The fluid in motion

A group of streamlines can be taken together to form a streamtube, and thus the whole area for flow can be regarded as being composed of bundles of streamtubes. 

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The governing flow equation describing flow through as porous medium is known as Darcy s law, which is a relationship between the volumetric flow rate of a fluid flowing linearly through a porous medium and the energy loss of the fluid in motion. 

By measuring the kinetic effects of the fluid in motion, since at a given pressure drop, low-density steam will move at a much greater velocity than will high-density condensate, and the conversion of pressure energy into kinetic energy can be used to position a valve. 

The transport of an adsorbable species from the bulk fluid flowing around an individual bead is a problem of molecular diffusion. With the fluid in motion the rate of transport to the surface of a bead or pellet of adsorbent material is generally treated as a linear driving force. Eor gas phase separations there are a variety of correlations available to describe the mass transport to the surface in terms of the particle Reynolds number, the Schmidt number, the size of the adsorbent particle and of course the binary diffusivity of the species of interest. 

Thin EDLs form at both the particle and the wall surfaces. The formation of EDLs at the surfaces sets the fluid in motion and consequently drives the particle. As the particle is located at the center of the microchaimel, it experiences neither vertical translation nor rotation. Figure 7 shows the instantaneous location of the particles with different zeta potentials. The translational velocity U of the particle is given by the gradient of the graph. For all cases, the gradient is cimstant. This implies that the particles accelerate in a very short time to a constant velocity and move with that constant velocity thereafter. This is not unexpected as the inertia force is negligible in such a small-scaled channel. 

If a fluid is flowing between the two plates, heat transfer is enhanced since energy is now also carried to the cold plate by fluid motion and not only by conduction. To describe this situation we have to consider that the fluid in motion comes to a complete stop at the surface of the plates thus the fluid layers in direct contact with the plates stick to the surface (no-slip condition, Section 3.2.2). An implication of this effect is that the heat transfer to the cold plate from the hot fluid layer adjacent to the cold surface (and vice versa from the hot plate to the cooler fluid at z = L) is only by pure conduction through the fluid and can be expressed by the thermal conductivity and the respective temperature gradient at z = 0 (surface of cold plate). Thus we have for steady state conditions ... 

The rotating disc differs from laminar flow chambers in that a motor is used to put the cell-seeded substrate in motion, rather than a pressure gradient to put the fluid in motion [47,107,108] (Figure 34.6). An advantage of this device is that generates a shear stress, r, that varies linearly with radial position, r, by... 

By applying the momentum theorem, calculate the minimum pressure difference, AP, that should be applied between the inlet and outlet of the pipe to set the fluid in motion. By applying the momentum theorem on a domain to be specified, determine the variation of (r) with r and AP. Justify the fact that the momentum theorem can be applied for a Bingham fluid. 

Inertial forces are developed when the velocity of a fluid changes direction or magnitude. In turbulent flow, inertia forces are larger than viscous forces. Fluid in motion tends to continue in motion until it meets a sohd surface or other fluid moving in a different direction. Forces are developed during the momentum transfer that takes place. The forces ac ting on the impeller blades fluctuate in a random manner related to the scale and intensity of turbulence at the impeller. 

The seeond Helmholtz law states that the vortieity of a frietionless fluid does not ehange with time. Henee, if the flow at the inlet to an impeller is irrotational, the absolute flow must remain irrotational throughout the impeller. As the impeller has an angular veloeity lu, the fluid must have an angular veloeity—lu relative to the impeller. This fluid motion is ealled the relative eddy. If there were no flow through the impeller, the fluid in the... 

In this section the correlations used to determine the heat and mass transfer rates are presented. The convection process may be either free or forced convection. In free convection fluid motion is created by buoyancy forces within the fluid. In most industrial processes, forced convection is necessary in order to achieve the most economic heat exchange. The heat transfer correlations for forced convection in external and internal flows are given in Tables 4.8 and 4.9, respectively, for different conditions and geometries. 

Boundary layer A layer of fluid, extending from the boundary into the bulk of the fluid, in which fluid motion is influenced by the frictional drag at the boundary. 

Dispersion modeling equations for water systems take the same form as those presented later in this chapter for the atmosphere. Analytical solutions tire not nearly as complicated or difficult, since the bulk motion of the fluid (in this case, wtiicr) is a weak vtiriablc with respect to m.ignitude, direction, lime, and position as it is when the fluid is air. 

Viewing things from the perspective of his physical theory of contact electricity, Volta was intrigued by the apparently endless power of the battery to keep the electric fluid in motion without the mechanical actions needed to operate the classical, friction, electrostatic machine, and the electrophorus. He called his batteiy alternately the artificial electric organ, in homage to the torpedo fish that had supplied the idea, and the electromotive apparatus, alluding to the perpetual motion (his words) of the electric fluid achieved by the machine. To explain that motion Volta relied, rather than on the concepts of energy available around 1800, on his own notion of electric tension. He occasionally defined tension as the effort each point of an electrified body makes to get rid of its electricity but above all he confidently and consistently measured it with the electrometer. 

An understanding of the behavior of fluids in motion, or solids for that matter, requires an understanding of the term inertia. Inertia is the term used by scientists to describe the property possessed by all forms of matter that make it resist being moved when it is at rest and to resist any change in its rate or motion when it is moving. 

Gravity, applied forces, and atmospheric pressure are examples of static factors that apply equally to fluids at rest or in motion. Inertia and friction are dynamic forces that apply only to fluids in motion. The mathematical sum of gravity, applied forces, and atmospheric pressure is the static pressure obtained at any one point in a fluid system at a given point in time. Static pressure exists in addition to any dynamic factors that may also be present at the same time. 

It is necessary to be able to calculate the energy and momentum of a fluid at various positions in a flow system. It will be seen that energy occurs in a number of forms and that some of these are influenced by the motion of the fluid. In the first part of this chapter the thermodynamic properties of fluids will be discussed. It will then be seen how the thermodynamic relations are modified if the fluid is in motion. In later chapters, the effects of frictional forces will be considered, and the principal methods of measuring flow will be described. 

The total energy of a fluid in motion is made up of a number of components. For unit mass of fluid and neglecting changes in magnetic and electrical energy, the magnitutes of the various forms of energy are as follows. 

In turbulent flow there is a complex interconnected series of circulating or eddy currents in the fluid, generally increasing in scale and intensity with increase of distance from any boundary surface. If, for steady-state turbulent flow, the velocity is measured at any fixed point in the fluid, both its magnitude and direction will be found to vary in a random manner with time. This is because a random velocity component, attributable to the circulation of the fluid in the eddies, is superimposed on the steady state mean velocity. No net motion arises from the eddies and therefore their time average in any direction must be zero. The instantaneous magnitude and direction of velocity at any point is therefore the vector sum of the steady and fluctuating components. 

It has been recognized for some time that fluids in motion, such as the atmosphere or the ocean, disperse added materials. This properly has been exploited by engineers in a variety of ways, such as the use of smoke stacks for boiler furnaces and ocean ontfalls for the release of treated wastewaters. It is now known that dilution is seldom the solution to an enviromnental problem the dispersed pollutants may accumulate to undesirable levels in certain niches in an ecosystem, be transformed by biological and photochemical processes to other pollntants, or have nnanticipated health or ecological effects even at highly dilute concentrations. It is therefore necessary to rmderstand the transport and transformation of chemicals in the natural environment and through the trophic chain ctrlminating in man. 

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