Serway & Jewett — Fluid Mechanics: Problem 16

A hydrometer is an instrument used to determine liquid density. A simple one is sketched in Figure P14.16. The bulb of a syringe is squeezed and released to let the atmosphere lift a sample of the liquid of interest into a tube containing a calibrated rod of known density. The rod, of length \(L\) and average density \(\rho_0\), floats partially immersed in the liquid of density \(\rho\). A length \(h\) of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by \[\rho = \rho_0 \frac{L}{L - h}\]