Role of pressure dependent viscosity in measurements with falling cylinder viscometer

The falling cylinder viscometer is frequently used in measuring the dependence of the viscosity on the pressure. The viscosity is calculated using an indirect procedure, namely by appealing to the linear relation between the time taken for the fall and the viscosity. Under certain assumptions, the coefficient of proportionality can be derived analytically, and one gets the classical formula for the viscosity as a function of geometric parameters of the device, density of the fluid and the sinker, gravitational acceleration, and the distance and the time of the fall. Although the classical formula is valid only for fluids with constant viscosity, it is indiscriminately used even for fluids with pressure dependent viscosity. We investigate the role of variable viscosity, and we derive a heuristic correction to the classical formula for the case of fluids with pressure dependent viscosities. The systematic error introduced by the unwarranted application of the classical formula for fluids with pressure dependent viscosity is analysed, and it is shown it is measurable and it can in some cases significantly influence the experimental results.

► We discuss measurements in the case of fluids with pressure dependent viscosity.
► The classical formula used for Navier–Stokes fluid is not valid.
► A correction of the classical formula is derived and its implications are discussed.