Hydrodynamic drag force in liquids
Laing, Ronald A.
Doctor of Philosophy thesis
A number of spheres of different radii and masses have been dropped in liquid helium I and II, liquid air, ethyl acetate, and water. The terminal velocity of each sphere falling in the confined liquid was measured. When falling at constant velocity, the hydrodynamic drag force, D, is equal to the weight of the sphere, and the drag coefficient, CD, in the formula for the drag force, D = CD( 12rv2 )A could be evaluated as a function of Reynolds number, NR = rvah , and ball radius, a. In these formulas D is the drag force on a sphere of cross sectional area A, moving through a liquid of density r and viscosity h with a velocity v. The drag coefficient for spheres falling in an infinite liquid has been measured by many observers and found to be a function only of the Reynolds number, NR. Our experiments were done in a cylinder of radius, R; spheres have been used with radii such that 0.18 ≲ a/R ≲ 0.83. By comparing our results for the drag coefficient, CD, with the published values of the drag coefficient in an infinite liquid, C D a wall correction factor, K = CD/ CExpD , has been determined as a function of NR and aR . Due to the equality of the drag coefficients in helium I and helium II at high Reynolds numbers it has been shown that at high Reynolds numbers helium II behaves as an ordinary fluid of density r=rn+rs .