Interdisciplinary Applied Mathematics

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The estimated Fanning friction factor (/fanno), experimental Fanning friction factor (/exp), and the theoretical friction factor for laminar incom-


pressible flows (^|) are given in Table 4.2. The experimental friction factor (/exp)    is calculated    by    using    both    the    adiabatic    flow    model    (equivalent


to the Fanno flow approximation), and the isothermal flow model for all three cases. The differences in the two predictions are negligible. For the JP9 case,    the    friction    factor    f and    the    Poiseuille    number    (Po)    are inde


pendent of the Reynolds number. However, for cases 2 and 3 there is a steep trend of decreasing Poiseuille number (Po) with decreasing Reynolds number (Harley, 1993). The reason for this trend may be associated with the portion of the channel JP6 being in the early transitional flow regime (Kn > 0.1). The theoretical values are calculated assuming laminar, fully developed, incompressible flows, where the Fanning friction factor is given as


Po


Re


f


Here the Poiseuille number (Po) is a parameter that depends on the channel’s cross sectional geometry, and it is independent of the Reynolds number of the flow. Values of Po are given as a function of the ratio of the channel depth    to the    channel    width    (see equation    (54)    in    (Harley,    1993)).    The


theoretical values of friction factor are based on the incompressibility assumption, because calculations for the friction factor of compressible flows are not available. The theoretical values of the friction factor are greater than the experimental predictions for all of the cases. There are three main reasons for this trend:


   compressibility effects,


   rarefaction effects, and


   two-dimensionality effects.


Here both the predicted and the experimental friction factors are based on one-dimensional arguments.

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