to carry this activity out with a gas. If the container is not closed as shown above , there would be diffusion of gas to atmosphere which would need to be taken into consideration. Mar 31, 2019 at 2:17
• Oh I am sry please assume that the container is totally closed Mar 31, 2019 at 9:04

## 1 Answer

Short answer is "yes". The preassure of gas/liquid in different parts of the container would be $$\Delta{P} = \rho g \Delta{h} + \rho a \Delta{l}$$ (it depends on both $$x$$ and $$y$$ position in the container).

Note, effects of gravity and "moving with acceleration" are very similar. Actually they are indistinguishable (that is "principle of equivalence").

• Wouldn't density be a function of position, since it is a gas. Mar 31, 2019 at 11:16
• But how can we relate the pressure variation in gases just like that of a liquid the pressure of liquid changes with height but it's not so for an ideal gas Mar 31, 2019 at 12:12
• @VaishakhSreekanthMenon You are right, the density of gas is a function of position. But in usual scales (if we are talking about some tank and wehicle) the effect is quite small. That's why I did not mention this effect in my answer. Then again, even for liquids the density is a function of pressure! This effect is much-much-much smaller than for gases, but it exists. Mar 31, 2019 at 15:12
• @RifatSafin The pressure of gases does change with height! Usually you do not have to take this effect into account when solving problems because the effect is quite small. If you take a container with height 1 m and fill it with air with usual conditions (room temperature, normal atmospheric preassure) the preasure at the top of container would be 0.01% smaller than the preassure at the bottom. The difference is exactly the same as would be the difference between the preassures at the front wall and the back wall of the 1m-long container moving with $a = 9.8 m / s^2$. Mar 31, 2019 at 15:24
• @lesnik ,But if the container is closed, wouldn't the gas spread out? . Im not able to understand how there would be a height difference. Mar 31, 2019 at 15:27