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Working equations for the oscillating-cup viscometer

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Abstract

The paper briefly recapitulates the exact theory of the oscillating-cup viscometer given by Newell and his co-workers. The complexity of the exact solution explains the bewildering variety of approximate theories encountered in the literature.

The exact equation is reduced to two simple analytic forms which can be used in practice, respectively, for design and for the evaluation of results.

The exact solution has been programmed on a computer to generate accurate values of the decrement and period that would be encountered if measurements were performed under a variety of conditions. These are then used critically to assess the quality of several theories proposed earlier.

It is concluded that for ξ0>10 and R/h<-2, an accuracy of 0.1% or better can be secured only if the simplified form of the equation proposed by Beckwith and Newell is used. The other simplified equations introduce systematic computational errors ranging from a few tenths of one percent to as much as 8–10%. Roscoe's equation provides a very good approximation over most of this range, its computational error amounting to no more 0.2% at ξ0=10.

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Grouvel, J.M., Kestin, J. Working equations for the oscillating-cup viscometer. Appl. Sci. Res. 34, 427–443 (1978). https://doi.org/10.1007/BF00383975

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Keywords

  • Exact Solution
  • Analytic Form
  • Computational Error
  • Exact Equation
  • Exact Theory