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High velocity compressible viscous flow
Author(s) -
Schwartzberg Henry G.,
Gurevich Michael
Publication year - 1970
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690160514
Subject(s) - hagen–poiseuille equation , mach number , isothermal process , mechanics , isothermal flow , shear velocity , flow velocity , flow (mathematics) , physics , compressibility , compressible flow , thermodynamics , classical mechanics , open channel flow , turbulence
Pressure drops were measured for the high velocity isothermal viscous flow of steam in circular tubes. For the velocities tested, up to 0.48 times the isothermal sonic velocity, these flows obeyed the following equation with an average deviation of 2.4%.\documentclass{article}\pagestyle{empty}\begin{document}$$ P_1 2 - P_2 2 = \frac{{8\mu RTG}}{{DM}}\left[{\frac{{8L}}{D} + \frac{{N_{{\mathop{\rm Re}\nolimits} } }}{3}In\left({\frac{{P_1 }}{{P_2 }}} \right)} \right] $$\end{document}This equation differs from the Poiseuille‐Meyer equation commonly used to correlate isothermal viscous flow in that it includes the term ( N Re /3) In ( P 1 / P 2 ) which accounts for the change in momentum caused by expansion. In deriving this equation, the mean velocity, mean squared velocity, and wall shear stress were obtained from the parabolic velocity distribution for normal viscous flow. The velocity profile should flatten as the isothermal Mach number increases, and it is therefore anticipated that somewhere above the range tested the equation will no longer prove applicable. Variants of the equation, which take into account the flattening of the velocity profile in the range tested, did not fit the experimental data quite as well.