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Pressure at same level in a liquid in U-tube

Physics Asked by Forex007 on January 10, 2021

Why does the pressure at same level in a liquid with uniform density same in both arm of a U-tube even when there is a liquid of another density at one arm? Please give me an intuitive explanation

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2 Answers

The region to focus upon is not above dotted line AB, but below this line. Since, according to Pascal's law, at a given location in the fluid, pressure is the same in all directions, the pressure at static equilibrium does not vary horizontally; it only varies vertically, according to $$frac{dp}{dz}=-rho g$$where z is the elevation. So, if you integrate around the U from A to B, you get p(B)=p(A).

Correct answer by Chet Miller on January 10, 2021

In your diagram, if the pressure were higher on one side then it would push the other side up until pressures were equal. If you have liquids of different densities, that means that their weights will be different for the same volumes. You can think of the U tube as being in balance, you will have the same weight of liquid on each side of the center even if they are of different volumes.

Answered by Adrian Howard on January 10, 2021

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