An indirect pressure-gradient technique for measuring instantaneous flow rates in unsteady duct flows

A new technique is presented for making measurements of the instantaneous flow rate in unsteady laminar pipe flows. It utilizes a relationship between flow rate and pressure-gradient history that is an exact solution to the Navier–Stokes equations for parallel, developed flow of constant-property Newtonian fluids undergoing arbitrary unsteadiness from an initially steady or stationary state. The method does not rely on any assumption about velocity profiles, and applies instantaneously in momentarily reversing flow. Experimental comparisons between direct measurements of the cumulative flow and the results of this technique indicate that it is capable of providing measurements of cumulative flow and flow rate which are accurate to within a few percent at any instant during a flow transient, provided the instantaneous pressure gradient can be measured with this accuracy.