The hole-pressure problem

There is a need to unify present hypotheses of the nature and role of the hole-pressure,p_e, and thus provide consolidation on which to base future research and understanding. This paper is intended to meet this need. Attention is directed towards the calculation ofp_e from the velocity and stress fields for viscoelastic fluids flowingacross rectangular holes. The constitutive models used are the Newtonian, Second-order and Maxwell models, for values of Reynolds number up to 10 and Weissenberg number up to 0.1.The numerical complications involved are studied through an investigation of the constituent parts ofp_e. Verification of present theory is then sought, from which justification may be derived for the estimation of elasticity fromp_e measurements. Attention is directed towards the predictions of Higashitani and Pritchard and the extension to the Tanner and Pipkin theory for Second-order fluids. The effects of variation of geometric dimensions and flow type uponp_e are also discussed.