The development of radiotracer methods for laminar flow measurements in small channels—I. The basic response model principle and rationale

Abstract

A general tracer principle is identified for the determination of laminar flow rate in channels of constant cross section. It is based on the development of a mathematical model that relates the detector response to the tracer initial condition and the pertinent flow parameters in the channel. The flow rate and other flow parameters of interest are obtained by fitting the model predictions to the experimental responses obtained. The principle is generally applied by: (1) injecting the tracer in a reproducible way so that a known initial condition is obtained, (2) monitoring the resulting tracer concentration at a suitable downstream point, and (3) obtaining the flow rate and other flow parameters of interest by a nonlinear search for the minimum reduced χ 2 value obtained from model predictions and experimental responses. Considerations pertinent to the principle and general method are discussed in this present part while two specific methods are treated subsequently in Parts II and III.