An equation based on the hydrodynamical equations of change is solved, analytically and numerically, for the calculation of the viscosity from the mass-flow rate of a steady, isothermal, compressible and laminar flow in a capillary. It is shown that by far the most dominant correction is that due to the compressibility of the fluid, computable from the equation of state. The combined correction for the acceleration of the fluid and the change of the velocity profile appears to be 1.5 times larger than the correction accepted to date.