We consider the Newtonian Poiseuille flow in a duct the cross section of which is either a circular or an annular sector assuming that Navier slip occurs either along both the cylindrical walls or only along the outer cylindrical wall. Cartellier, Alain The results are used to obtain an approximate expression for the flow strength in such a pipe as a function of the size and shape of the cross section. This is termed as annular Poiseuille flow (aPf). exactly what eq. Example \(\PageIndex{1}\): Using Flow Rate: Plaque Deposits Reduce Blood Flow Suppose the flow rate of blood in a coronary artery has been reduced to half its normal value by plaque deposits. For Poiseuille flow in channels or ducts of noncircular crosssection, analogous expressions can be obtained for velocity and temperature [see Happel and Brenner (1973) and Shah and London (1978)]. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip. if the flow is turbulent you can use the relations for circular ducts and replace the diameter with the hydraulic diameter Dh = 4*A/P (A: cross section, P: perimeter). This no-slip boundary condition (BC) has been applied successfully to model many macroscopic experiments, but has no microscopic justification. The numerical method used in this case is the finite-element method. The fluid flow in an annulus is due to the rotation of the outer cylinder with constant velocity. shear instability in spiral Poiseuille flow, Disturbance energy growth in core–annular flow, Instabilities of plane Poiseuille flow with a streamwise system rotation, Stability of fluid flow in a flexible tube to non-axisymmetric disturbances, Axisymmetric and non-axisymmetric instability of an electrified viscous coaxial jet, The connection between centrifugal instability and Tollmien–Schlichting-like instability for spiral Poiseuille flow. Then compare that solution with the hydraulic diameter approach and decide if the error is acceptable for you or not. circular and rectangular ducts are obtained. The method is general for any two-dimensional duct with single or multiple connected regions cross section. All rights reserved. Due to a circular obstacle, both the drag and lift coefficients are evaluated around the outer surface of an obstacle towards the higher values of the Power law index. Above the second critical pressure gradient non-uniform slip occurs everywhere at the wall. Part II, On the stability of the developing flow in a channel or circular pipe, Amplitude-dependent neutral modes in the Hagen–Poiseuille flow through a circular pipe, Inviscid centre-modes and wall-modes in the stability theory of swirling Poiseuille flow, The linear and nonlinear stability of thread-annular flow, https://doi.org/10.1017/S0022112008002577, Viscous and inviscid instabilities of a trailing vortex, Observations of purely elastic instabilities in the Taylor–Dean flow of a Boger fluid, A quasi-steady approach to the instability of In fluid dynamics, the Hagen–Poiseuille equation, also known as the Hagen–Poiseuille law, Poiseuille law or Poiseuille equation, is a physical law that gives the pressure drop in a fluid flowing through a long cylindrical pipe. We developed an in vitro ureter-stent experimental setup, using latex tubing to simulate a flexible ureter connecting a renal unit and a bladder side. Navier slip is assumed to occur along the circular walls. Part I, Instability of flow through pipes of general cross-section. The effects of the sector angle, the radii ratio and the slip number are analysed. Matas, Jean-Philippe ZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik. my fault -- should have read your original post more carefully. The ureter-stent configuration was varied, simulating four levels of deformation (0°, 20°, 40°, 60°) and then simulating different external compressive forces on a stented ureter with 40° deformation. This paper investigates incompressible laminar rectangular channel and circular pipe flows driven by uniform and traveling wave in-plane wall oscillations. We dedicate particular attention to the effects that factors such as surface roughness, wettability and the presence of gaseous layers might have on the measured interfacial slip. Both friction factor-Reynolds number product and Nusselt number are determined. Fully developed laminar forced convection inside a semi-circular channel filled with a Brinkman-Darcy porous medium is studied. The computed first-order dimensionless Since the representative equations are complex in nature so an efficient computational procedure based on finite element method (FEM) is executed. The purpose of this work was to determine whether or not stent failure is due only to stent compression and deformation in the presence of extrinsic obstruction. 2017. Ishida, Takahiro Methods: It turns out that there are three flow regimes defined by two critical values of the pressure gradient. incompressible, Newtonian fluid through a porous medium in channels with a I explore the evidence for slip, the possible mechanisms of slip, and the relation between slip and extrusion instabilities. A square cylinder is placed in the channel with varying positions giving rise to three computational grids named as G1,G2 and G3. 19.1 we present a brief history of the no-slip boundary condition for Newtonian fluids, introduce some terminology, and discuss cases where the phenomenon of slip (more appropriately, this may often be apparent slip) has been observed. In addition for more physical insight of problem velocity and pressure plots and line graphs are added.

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