Uncertainty assessment in friction factor measurements as a tool to design experimental set-ups

The promising performance of microchannels has given rise to intensive research on pressure drop and heat transfer characteristics of flows at the small scale. To check the classical models and to validate new ones, experiments need to be conducted, which are particularly difficult given the characteristic dimensions involved and the magnitude of the fluxes to be measured. Although more care has been devoted lately to the design of experiments in terms of control of the geometry and of the boundary conditions, the uncertainties which inevitably affect each measurement do not seem to have been given the proper consideration. Correctly calculating uncertainties not only allows a correct assessment of the experimental data obtained, but can also be used to decide which measurements need to have the highest precision to achieve a certain accuracy, thus saving money on the others. In this paper, a quantitative criterion is given to assess the accuracy achievable in the determination of the friction factor in the laminar regime for the flow of a fluid in a circular microtube. The influence of the six quantities (pressure drop, outlet pressure, temperature, length, diameter and volume flow rate) measured to determine f in the laminar regime are studied separately and when combined. It is found that at low Reynolds numbers flow rate and pressure drop measurements are determinant for the final value of the uncertainty, while at larger Reynolds numbers the influence of the accuracy in measuring the hydraulic diameter prevails and also limits the minimum value that the total uncertainty can take.