PoiseuiUe

Velocity Profiles In laminar flow, the solution of the Navier-Stokes equation, corresponding to the Hagen-PoiseuiUe equation, gives the velocity i as a Innction of radial position / in a circular pipe of radius R in terms of the average velocity V = Q/A. The parabolic profile, with centerline velocity t ce the average velocity, is shown in Fig. 6-10. 

The geometry of the flow is supposed infinite i.e. very large in one direction), such as in the case of a flow around an obstacle, or in a long die. The flow at infinity is assumed to be known (uniform, PoiseuiUe flow,. ..). For computational purposes, one introduces artificial boundaries, at a finite, hopefully not too large, distance. The problem is to define which conditions to impose on the artificial boundaries in order to obtain a solution of the truncated problem, which is as close as possible to the solution of the original problem. 

It is worth noticing that Tlapa and Bernstein [71] have proven that the Squire theorem holds true for the PoiseuiUe flow of m upper-convected Maxwell fluid. It means that any instability, which may be present for three dimensional disturbances, is also present for two dimensional ones at a lower value of the Reynolds number. This property is not true, in general, for non-Newtonian fluids [72]. 

II) The same can be said about the bulk part of the conduction. However, surface conduction proceeds along the particle surfaces and the paths chosen by fluid flow Euid surface conduction are different. TTie former tends to be strongly dominated by the wider channels, because PoiseuiUe s law [1.6.4,17) predicts a proportionsitity to the fourth power of the radius, whereas surface conduction... 

This relation, which is analogous to PoiseuiUe s relation, gave rise to various models taking into account the irregularity of the porous medium (tortuosity, noncircular sections, etc.). Carman-Kozeny s model is a simple and usually precise model which leads to the following expression of D ... 

From an experimental point of view, the two measured quantities are the pressure and the flow rate. The PoiseuiUe number can be determined directly from these quantities as... 

In table 1, the values of the PoiseuiUe number for different geometries are given Table 1. PoiseuiUe numbers for fuUy developed laminar flows... 

For parallel plates, Shah and London [14] propose the following law for the PoiseuiUe number which takes the entrance length into account ... 

Experimental data were obtained for water flows at room temperature. PoiseuiUe number is plotted versus the Reynolds number in figure 17. It can be observed that a classical value for a laminar flow is found, as expected. The slight underestimation observed is probably due to the experimental imprecision on the estimation of the channel height... 

Figure 17 PoiseuiUe number as a function of the Reynolds number for water flowing in a microchannel with smooth walls...

Figure 18 Effect of water conductivity on the PoiseuiUe number.

Segre G and Silberberg A, Behavior of microscopic rigid spheres in PoiseuiUe flow. Part 1 and 2, Fluid Mech. 1962 14 115-157. 

Schofield, R.W., Fane, A.G., and Fell, C.J.D. Gas and vapor transport through microporous membranes I. Knudsen-PoiseuiUe... 

The single-capillary viscometer (SCV) is represented in Fig. la. Its design is a direct extrapolation of classical viscometry measurement. It is composed of a small capillary, through which the solvent flows at a constant flow rate, and a differential pressure transducer (DPT), which measures the pressure drop across the capillary. SCV obeys PoiseuiUe s law and the pressure drop AP across the capillary depends on the geometry of the capillary, on flow rate Q, and on viscosity of the fluid 7j according to... 

With the assumption of a constant flow rate, the flow time t can be related to the viscosity 77 of the liquid by the Hagen-PoiseuiUe equation... 

Eor a fully developed laminar flow in a pipe, the Hagen-PoiseuiUe equation is used to calculate... 

PoiseuiUe (capillary or slit), large yes functions of spatial functions of spatial coor- for laminar flows small ... 

PoiseuiUe s Law The relationship between volumetric flow rate and pressure difference for steady flow of a Newtonian fluid in a long circular tube. 

As a consequence, small muscles encircling the entrance to the arterioles (small arteries) are caused to relax by the CNS. Since, by PoiseuiUe s Law ... 

In the case where pore can be considered as cylinders with the same radins, the volume flux through the pore may be described by the following Hagen-PoiseuiUe equation, for... 

Hagen-PoiseuiUe equation - if the membrane is assumed to be composed of more or less cyhndrical pores... 

Two Hagen-PoiseuiUe models (a one-parameter model and a two-parameter model) were also used to describe the experiinental solvent flux data shown in... 

The model most firequendy used for describing flow through pores is based on the well-known Hagen—PoiseuiUe equation for laminar convective flow through straight capillaries with... 

PoiseuiUe s law Describes the behaviour ofliquids flowing through capillary tubes in relation to their viscosity fi L)]. 

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