AbstractPoncin's Navier‐Stokes solution for the falling head viscometer is obtained more directly by a Laplace transform method. Approximations which facilitate numerical evaluation are derived and Grumbach's result for an infinite capillary is obtained as a limiting case. A systematic series of approximations to the general, unsteady Euler duct equation are solved analytically. All solutions are compared with a numerical integration of the complete Euler duct equation. It is shown that all results become indistinguishable for sufficiently small Reynold's number and that the kinetic energy effect is clearly the major inertial effort.