scholarly journals Bending of a Curved Tube of Circular Cross Section

1926 ◽  
Vol 12 (6) ◽  
pp. 365-370 ◽  
Author(s):  
W. Hovgaard
Keyword(s):  
Cross Section ◽  
Circular Cross Section ◽  
Curved Tube

scholarly journals Secondary flow in a curved tube

1973 ◽  
Vol 57 (1) ◽  
pp. 167-176 ◽  
Author(s):  
D. Greenspan
Keyword(s):  
Nonlinear System ◽  
Incompressible Fluid ◽  
Cross Section ◽  
Finite Differences ◽  
Entire Range ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Reynolds Numbers ◽  
Curved Tube ◽  
Computer Calculations

The work of Dean and that of McConalogue & Srivastava on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended through the entire range of Reynolds numbers for which the flow is laminar. The coupled nonlinear system of partial differential equations which defines the motion is solved numerically by finite differences. Computer calculations are described and physical implications are discussed.

Experimental study of wall shear rates in the entry region of a curved tube

1979 ◽  
Vol 93 (3) ◽  
pp. 465-489 ◽  
Author(s):  
U. S. Choi ◽  
L. Talbot ◽  
I. Cornet
Keyword(s):  
Experimental Study ◽  
Cross Section ◽  
Circular Cross Section ◽  
Current Method ◽  
Limiting Current ◽  
Dean Number ◽  
Shear Rates ◽  
Rigid Tube ◽  
Curved Tube ◽  
Wall Shear

Local wall shear rates in steady flow in the entry region of a curved tube have been measured by the electrochemical limiting current method. A semi-circular rigid tube of circular cross-section with radius ratio 1/7 has been employed for a range of Dean number between 139 and 2868. The circumferential and axial distributions of the wall shear rates have been measured at 20° circumferential increments at five different sections of the entry region.

Pulsating flow in a curved tube

1973 ◽  
Vol 59 (4) ◽  
pp. 693-705 ◽  
Author(s):  
R. G. Zalosh ◽  
W. G. Nelson
Keyword(s):  
Flow Field ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Analytic Solutions ◽  
Radius Of Curvature ◽  
Dean Number ◽  
Tube Cross Section ◽  
Curved Tube

An analysis is presented of laminar fully developed flow in a curved tube of circular cross-section under the influence of a pressure gradient oscillating sinusoidally in time. The governing equations are linearized by an expansion valid for small values of the parameter (a/R) [Ka/ων]2, where a is the radius of the tube cross-section, R is the radius of curvature, ν is the kinematic viscosity of the fluid and K and ω are the amplitude and frequency, respectively, of the pressure gradient. A solution involving numerical evaluation of finite Hankel transforms is obtained for arbitrary values of the parameter α = a(ω/ν)½. In addition, closed-form analytic solutions are derived for both small and large values of α. The secondary flow is found to consist of a steady component and a component oscillatory at a frequency 2ω, while the axial velocity perturbation oscillates at ω and 3ω. The small-α flow field is similar to the low Dean number steady flow configuration, whereas the large-α flow field is altered and includes secondary flow directed towards the centre of curvature.

Motion of a fluid in a curved tube

1968 ◽  
Vol 307 (1488) ◽  
pp. 37-53 ◽  
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Outer Boundary ◽  
Steady Motion ◽  
Circular Cross Section ◽  
Polar Angle ◽  
Straight Tube ◽  
Curved Tube ◽  
Series Development

Dean’s work on the steady motion of an incompressible fluid through a curved tube of circular cross-section is extended. A method using a Fourier-series development with respect to the polar angle in the plane of cross-section is formulated and the resulting coupled non­linear equations solved numerically. The results are presented in terms of a single variable D = 4 R √(2 a/L ), where R is the Reynolds number, a the radius of cross-section of the tube, and L the radius of the curve. The results cover the range of D from 96 (the upper limit of Dean’s work) to over 600. From these it is found that the secondary flow becomes very appreciable for D = 600, moving the position of maximum axial velocity to a distance less than 0.38 a from the outer boundary, and decreasing the flux by 28% of its value for the straight tube. These calculations fill a large part of the gap in existing knowledge of secondary flow patterns, which lies in the upper range of Reynolds number for which flow is laminar. This range is of particular interest in the investigation of the cardiovascular system

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

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