Moment relations in indicator dilution theory (Q1116866)

The indicator dilution method consists of injection of an indicator into the tube system and of measurement of its concentration c(t) at a downstream sampling site. The connection between the volume V of the system and the flux F (which is the integral of the velocity profile) was posed by Stewart-Hamilton equations: (*) \(F=q/\int^{\infty}_{0}c(t)dt\), \((V/F)=\int^{\infty}_{0}tc(t)dt/\int^{\infty}_{0}c(t)dt)\), where q is the total amount of indicator applied. The authors investigated the validity of the first equation in SIAM J. Appl. Math. 34, 666-675 (1978; Zbl 0381.76100) with the following result: The Stewart-Hamilton equations are not universally true, but there are indeed some experimental set-ups where they are fulfilled. In these cases the equations (*) can be used to calculate V and F by the first two moments of the dilution curve c(t). In this paper we investigate the possibility to calculate the most important hydromechanical parameter - the velocity profile - by means of all moments of c(t).