Question

A U-shaped tube is partly filled with water and partly filled with a liquid that does not mix with water. Both sides of the tube are open to the atmosphere. If h1 = 0.53 m and h2 = 0.25 m, what is the density of the liquid?

Answer 1

The static pressure of a column of liquid is\[P=\rho gh\]and because both ends of the u-tube are open to the atmosphere, we can neglect atmospheric pressure. Because this u-tube is in static equilibrium, the pressure exerted by both liquids must cancel. Therefore, \[P_1 = P_2\]\[\rho_1gh_1=\rho_2gh_2\]\[\rho_1h_1=\rho_2h_2\]Solving here is a matter of arithmetic; however, water is 1 or 2 depends on if the liquid is more or less dense than water.

I hope that helps.