On The Uncertainty Of The Measurements Of Friction Factor In Trapezoidal Microchannels, A Statistical Analysis
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On the uncertainty of the measurements of friction factor in trapezoidal microchannels, a statistical analysis G. Bizzarri Dipartimento di Architettura, Università di Ferrara, Italy Abstract A large body of literature exists on fluid flow in microchannels, and several studies are specifically concerned with evaluation of the friction factor. Given the shape of the cross section, the value of the friction factor can be estimated from laminar pipe flow theory. However, a number of laboratory investigations found the experimental value of the friction factor to differ significantly from that predicted by the classical theory. To explain this discrepancy, several approaches are possible. In this paper, a stochastic approach is adopted to study laminar flow in trapezoidal microchannels. The friction factor is evaluated as a function of random variables: geometrical parameters characterizing the cross section, pipe hydraulic diameter, flow rate, and pressure drop over a given length; an effective (true) value of the friction factor is calculated assuming that the former variables fluctuate in space and time in accordance with sinusoidal functions. The effective friction factor is then compared with its apparent value computed from the mean (measured) quantities; a numerical example is also provided. Results show that, even though the difference between the effective and apparent value is often negligible, the statistical theory can nevertheless provide a possible explanation of the deviations between the experimental values of the friction factor reported in literature and those predicted from the conventional theory. Keywords: friction factor, trapezoidal microchannels, statistical analysis. 1 Introduction The knowledge of the flow behaviour at the microscale is an important issue in many engineering applications. In particular, to get a reliable prediction of friction factor is helpful in the design of microfluidic devices. This is for the
friction factor, trapezoidal microchannels, statistical analysis.