A theoretical analysis has been made of the effect of different velocity profiles on the dispersion of a non-diffusable solute in fluid flow down a straight tube. An experimental investigation of this type of dispersion was made by monitoring the transport of radioactively labelled red blood cells in whole blood at flow rates within the non-Newtonian viscosity range. The dispersion curves obtained are consistent with a progressive flattening of the velocity profile as the flow rate is reduced, though a more rapid clearance than that predicted theoretically occurs in the tail region of the curves. The accepted indicator dilution techniques of estimating the flow rate and vessel volumes are considerably in error. An alternative method of accurately estimating the vessel volume is suggested.