Jenny devises a clever way to measure the unknown density of a liquid. She build

Question

Jenny devises a clever way to measure the unknown density of a liquid. She builds a water tank that is divided into two parts with a partition wall as sketched. A liquid of known density rho k is poured into the tank, and then the liquid of unknown density rho u is carefully poured into the left half until it almost spills under the partition into the right side. The final condition has heights as sketched. The liquids do not mix. Derive an expression for the unknown density rho u in terms of the other variables in the problem, as needed. Stay in variables - no numbers.

Explanation / Answer

buoyancy force = weight of the liquid of density u

k([h2 - ho]Wg = uh1Wg

u = k[h2-ho]/h1

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