Appendix: Analysis of a hot-film anemometer

Summary

Introduction

All the velocity profiles measured in arteries (and reported in chapter 1), almost all the profiles measured in models or casts of arterial junctions (chapter 5) and all direct measurements of wall shear-rates in models have been obtained by the use of a hot-film anemometer (or its close relation, an electrochemical shear probe). Therefore it is important to understand how such a device operates, particularly since the main justification for the detailed theoretical analysis of flow in bends and bifurcations (chapters 3 to 5) rests on the claim that hot-film anemometry is not at present capable of the accurate measurement of unsteady wall shear in arteries.

A constant-temperature hot-film anemometer consists of a thin metallic (usually gold) film mounted flush with the surface of an insulated solid probe, which is inserted into the fluid whose velocity is to be measured. The temperature of the film is maintained by an electronic feedback circuit at a fixed value, T₁, slightly higher than the temperature of the fluid, T₀, which is also assumed to be constant. The power required to maintain it is proportional to the rate at which heat is lost to the fluid, which is in turn related to the velocity of the fluid flowing past the probe. In steady flow, this latter relation is obtained by calibration in known flows, after which the probe can, in principle, be used in any steady flow of the same fluid.