Analysis of Steady Laminar Flow of an Incompressible Newtonian Fluid Through Curved Pipes of Small Curvature

1973 ◽  
Vol 95 (1) ◽  
pp. 75-80 ◽  
Author(s):  
M. Sankaraiah ◽  
Y. V. N. Rao
Keyword(s):  
Pressure Drop ◽  
Laminar Flow ◽  
Secondary Flow ◽  
Newtonian Fluid ◽  
Axial Velocity ◽  
Axial Pressure ◽  
Small Curvature ◽  
Curved Pipes ◽  
Incompressible Newtonian Fluid ◽  
Steady Laminar

Steady laminar flow of an incompressible Newtonian fluid through a curved pipe of small curvature is considered. The governing equations of flow are obtained in terms of secondary flow stream function and axial velocity component as suggested by Dean. A method of successive approximations is developed to solve these equations. The first five approximations are computed. The solution obtained is used to determine the axial velocity distribution, secondary flow pattern, axial pressure drop, and pressure distribution along the pipe wall. A semiempirical equation is obtained for axial pressure drop. The theoretical results obtained are compared with the available experimental data on axial pressure drop.

A Mathematical Model for the Laminar Entrance Region of a Newtonian Fluid in a Cylindrical Pipe

2020 ◽  
Vol 143 (3) ◽  
Author(s):  
Richard J. Gross ◽  
Nicholas G. Garafolo ◽  
Garrett R. McHugh
Keyword(s):  
Shear Stress ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Wall Shear Stress ◽  
Velocity Profile ◽  
Newtonian Fluid ◽  
Axial Velocity ◽  
Entrance Region ◽  
Velocity Data ◽  
Cylindrical Pipe

Abstract This paper develops equations for velocity, pressure drop, and wall shear stress in the entrance or development region of a cylindrical pipe. The model quantifies the velocity and wall shear stress contributions to the entrance region pressure drop and illustrates how data are used to determine the numerical values of parameters needed to complete the model. It assumes a Newtonian fluid, laminar flow, steady-state, and a constant mass density fluid. The fluid axial velocity profile at the entrance region inlet is modeled by an equation that is close to a flat axial velocity and drops off to zero as the radius approaches the wall. The fluid velocity at the entrance region exit is modeled as the axial, fully developed, laminar flow parabolic velocity profile. The inlet velocity profile is multiplied by a decaying function F(x) that is unity at the entrance region inlet and decreases to zero at the entrance region exit. The exit velocity profile is multiplied by a growing function G(x) that is zero at the entrance region inlet and increases to unity at the entrance region exit. The pressure drop through the entrance region is expressed in terms of the wall viscous friction and the change in axial momentum of the fluid. Two mathematical models for F(x) and G(x) are presented. One is more advantageous when pressure drop data and a few centerline velocity data points are available, and the second is more advantageous when only velocity data are available.

Steady laminar flow of blood through successive restrictions in circular conduits of small diameter

2008 ◽  
Vol 222 (8) ◽  
pp. 1557-1573 ◽  
Author(s):  
D Nag ◽  
A Datta
Keyword(s):  
Blood Flow ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Small Diameter ◽  
Rigid Wall ◽  
Pressure Loss Coefficient ◽  
Axial Velocity Distribution ◽  
Recirculation Zones ◽  
Flow Through ◽  
Steady Laminar

In this paper, numerical results on steady laminar flow of blood through an artery having two successive identical axisymmetric restrictions are presented, at varying degrees of restrictions. Physically, such a flow has features in common with steady blood flow through an artery with multiple stenoses. Additionally, results are presented for the blood flow through an artery in the presence of a single restriction, for comparison. The artery has been modelled as a tube with a rigid wall. The rheological characteristics of blood have been assumed both as Newtonian and non-Newtonian. Three different non-Newtonian models of blood — power law, Quemada, and Carreau—Yasuda models — have been considered in the analysis. The haemodynamic effects of the restrictions on the axial velocity distribution, recirculation zones formed downstream to the restrictions, the wall shear stress, and the pressure drop in the artery have been analysed. The irreversible pressure loss coefficient is calculated from the pressure drop and its variation with the degree of stenosis is obtained.

scholarly journals Numerical Flow Analysis in a Rotating Square Duct and a Rotating Curved-Duct

2000 ◽  
Vol 6 (1) ◽  
pp. 1-9
Author(s):  
Je Hyun Baekt ◽  
Chang Hwan Ko
Keyword(s):  
Laminar Flow ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Centrifugal Force ◽  
Coriolis Force ◽  
Axial Velocity ◽  
Numerical Study ◽  
Axial Direction ◽  
Square Duct ◽  
Rotation Rates

A numerical study is conducted on the fully-developed laminar flow of an incompressible viscous fluid in a square duct rotating about a perpendicular axis to the axial direction of the duct. At the straight duct, the rotation produces vortices due to the Coriolis force. Generally two vortex cells are formed and the axial velocity distribution is distorted by the effect of this Coriolis force. When a convective force is weak, two counter-rotating vortices are shown with a quasi-parabolic axial velocity profile for weak rotation rates. As the rotation rate increases, the axial velocity on the vertical centreline of the duct begins to flatten and the location of vorticity center is moved near to wall by the effect of the Coriolis force. When the convective inertia force is strong, a double-vortex secondary flow appears in the transverse planes of the duct for weak rotation rates but as the speed of rotation increases the secondary flow is shown to split into an asymmetric configuration of four counter-rotating vortices. If the rotation rates are increased further, the secondary flow restabilizes to a slightly asymmetric double-vortex configuration. Also, a numerical study is conducted on the laminar flow of an incompressible viscous fluid in a90°-bend square duct that rotates about axis parallel to the axial direction of the inlet. At a90°-bend square duct, the feature of flow by the effect of a Coriolis force and a centrifugal force, namely a secondary flow by the centrifugal force in the curved region and the Coriolis force in the downstream region, is shown since the centrifugal force in curved region and the Coriolis force in downstream region are dominant respectively.

Approximate Calculation of Pressure Drop in Laminar Flow of Generalized Newtonian Fluid Through Channels with Insert

1995 ◽  
Vol 60 (9) ◽  
pp. 1476-1491
Author(s):  
Václav Dolejš ◽  
Petr Doleček ◽  
Ivan Machač ◽  
Bedřich Šiška
Keyword(s):  
Reynolds Number ◽  
Pressure Drop ◽  
Laminar Flow ◽  
Numerical Solution ◽  
Newtonian Fluid ◽  
Calculation Method ◽  
Approximate Calculation ◽  
Creeping Flow ◽  
Experimental Results ◽  
Generalized Newtonian Fluid

An equation of Rabinowitsch-Mooney type has been suggested for approximate calculation of pressure drop in flow of generalized Newtonian fluid through channels with insert both in the region of creeping flow and at higher values of the Reynolds number, and this calculation method has been verified for four types of insert using own numerical solution and experimental results as well as literature data.

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