Any object kept in an accelerating container of water feels different pressure than unaccelerated. Because if we go into the frame of water the g effective changes. Since air is also a fluid  , a container of liquid accelerating upwards should experience more atmospheric pressure than it feels at rest, but intuitively it does not feel so. Am I correct in assuming that liquid feels more atmospheric pressure? (Quantiatively, P×(g+a)/g)

Any object kept in an accelerating container of water feels different pressure than unaccelerated. Because if we go into the frame of water the g effective changes. Since air is also a fluid, a container of liquid accelerating upwards should experience more atmospheric pressure than it feels at rest, but intuitively it does not feel so. Am I correct in assuming that liquid feels more atmospheric pressure? (Quantitatively, $P×(g+a)/g$)