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Suppose you have a U tube filled with a liquid. The height of the liquid column in both the arms of the U tube is not the same. Will the pressure be the same at two points in the two arms of the U tube which are at the same height from the base of the U tube or will it vary depending on height of liquid column above these two points?

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    $\begingroup$ This depends on how the height difference is caused. I assume you mean a stationairy situation. Because if this is due to different air pressure, than yes. But if this is due to capillary action, than it will depend on the shape/material of the tube. $\endgroup$
    – fibonatic
    Dec 15, 2013 at 16:32
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    $\begingroup$ '-1' clarify your question. 1 does the diameter of U-shaped tube is same throughout. 2 is it in steady state or oscillating. 3 you should add a picture. show what you have tried to find the pressure difference i.e have you considered the weight and atmospheric pressure or your tube is in vacuuo, $\endgroup$
    – user31782
    Dec 15, 2013 at 18:51

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Assume that the liquid has a uniform density, $\rho$, and that the diameter of the U-tube is large enough to preclude capillary effects. Tha acceleration of gravity, $g$, is the same for both arms of the U-tube.

Pick a reference point at the bottom of the U-tube, where the absolute pressure is defined as $P_0 \text{ }$. Move from this point up each arm in the U-tube in turn, keeping track of how far up, $(h)$, you move in each arm. Of course, you can't leave the fluid.

The pressure $P$ at any point is given by:$$P=P_0-\rho g h$$ If $h$ is the same, then $P$ is the same.

Warming one arm is one way to invalidate the assumption of unifrom density...

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