Calculation of the gas flow rate in a microchannel


Approximation formulas are obtained for calculation of the gas flow rate in long isothermal microchannels. The quasi-gas-dynamic equations with Maxwell’s slip conditions are shown to predict a minimum in the flow rate within a channel that is called the Knudsen minimum. Corrections are proposed enabling derivation of approximate formulas for flow rates valid for any Knudsen number.

This is a preview of subscription content, log in to check access.


  1. 1.

    Present, R.D., Kinetic Theory of Gases, New York, 1958.

  2. 2.

    Cercigniani, C., Theory and Application of the Boltzmann Equation, Edinburgh, 1975.

  3. 3.

    Cercigniani, C. and Sernagiotto, F., Phys. Fluids, 1966, vol. 9, no. 1, p. 40.

    Article  Google Scholar 

  4. 4.

    Cercigniani, C., Lampis, M., and Lorenzani, S., Phys. Fluids, 2004, vol. 16, no. 9, p. 3426.

    Article  ADS  MathSciNet  Google Scholar 

  5. 5.

    Kun, Xu and Zhihui, Li, J. Fluid Mech., 2004, vol. 513, p. 87.

    MATH  Article  MathSciNet  Google Scholar 

  6. 6.

    Elizarova, T.G. and Sheretov, Yu.V., Rev. Int. de l’Eau, 2003, no. 5, p. 66.

  7. 7.

    Sheretov, Yu.V., Primenenie funktsional’nogo analiza v teorii priblizhenii (Application of Functional Analysis in the Approximation Theory), Tver, 1997.

  8. 8.

    Sheretov, Yu.V., Matematicheskoe modelirovanie techenii zhidkosti i gaza na osnove kvazigidrodinamicheskikh and kvazigazodinamicheskikh uravneni (Mathematical Simulation of Fluid Flow on the Basis of Quasi-Hydrodynamic and Quasi-Gas-Dynamic Equations), Tver, 2000.

  9. 9.

    Elizarova, T.G., Matematcheskie modeli i chislennye metody v dinamike zhidkosti i gaza (Mathematical Models and Numerical Methods in Fluid Dynamics), parts 1 and 2, Moscow, 2005.

  10. 10.

    Landau, L.D. and Lifshitz, E.M., Gidrodinamika (Hydrodynamics), Moscow, 1986.

  11. 11.

    Abramovich, G.N., Prikladnaya gazovaya dinamika (Applied Gas Dynamics), Moscow, 1991.

  12. 12.

    Bird, G.A., Molecular Gas Dynamics and the Direct Simulation of Gas Flows, Oxford, 1994.

Download references

Author information



Additional information

Original Russian Text © T.G. Elizarova, D.G. Ershov, 2007, published in Vestnik Moskovskogo Universiteta. Fizika, 2007, No. 1, pp. 21–24.

About this article

Cite this article

Elizarova, T.G., Ershov, D.G. Calculation of the gas flow rate in a microchannel. Moscow Univ. Phys. 62, 19–22 (2007).

Download citation


  • Knudsen Number
  • Approximate Formula
  • Channel Cross Section
  • Cylindrical Channel
  • Burnett Equation