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In fluid power applications, pipes may have important effects on the system performances. In hydraulics, simple pipe models could give a good approximation of the pressure drop, but in pneumatics, accurate approximations are more complex because of the fluid compressibility. Therefore, simple but accurate models of air mass flow rate in pipes are still needed for system design and control purposes. The main contribution of this article is to propose a novel analytical formulation of the mass flow rate in pneumatic pipes by taking into account the pipe friction factor and more specifically its dependency on the flow Reynolds number. Accordingly, it makes it applicable to any circuit conditions (variable pressure at upstream or downstream pipe sides). The proposition here is a physically based adaptation of the flow approximations as defined in the first edition of the ISO 6358 standard and only uses the two conventional flow rate parameters; the novelty is to introduce a specific relationship between these flow parameters and the pipe friction factor. The proposed formulation provides a simple analytical way to predict accurately pipe behaviour in pneumatic circuits for sonic and subsonic flows. Based on this formulation, the calculated mass flow rates show a good agreement with measurements obtained with pipes of different diameters and lengths, even for variable upstream pressure conditions. Finally, limitations of existing formulations are discussed and advantages of the proposed approach highlighted. [ABSTRACT FROM PUBLISHER]

The aim of this note is to obtain a flow rate equation for subsonic Fanno flow, which has a form similar to the flow rate equation for isothermal flow. When pipe dimensions and the proper values of pressures and temperatures at two sections along a pipe, namely P1, P2, T1 and T2 are given, the mass flow rate is obtained by simple substitution into the obtained formula. However, only three of the above four quantities are independently given, since the steady Fanno flow problem involves three first-order differential equations. Therefore, the problem has three degrees of freedom. The theory in this note shows an algebraic equation that determines the fourth quantity by using the given three quantities. The method for finding the mass flow rate and state variables of the gas in the pipe are substantially simplified compared with the commonly distributed method. The relative difference of mass flow rates between the subsonic Fanno and isothermal flows is smaller than 1% in practical combinations of P2/P1 and the pipe-friction parameter fL/D. [ABSTRACT FROM AUTHOR]

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 μm by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime. [ABSTRACT FROM AUTHOR]