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Slow Viscous Flow of Rarefied Gases through Short Tubes

 

作者: Richard W. Hanks,   Harold L. Weissberg,  

 

期刊: Journal of Applied Physics  (AIP Available online 1964)
卷期: Volume 35, issue 1  

页码: 142-144

 

ISSN:0021-8979

 

年代: 1964

 

DOI:10.1063/1.1713055

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The semiempirical equation which was shown by Weissberg to be a very close approximation to the rigorous variational calculation of the pressure drop for creeping flow of incompressible viscous fluids through short tubes has been generalized to take into account the slip of a rarefied gas at the tube wall. The generalized equation is&ohgr;=&ohgr;s+&bgr;a/&lgr;¯, whereais the tube radius,&lgr;¯=(&mgr;/P¯)(12&pgr;RT/M)12, and&ohgr;=F/[14&pgr;a2&Dgr;P(8RT/&pgr;M)12]. Here, &mgr; andMare the viscosity and molecular weight of the gas, &Dgr;Pis the pressure dropP1−P2,P¯is the average pressure ½(P1+P2),Ris the gas constant per mole,Tis the absolute temperature, andF=P¯QwhereQis the volume flow. The coefficient &bgr; and the slip parameterwsdepend only onL/a, the length to radius ratio of the tube:&bgr;=(&pgr;/8)/[(L/a)+(3&pgr;/8)], &ohgr;s=(&bgr;2/3&pgr;)[(128L/a)+(27&pgr;2/4)]. Excellent agreement is noted between values ofwcalculated from the equation given here and values obtained by Knudsen for long tubes and by Lund for short tubes.

 

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