# Pressure difference in u tube

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?

• 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. Commented Dec 15, 2013 at 16:32
• '-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, Commented Dec 15, 2013 at 18:51

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.