Question

A hydrometer is an instrument used to determine liquid density. A simple one is sketched in the figure below. 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. The density of the liquid is given by rho = rho_0 L/L - h. A hydrometer is to be constructed with a cylindrical floating rod. Nine fiduciary marks are to be placed along the rod to indicate densities of 0.98 g/cm^3, 1.00 g/cm^3, 1.02 g/cm^3, 1.04 g/cm^3, ..., 1.14 g/cm^3. The row of marks is to start 0.170 cm from the top end of the rod and end 1.37 cm from the top end. (a) What is the required length of the rod? cm (b) What must be its average density? g/cm^3 (c) Should the marks be equally spaced? Explain your answer. Yes. The density rho is not linear in L; as L increases at a constant rate, the fluid becomes more and more dense at a constant rate. Yes. The total length L and length above the surface h depend on each other, so in fact the density p depends on neither L nor h. No. The density rho is not linear in h; as rho increases, h increases at an increasing rate. No. The density rho is not linear in h; as rho increases, h increases at a decreasing rate.

Answer 1

a) required length of rod = 1.37 - 0.170

                                        = 1.2 cm

b) average density =   1.06 * (1.2 - 0.170)/1.2

                               = 0.9098 g/cm³

c) Yes, the density is not linear in L , as L increases at constant rate , the fluid becomes more and more dense at constant rate .