Velocity Distribution and Fluid Friction in Smooth Concentric Annuli

Rothfus, R. R.; Monrad, C. C.; Senecal, V. E.

doi:10.1021/ie50492a033

Cited by 79 publications

(42 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…On the other hand, their results for concentric annuli indicate an initial deviation from entirely viscous flow a t Reynolds numbers in the vicinity of 700. The pressure-drop data of Carpcnter and coworkers (8) for one annulus confirm Equation (7) up to a Reynolds number of about 800.…”

Section: Geometrical Considerationssupporting

confidence: 56%

“…More recent data on local velocities as well as friction (4,8) have pointed toward a more consistent dependence of friction factor on the geometry of the conduit.…”

Section: Turbulent Flowmentioning

confidence: 89%

“…The two skin frictions therefore, would have to be averaged in order to reproduce the form of Equation (8). It seems unlikely that any more than a rough approximation of the actual pressure drop would be forthcoming from the over-all application of hydraulic radius.…”

Section: Turbulent Flowmentioning

confidence: 99%

“…The portion of the fluid between the radius of maximum velocity and the outer surface of the annulus is of more immediate concern for purposes of correlation. The pressure gradient due to friction is related to the skin friction, ~~g~, a t the outer boundary through the force balance which is the equivalent of Equation (8). By analogy with Equation ( 5 ) ) a friction factor fz for the outer surface can be defined in such manner as to make It is, therefore, reasonable to investigate the merit of the hydraulic-radius method of correlating fully turbulent friction by applying the concept to that part of the fluid lying outside the radius of maximum velocity.…”

Section: It Is Apparent That R H L Loses Significancementioning

confidence: 99%

See 3 more Smart Citations

Fluid friction in noncircular ducts

Walker¹,

Whan²,

Rothfus³

1957

AIChE Journal

Self Cite

View full text Add to dashboard Cite

Section: Geometrical Considerationssupporting

confidence: 56%

“…More recent data on local velocities as well as friction (4,8) have pointed toward a more consistent dependence of friction factor on the geometry of the conduit.…”

Section: Turbulent Flowmentioning

confidence: 89%

Section: Turbulent Flowmentioning

confidence: 99%

Section: It Is Apparent That R H L Loses Significancementioning

confidence: 99%

See 2 more Smart Citations

Fluid friction in noncircular ducts

Walker¹,

Whan²,

Rothfus³

1957

AIChE Journal

Self Cite

View full text Add to dashboard Cite

“…The friction factor for the outer wall f2 is computed from pressure drop data through the mod8ed Fanning equation which is consistent with the definition of f2 shown in Equation ( 4 ) . Since fi in turn, is calculated by means of Equation ( 5 ) , both fi and f2 depend on the measured radius of maximum velocity.…”

Section: Page 28mentioning

confidence: 61%

Skin friction patterns for transitional flow in annuli

Croop¹,

Rothfus²

1962

AIChE Journal

Self Cite

View full text Add to dashboard Cite

Main stream velocity profiles have been obtained by means of impact probes for the steady, isothermal flow of water in three smooth, concentric annuli having widely different diameter ratios. The point of maximum local velocity has been determined, thus permitting the ratio of skin frictions a t the inner and outer boundaries t o be calculated. Previously published data on pressure drop have been used to obtain separate friction factor correlations for the two surfaces. Attention has been centered on the transition range, where the position of maximum velocity is a function of both the diameter ratio and the Reynolds number.Not much is known about the transitional behavior of fluids flowing in noncircular ducts, especially those in which the profiles of shearing stress and velocity are asymmetric about their minimum or maximum points.The concentric annulus is such a configuration and offers the advantage for study of uniform but d8erent skin frictions on its two boundaries. The present work seeks to determine the separate transitional skin frictions at the inner and outer surfaces as functions of the Reynolds number and diameter ratio. For this purpose temporal mean, main stream, local velocities, as averaged by an ordinary impact probe, are experimentally measured in order to determine the radius of maximum velocity. With the radial position of zero shear thus established, previously published frictional data permit the individual skin frictions to be calculated.If the inner radius of an annulus is rl and the outer radius is r,, the corresponding skin frictions r1 and T~ are uniform over their respective boundaries but differ from one another in a definite fashion. Under steady flow conditions a simple force balance on the fluid shows that regardless of whether the flow is viscous or turbulent.For fully viscous, isothermal flow it can be shown that rm' = (r: -T:) /In (r;/r,2) ( 2 ) The ratio of skin frictions is therefore fixed by geometrical factors alone. Whether the same is true for transitional and fully turbulent flow however remains a matter to be determined through experiment. Page 26radius of maximum velocity is essentially independent of Reynolds number in fully turbulent flow and is given by Equation ( 2 ) within experimental error. In at least one instance however disagreement with this view has been reported ( 2 ) .In the region of viscous-turbulent transition skin friction measurements ( 5 ) and velocity data (9) have indicated that the radius of maximum velocity depends on the Reynolds number, but the influence of diameter ratio has not been established. The present experiments extend the previous work by dealing with a much wider range of diameter ratios.With the radius of maximum velocity experimentally determined the skin friction ratio can be obtained from Equation (1). It is more usual however to express results in terms of the Fanning type of friction factors defined by means of the following equations:Since the friction factors are defined on the basis of the average velocity over the whole...

show abstract