Laminar Flow in the Entrance Region of Elliptical Ducts

1983 ◽  
Vol 105 (3) ◽  
pp. 290-296 ◽  
Author(s):  
M. S. Bhatti
Keyword(s):  
Laminar Flow ◽  
Aspect Ratio ◽  
Unsolved Problem ◽  
Circular Tube ◽  
Entrance Region ◽  
Momentum Balance ◽  
Velocity Measurements ◽  
Fully Developed Flow ◽  
Closed Form Analytical Solution ◽  
Steady Laminar

A closed-form analytical solution is developed to hitherto unsolved problem of steady laminar flow of a Newtonian fluid in the entrance region of elliptical ducts. The analysis is based on the Karman-Pohlhausen integral method and entails solution of the integrated forms of the mass and the momentum balance equations. According to this analysis, the hydrodynamic entrance length based on 99 percent approach to the fully developed flow is equal to 0.5132λ/(1+λ2) where λ is the aspect ratio. Also, the fully developed incremental pressure defect is found to be 7/6 which is independent of the aspect ratio. In the limit when the flow becomes fully developed, the solution converges to the known exact asymptotic solution. Available, wide-ranging velocity measurements for a circular tube agree with the analytical predictions within 7 percent. Also, available pressure drop measurements near the inlet of a circular tube agree with the analytical predictions within 2 percent.

Laminar Flow in a Porous Tube With Suction

1975 ◽  
Vol 97 (1) ◽  
pp. 66-71 ◽  
Author(s):  
J. P. Quaile ◽  
E. K. Levy
Keyword(s):  
Experimental Investigation ◽  
Laminar Flow ◽  
Velocity Profile ◽  
Circular Tube ◽  
Wall Suction ◽  
Porous Tube ◽  
Inlet Velocity ◽  
Uniform Wall ◽  
Steady Laminar

A theoretical and experimental investigation of the flow in a porous tube with wall suction is described. The flow is steady, laminar, and incompressible with the fluid entering at one end of the circular tube and flowing out through the porous circumferential surface. The study is limited to an inlet velocity profile parabolic in shape and to the case of uniform wall suction.

Entrance Region Flow of Casson Fluid in a Circular Tube

2011 ◽  
Vol 110-116 ◽  
pp. 698-706 ◽  
Author(s):  
A. Kandasamy ◽  
Rekha G. Pai
Keyword(s):  
Circular Tube ◽  
Casson Fluid ◽  
Entrance Region ◽  
Momentum Balance ◽  
Balance Equations ◽  
Cross Sectional ◽  
The Core ◽  
Region Flow ◽  
Boundary Layer Region ◽  
Layer Region

The entrance region flow of a Casson fluid in a tube has been investigated numerically without making prior assumptions on the form of velocity profile within the boundary layer region, which is determined by a cross sectional integration of the momentum differential equation for a given distance from the channel entrance. Using the macroscopic mass and momentum balance equations, the thickness of the core, the entrance length, and the pressure drop have been obtained at each cross section of the entrance region of the tube for specific values of Casson number.

The Developing Laminar Flow and Pressure Drop in the Entrance Region of Annular Ducts

1964 ◽  
Vol 86 (4) ◽  
pp. 827-833 ◽  
Author(s):  
E. M. Sparrow ◽  
S. H. Lin
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Circular Tube ◽  
Outer Radius ◽  
Radius Ratio ◽  
Entrance Region ◽  
Flow Development ◽  
Inner Radius ◽  
Wide Range ◽  
Plate Channel

A new analytical method has been applied for determining the developing laminar flow in the hydrodynamic entrance region of annular ducts. Detailed results are presented for the development of the velocity distribution and the pressure drop over a wide range of annulus radius ratios r1/r2 (r1 = inner radius of annulus, r2 = outer radius of annulus). It is found that the pressure drop and flow development in annular ducts with radius ratios substantially less than unity is quite similar to that in a parallel-plate channel (r1/r2 → 1). On the other hand, the results far an annular duct with radius ratio as small as 0.001 depart significantly from those for a circular tube (r1/r2 = 0). The hydrodynamic entrance length, measured as a multiple of the hydraulic radius, increases as the duct radius ratio decreases at a fixed Reynolds number.

Laminar Pressure Drop Associated With the Continuum Entrance Region and for Slip Flow in a Circular Tube

1965 ◽  
Vol 32 (4) ◽  
pp. 765-770 ◽  
Author(s):  
S. T. McComas ◽  
E. R. G. Eckert
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Circular Tube ◽  
Slip Flow ◽  
Mean Free Path ◽  
Entrance Region ◽  
Absolute Pressure ◽  
Fully Developed Flow ◽  
Number Range ◽  
A Value

The pressure drop in the entrance region of an abrupt inlet circular tube was determined experimentally. Local values of K, the dimensionless factor for laminar flow which expresses the excess of pressure drop over that of fully developed flow, were determined for the Reynolds range from 200 to 600. Variations in absolute pressure were used at each Reynolds number in order to produce different bulk velocities. The results for this Reynolds number range agreed with the analyses for smooth entrance tubes, and no dependency on bulk velocity was observed. The absolute pressure of the test section was also reduced sufficiently to obtain a large mean free path for air, thus producing a slip effect at the tube wall. Pressure-drop measurements were made for a Knudsen number range of 0.001 to 0.07, and the slip-flow correction was determined in this range. The data agreed well with Kennard’s prediction for slip flow in a tube if a value of 0.9 was used for the diffuse factor.

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