Unifying the Teaching of Mechanics and of Centrifugal Pump Theory

Abstract

Using the equation of motion of a particle in a rotating co-ordinate system, it is shown that the head developed and the power required by a centrifugal pump are uniquely obtained from centrifugal forces. An expression is then obtained for the optimum outlet blade angle which is used to demonstrate that the phenomenon of slip has a dynamical basis.

A dynamical basis for slip in centrifugal impellers

“…The following expressions 1 define the trajectory of a fluid particle in a rotating coordinate system with origin at the centre of a radial impeller where θ is the polar angle of the position of a particle at a radial distance, r , from the centre, β the angle which an element of the trajectory makes with the radial direction and r· and θ· the rates of change with respect to time of the parameters. The above equations then yield the following expression for the polar angle, θ , as function of the radial distance, r , of the particle 5 where β 1 is the inlet relative flow angle at the radial distance r 1 .…”

“…The basic equations of fluid mechanics are based on the notion of the motion of fluids being that of a collection of particles. This fact has been used 1 to obtain performance equations for centrifugal impellers using mechanics of particles in a rotating or non-inertial coordinate system. Such inviscid motion which was found to result from a balance between the Coriolis and tangential forces of the vanes of a two-dimensional (2D) impeller was characterized by the conservation of angular momentum.…”