Chapter 14, Problem 36P

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 ρ₀, floats partially immersed in the liquid of density ρ. A length h of the rod protrudes above the surface of the liquid. Show that the density of the liquid is given by

$\rho =\frac{{\rho }_{0}L}{L-h}$

Figure P14.16 Problems 16 and 17