Laminar flow, viscosity

It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a flowing liquid with laminar flow. This makes it possible to compute properties not measurable in a static fluid, such as the viscosity. Nonequilibrium simulations give rise to additional technical difficulties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work. 

Economic Pipe Diameter, Laminar Flow Pipehnes for the transport of high-viscosity liquids are seldom designed purely on the basis of economics. More often, the size is dictated oy operability considerations such as available pressure drop, shear rate, or residence time distribution. Peters and Timmerhaus (ibid.. Chap. 10) provide an economic pipe diameter chart for laminar flow. For non-Newtouiau fluids, see SkeUand Non-Newtonian Flow and Heat Transfer, Chap. 7, Wiley, New York, 1967). 

Shear stresses are developed in a fluid when a layer of fluid moves faster or slower than a nearby layer of fluid or a solid surface. In laminar flow, the shear stress is equal to the product of fluid viscosity and velocity gradient or rate of shear. Under laminar-flow conditions, shear forces are larger than inertial forces in the fluid. 

Fluid circulation probably can be increased at the same power consumption and viscosity in laminar flow by increasing impeller diameter and decreasing rotational speed, but the relationship between Q, N, and for laminar flow from turbines has not been determined. 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

Equations (22-86) and (22-89) are the turbulent- and laminar-flow flux equations for the pressure-independent portion of the ultrafiltra-tion operating curve. They assume complete retention of solute. Appropriate values of diffusivity and kinematic viscosity are rarely known, so an a priori solution of the equations isn t usually possible. Interpolation, extrapolation, even precuction of an operating cui ve may be done from limited data. For turbulent flow over an unfouled membrane of a solution containing no particulates, the exponent on Q is usually 0.8. Fouhng reduces the exponent and particulates can increase the exponent to a value as high as 2. These equations also apply to some cases of reverse osmosis and microfiltration. In the former, the constancy of may not be assumed, and in the latter, D is usually enhanced very significantly by the action of materials not in true solution. 

Visi-osity High viscosity crudes may flow in the laminar flow regime which causes high pressure drops. This is especially true of emulsions of water in high-viscosity crudes where the effective velocity of the mi slur e could be as much as ten times that of the base crude (see Volume 11... 

Figure 5-18. Laminar flow mixing. For known impeller type, diameter, speed, and viscosity, this nomograph will give power consumption. Connect RPM and diameter, also viscosity and impeller scale. The intersection of these two separate lines with alpha and beta respectively is then connected to give horsepower on the HP scale. By permission, Quillen, C. S., Chem. Engr., June 1954, p. 177 [15].

To describe laminar flow of a fluid, the unit shear stress x is some function of the dynamic viscosity l(lb/ft ), and the velocity difference dV(ft/sec) between adjacent laminae that are separated by the distance dy(ft). Develop a relationship for x in terms of the variables l, dV and dy. 

The plate heat exchanger, for example, can be used in laminar flow duties, for the evaporation of fluids with relatively high viscosities, for cooling various gases, and for condensing applications where pressure-drop parameters are not excessively restrictive. 

Assume laminar flow of filtrate of liquid through the filter cake. Rate of filtration is usually measured as the rate at which liquid filtrate is collected. The filtration rate depends on the area of the filter cloth, the viscosity of the liquid, the pressure drop across the filter and filter cake resistance. At any instant during filtration, the rate of filtration is given by the equation ... 

NPei and NRtt are based on the equivalent sphere diameters and on the nominal velocities ug and which in turn are based on the holdup of gas and liquid. The Schmidt number is included in the correlation partly because the range of variables covers part of the laminar-flow region (NRei < 1) and the transition region (1 < NRtl < 100) where molecular diffusion may contribute to axial mixing, and partly because the kinematic viscosity (changes of which were found to have no effect on axial mixing) is thereby eliminated from the correlation. 

In the previous sections of this chapter, the calculation of frictional losses associated with the flow of simple Newtonian fluids has been discussed. A Newtonian fluid at a given temperature and pressure has a constant viscosity /r which does not depend on the shear rate and, for streamline (laminar) flow, is equal to the ratio of the shear stress (R-,) to the shear rate (d t/dy) as shown in equation 3.4, or ... 

As in the case of Newtonian fluids, one of the most important practical problems involving non-Newtonian fluids is the calculation of the pressure drop for flow in pipelines. The flow is much more likely to be streamline, or laminar, because non-Newtonian fluids usually have very much higher apparent viscosities than most simple Newtonian fluids. Furthermore, the difference in behaviour is much greater for laminar flow where viscosity plays such an important role than for turbulent flow. Attention will initially be focused on laminar-flow, with particular reference to the flow of power-law and Bingham-plastic fluids. 

Because concentrated flocculated suspensions generally have high apparent viscosities at the shear rates existing in pipelines, they are frequently transported under laminar flow conditions. Pressure drops are then readily calculated from their rheology, as described in Chapter 3. When the flow is turbulent, the pressure drop is difficult to predict accurately and will generally be somewhat less than that calculated assuming Newtonian behaviour. As the Reynolds number becomes greater, the effects of non-Newtonian behaviour become... 

For developed laminar flow in smooth channels of t/h > 1 mm, the product ARe = const. Its value depends on the geometry of the channel. For a circular pipe ARe = 64, where Re = Gdh/v is the Reynolds number, and v is the kinematic viscosity. 

Experimental work with styrene in tubular reactors has been reported (39) where viscosities were relatively low due to conversions below 32%. However, Lynn ( ) has concluded that a laminar flow tubular reactor for styrene polymerization is probably technically infeasible due to the distortion in velocity... 

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