Poiseuille’s law for laminar flows

Poiseuille s law for laminar flow of liquids. The time required for a specihc volume of a liquid to flow through a capillary of dehned length and radius is proportional to the ratio of the viscosity by the density of the liquid itself. As the density of a dilute solution may be considered practically equal to that of the pure solvent, the ratio of efflux time of the solution, t, to that of solvent to, gives the relative viscosity ... 

Poiseuille s law for laminar flow of fluids states that the flow rate is proportional to the radius (R) of the flow passage to the fourth power, indicating that longitudinal flow through pits and lumens is limited by the small openings in the pit membrane ... 

Theoretical flow equations were derived for the molecular flow region by Knudsen (Kl) as far back as 1909. These equations for molecular flow and Poiseuille s Law for laminar flow, were the basis for vacuum flow computation until the later years of World War II. Normand (Nl) was the first to translate these equations into practical forms for engineering applications. In this reference Normand gives useful empirical rules for applying Knudsen s equations to ducts of rectangular cross-section, non-uniform cross-section, baffles, elbows, etc. 

The determination of the intrinsic viscosity of a polymer essentially requires the measurement of the flow time of a polymer solution through a glass capillary at different solution concentrations. A polymer solution passing through a capillary obeys the Poiseuille s law for laminar flow through capillaries, which indicates that the pressure drop AP is directly proportional to the viscosity r] of the fluid [29, 30]. 

There is a maximum drag reduction limit for polymer drag reduction [Castro and Squire, 1967 Giles and Pettit, 1967 Virk et al., 1970 Virk, 1975]. The maximum drag reduction asymptote (MDRA) proposed by Virk is generally accepted for high-polymer drag reduction [Virk, 1975]. Poiseuille s law for laminar flow [Eq. (2.3)], the von Karman law for Newtonian turbulent flow [Eq. (2.4)], and Virk s maximum... 

An alternative molecular weight-sensitive detector is the on-line viscometer. All current instrument designs depend upon the relationship between pressure drop across a capillary through which the polymer sample solution must flow and the viscosity of the solution. This relationship is based upon Poiseuille s law for laminar flow of incompressible fluids through capillaries ... 

The Knudsen equation can only be applied to the viscous laminar flow regime, the molecular flow regime or the transition flow regime. For predominantly laminar flow, the calculated contribution for molecular flow becomes negligible, and similarly for predominantly molecular flow, the calculated contribution for laminar flow becomes negligible. The first part of this equation represents the viscous laminar flow component, Q, which is derived from Poiseuille s law for laminar flow, and the second part represents the molecular flow component, Q, which is derived from Knudsen s law for free molecular flow. 

The flow of the filtrate through the packed bed of cake can be described by an equation similar to Poiseuille s law, assuming laminar flow occurs in the filter channels. Equation (2.10-2) gives Poiseuille s equation for laminar flow in a straight tube, which can be written... 

The most basic state of motion for fluid in a pipe is one in which the motion occurs at a constant rate, independent of time. The pressure flow relation for laminar, steady flow in round tubes is called Poiseuille s Law, after J.L.M. Poiseuille, the French physiologist who first derived the relation in 1840 [12]. Accordingly, steady flow through a pipe or channel that is driven by a pressure difference between the pipe ends of just sufficient magnitude to overcome the tendency of the fluid to dissipate energy through the action of viscosity is called Poiseuille flow. 

If a viscometer is really to furnish exact measurements of -q then it must satisfy the conditions assumed tn the deduction of Poiseuille s law (no turbulence, no laminar flow outside the capillary, etc.). An instrument, which to a great extent satisfies these requirements, provided it is well constructed and used with judgement , is the Ostwald viscometer which is depicted in Fig, 9, The instrument is however less suitable for the absolute determination of by means of Poiseuille s law, but there is hardly any need for that in colloid science. The instrument is calibrated with water for which... 

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