The nature of fluid flow

In the present discussion only the problem of steady flow will be considered in which the time average velocity in the main stream direction X is constant and equal to u. In laminar flow, the instantaneous velocity at any point then has a steady value of Ux and does not fluctuate. In turbulent flow the instantaneous velocity at a point will vary about the mean value of Ux. It is convenient to consider the components of the eddy velocities in two directions—one along the main stream direction X and the other at right angles to the stream flow Y. Since the net flow in the X-direction is steady, the instantaneous velocity may be imagined as being made up of a steady velocity % and a fluctuating velocity , so that  

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As noted below, the value of the Reynolds number indicates the nature of fluid flow in a duct or pipe ... 

Figure 3.4 Schematic diagram of apparatus for investigating the nature of fluid flow... 

Diffusional interception or Brownian motion, ie, the movement of particles resulting from molecular collisions, increases the probability of particles impacting the filter surface. Diffusional interception also plays a minor role in Hquid filtration. The nature of Hquid flow is to reduce lateral movement of particles away from the fluid flow lines. 

Flow boiling is distinguished f rom pool boiling by the presence of fluid flow caused by natural circulation in a loop or forced by an external pump. In both systems, when operating at steady state, the flow appears to be forced no distinction will be made between them, since only the flow pattern and the heat transfer are of interest in this section. 

Ruth, B. F. Ind. Eng. Chem. 27 (1935) 708 and 806. Studies in filtration. III. Derivation of general filtration equations. IV. Nature of fluid flow through filter septa and its importance in the filtration equation. 

These phenomena do not occur in a static domain chemical compounds migrate and are redistributed along the soil profile, down to the water table region and within the fully saturated aquifer zone, by flowing water. The extent of this redistribution and the kinetics of the geochemical interactions are controlled by the very nature of fluid flow in porous media, the water chemistry, and of course the properties of the soil and contaminant(s). 

Now return to a view of the nature of flow in the boundary layer. It has been called laminar, and so it is for values of the Reynolds number below a critical value. But for years, beginning about the time of Osborne Reynolds experiments and revelations in the field of fluid flow, it has been known that the laminar property disappears, and the flow suddenly becomes turbulent, when the critical VUv is reached. Usually flow starts over a surface as laminar but after passing over a suitable length the boundary layer becomes turbulent, with a thin laminar sublayer thought to exist because of damping of normal turbulent components at the surface. See Fig. 6. 

Hydrodynamic boundary layer — is the region of fluid flow at or near a solid surface where the shear stresses are significantly different to those observed in bulk. The interaction between fluid and solid results in a retardation of the fluid flow which gives rise to a boundary layer of slower moving material. As the distance from the surface increases the fluid becomes less affected by these forces and the fluid velocity approaches the freestream velocity. The thickness of the boundary layer is commonly defined as the distance from the surface where the velocity is 99% of the freestream velocity. The hydrodynamic boundary layer is significant in electrochemical measurements whether the convection is forced or natural the effect of the size of the boundary layer has been studied using hydrodynamic measurements such as the rotating disk electrode [i] and - flow-cells [ii]. 

The major problem in temperature control in bulk and solution batch chain-growth reactions is the large increase in viscosity of the reaction medium with conversion. The viscosity of styrene mixtures at I50°C will have increased about 1000-fold, for example, when 40 wt % of the monomer has polymerized. The heat transfer to a jacket in a vessel varies approximately inversely with the one-third power of the viscosity. (The exact dependence depends also on the nature of the agitator and the speed of fluid flow.) This suggests that the heat transfer efficiency in a jacketed batch reactor can be expected to decrease by about 40% for every 10% increase in polystyrene conversion between 0 and 40%. 

Studies on the effect of hydrodynamics on localized corrosion and electrochemical etching processes have been reviewed by West et al. Much of the work has been performed by Alkire and co-workers." They have used FIDAP, a commercial FEM code, to investigate the influence of fluid flow on geometries relevant to etching and to pitting corrosion. In most cases, Stokes flow was considered. The Stokes flow approximation is frequently valid inside the cavity because its characteristic dimension is small. However, the flow outside the cavity may not be in the Stokes flow regime. Since it is the external fluid motion that induces flow inside the cavity, under many (especially unsteady) situations, the use of the Stokes flow approximation may be problematic. Some of the work of Alkire and co-workers has been extended hy Shin and Economou, " who simulated the shape evolution of corrosion pits. Natural convection was also considered in their study. 

The measurements by Harley, Pfahler, and Urbanek not only provide a solid basis for modeling fluid flows in small ducts but also raise a question about the nature of that flow at elevated temperatures. The lower-temperature data justify the use of hydrodynamic theory in simple ducts. Whether this will hold in more complex flow structures needs further study. For gas flow in ducts where the Knudsen number is 0.05 or greater, slip flow is observed. Urbanek s data suggest that there may be increased wall interactions as the temperature approaches the boiling point. A more definitive study is needed to clarify this point. 

For the purpose of assessment of macroscopic equations, DNS data are generated for evaporating droplets dispersed in homogeneous shear flows by extending the previous study [17], In this particular case, some of the statistical properties of interests are droplet Reynolds stresses, rjt fluid-droplet velocity correlations, u Vj temperature correlation, O O and mean diameter, d, of the droplets. The temporal variations of n-i t, ujr, and O O are shown in Figs. 3.4a-3.4c, respectively. The varying evaporation rate for an individual droplet, which due to the stochastic nature of fluid flow field, results in polydispersed droplets even when the monodispersed droplets are injected in the flow. The variance droplet diameter and skewness indicates the extent of polydispersity. The temporal variations of mean diameter d, variance a. and skewness are shown... 

One natural approach to describing mixing is to solve the equations of motion of the fluid. In fluid systems, the type of fluid flow is obviously important, and we should consider both laminar and turbulent flow, and various mechanisms of diffusion (molecular diffusion, eddy diffusion). Using fluid mechanics to describe all cases of interest is a difficult problem, both from the modeling and computational perspectives. Rapid developments in computational fluid dynamics (CFD), however, make this approach increasingly attractive 1]. 

The resistance to flow is a strong function of vessel radius Q (x R. As blood vessels become smaller, the resistance to flow increases dramatically (Figure 6.4b). Therefore, an additional consequence of the branching pattern of blood vessels is that the majority of the overall resistance to blood flow resides in the smallest vessels (Figure 6.2b) the majority of the pressure drop ( 80%) occurs in arterioles and capillaries. This natural consequence of the physics of fluid flows is exploited in regulation of blood flow to organs of the body. Local blood flow to a tissue is controlled by constriction and dilation of... 

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