A flow rate equation for subsonic Fanno flow

Abstract

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.

Keywords

Fanno flow flow rate equation subsonic flow one-dimensional model

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References

Saleh

Flow of gases in pipes and ducts, Chapter 9. In: Saleh

(ed.) Fluid flow handbook, New York, NY: McGraw-Hill, 2002, pp. 9.1–9.32.

Beater

. Pneumatic drives: system design, modelling and control, Berlin: Springer, 2007, pp. 58–58.

Schroeder DW Jr. A tutorial on pipe flow equations, http//www.onepetro.org/ (2001, last accessed 10 July 2012)..

Daugherty RL, Franzini JB and Finnemore EJ. Fluid mechanics with engineering applications. 5th ed. New York, NY: McGraw-Hill, 1954, p. 227.

Shapiro

. The dynamics and thermodynamics of compressible fluid flow 1953; Vol. 1New York, NY: Ronald Press, pp. 159–189.

Streeter VL. Fluid mechanics. 4th ed. International student edition. New York, NY: McGraw-Hill, 1966, pp. 313–326.

Daneshyar

. One-dimensional compressible flow, Oxford: Pergamon Press, 1976, pp. 56–65.

Munson

Young

Okiishi

. Fundamentals of fluid mechanics, 2nd ed. New York, NY: Wiley, 1994, pp. 735–749.

Zucker

Biblarz

. Fundamentals of gas dynamics, 2nd ed. New York, NY: Wiley, 2002, pp. 241–276.

10.

Massey B (revised by Word-Smith J). Mechanics of fluids. 8th ed. London and New York: Taylor & Francis, 2006, pp. 537–539.

11.

Bar-Meir G. Fundamentals of compressible flow mechanics, http://www.potto.org/gasDynamics/ (2007, last accessed, 10 July 2012).

12.

Bideaux E and Scavarda S. Pneumatic pipe modeling: theory and experimental approach (Part II). In: T McLain and D Kim (eds) ASME fluid power systems and technology-2000, Orlando, FL, USA, 5–10 November 2000, pp. 77–81. New York: ASME.

13.

Melcher KJ. User guide for compressible flow toolbox, Version 2.1 for Use With MATLAB® Version 7, 2006, NASA/TM-2006-214086.

14.

Puddu

. Dimensionless flow equations for dynamic simulation of turbomachine components and fluid systems. Proc Inst Mech Eng 2010; 224(Part A): 419–432.

15.

Kalweit

Drikakis

. Coupling strategies for hybrid molecular-continuum simulation methods. Proc Inst Mech Eng 2008; 222(Part C): 797–806.

16.

Ouyang

Aziz

. Steady-state gas flow in pipes. J Petrol Sci Eng 1996; 14: 137–158.