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August 10, 2026Journal of Fluids Engineering

Exact Closed-Form Solution for Fanno Flow of a Calorically Perfect Ideal Gas

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Authors

ESElijah SierraOROwen ReschAVAslihan Vuruskan

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Overview

Randomized trial demonstrates a closed-form solution for Fanno flow in ideal gases, suggesting better efficiency in modeling.

Key Points

  • The aim is to present an explicit closed-form solution for downstream Mach number in Fanno flow of ideal gases.
  • Used Lambert-W inversion to express downstream Mach number as a function of upstream conditions and friction length.
  • Identified real branches of the Lambert-W function for different flow regimes (subsonic and supersonic).
  • Conducted numerical comparisons with classical Fanno relations to verify accuracy.
  • The closed-form solution matched classical results numerically in both subsonic and supersonic cases.
  • Eliminated the need for iterative methods in the Fanno equation for unchoked flows.
  • Facilitated rapid evaluation and sizing of compressible duct systems and microchannels.

Cite This Study

Sierra et al. (2026) studied this question.

synapsesocial.com/papers/6a797d3a9c20a9bbd31846dahttps://doi.org/10.1115/1.4072503
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