Generalization of Bernoulli's theorem for an elastic fluid and its application to some flow problems

Abstract

Viscoelastic fluids sometimes possess a dominant elastic stress relative to the viscous stress and in this case the viscous contribution can be neglected and the fluid is thought to be as an elastic fluid. In the present paper the author extends the theorem of Bernoulli for perfect fluid to a generalized theorem of Bernoulli for the elastic fluid in which a term of elastic stress is added to the dynamic pressure term, the static pressure term and the gravitational term. Based on this equation some flow problems are examined; the contraction of the flow in a reservoir discharging a elastic fluid, the pressure of the flow through a converging and diverging channel, the abnormal pressure rise just downstream of the inlet of a pipe flow, the diameter of the jet issuing from an orifice to the atmosphere and a falling liquid column in the gravitational field. It is shown that the results agree at least qualitatively with experimental data so far obtained.