Rate of energy dissipation

Similarly, the rate of energy dissipation in Eq. (2.6) has units energy volume time, so the dimensions of that equation are... [Pg.80]

In connection with Eq. (2.6), we used the fact that the product of a viscous force and a velocity gives a rate of energy dissipation, so F j v j + Fy j Vy j equals the rate of energy dissipation by segment i. Thus the energy loss per second for the ith segment (AW/At)j is... [Pg.110]

Figure 2.1 served as the basis for our initial analysis of viscosity, and we return to this representation now with the stipulation that the volume of fluid sandwiched between the two plates is a unit of volume. This unit is defined by a unit of contact area with the walls and a unit of separation between the two walls. Next we consider a shearing force acting on this cube of fluid to induce a unit velocity gradient. According to Eq. (2.6), the rate of energy dissipation per unit volume from viscous forces dW/dt is proportional to the square of the velocity gradient, with t]q (pure liquid, subscript 0) the factor of proportionality ... [Pg.587]

Thus, to maintain a unit gradient, a volume rate of energy dissipation equal to 77o is required. [Pg.587]

Now we return to consider the energy that must be dissipated in a unit volume of suspension to produce a unit gradient, as we did above with the pure solvent. The same fraction applied to the shearing force will produce the unit gradient, and the same fraction also describes the volume rate of energy dissipation compared to the situation described above for pure solvent. Since the latter was Po, we write for the suspension, in the case of dv/dy = 1,... [Pg.588]

This is only one of the contributions to the total volume rate of energy dissipation a second term which arises from explicit consideration of the individual spheres must also be taken into account. This second effect can be shown to equal 1.5 [Pg.588]

An alternative point of view assumes that each repeat unit of the polymer chain offers hydrodynamic resistance to the flow such that f-the friction factor per repeat unit-is applicable to each of the n units. This situation is called the free-draining coil. The free-draining coil is the model upon which the Debye viscosity equation is based in Chap. 2. Accordingly, we use Eq. (2.53) to give the contribution of a single polymer chain to the rate of energy dissipation ... [Pg.610]

In this equation, represents the rate of energy dissipation per unit mass of fluid. In pulsed and reciprocating plate columns the dimensionless proportionahty constant K in equation 38 is on the order of 0.3. In stirred tanks, the proportionaUty constant has been reported as 0.024(1 + 2.5 h) in the holdup range 0 to 0.35 (67). The increase of drop si2e with holdup is attributed to the increasing tendency for coalescence between drops as the concentration of drops increases. A detailed survey of drop si2e correlations is given by the Hterature (65). [Pg.69]

The turbulent kinetic energy is calculated from equation 41. Equation 43 defines the rate of energy dissipation, S, which is related to the length scale via... [Pg.102]

The component with the lower viscosity tends to encapsulate the more viscous (or more elastic) component (207) during mixing, because this reduces the rate of energy dissipation. Thus the viscosities may be used to offset the effect of the proportions of the components to control which phase is continuous (2,209). Frequently, there is an intermediate situation where a cocontinuous or interpenetrating network of phases can be generated by careflil control of composition, microrheology, and processing conditions. Rubbery thermoplastic blends have been produced by this route (212). [Pg.416]

In the free-draining case sy/2 is also the relative velocity of the medium in the vicinity of a bead at a distance s from the center. Hence the frictional force acting on the bead is sy/2, and the rate of energy dissipation by the action of the bead is the product of the force and the velocity, or sy/2y. The total energy dissipated per unit time by the molecule will be given by the sum of such terms for each bead, or... [Pg.604]

Figure 5.4-50. Distribution of rate of energy dissipation (adapted from Baldyga and Bourne, 1988b).

One might then expect that the yield of the desired product would correlate well with the local rate of energy dissipation. Villermaux et al. (1994) studied a system of the following parallel competing reactions ... [Pg.352]

Power input per unit mass of the system is equal to the rate of energy dissipation per unit mass of the liquid and it is estimated by considering the permanent pressure head loss across the orifice. The rate of energy dissipation due to eddy losses is the product of the head loss and the volumetric flow rate. Frictional pressure drop at downstream of the orifice can be calculated as,... [Pg.76]

Ten Cate et al. (2004) were able to learn from their DNS about the mutual effect of microscale (particle scale) events and phenomena at the macroscale the particle collisions are brought about by the turbulence, and the particles affect the turbulence. Energy spectra confirmed that the particles generate fluid motion at length scales of the order of the particle size. This results in a strong increase in the rate of energy dissipation at these length scales and in a decrease... [Pg.193]

Fig. 12. Snapshot from a two-phase DNS of colliding particles in an originally fully developed turbulent flow of liquid in a periodic 3-D box with spectral forcing of the turbulence. The particles (in blue) have been plotted at their position and are intersected by the plane of view. The arrows denote the instantaneous flow field, the colors relate to the logarithmic value of the nondimensional rate of energy dissipation.

The rate of energy dissipation, Q, is related to the adiabatic polymer temperature increase as follows ... [Pg.66]

Rowell and Finlayson described leakage flow through the flight clearance as flow between two parallel plates [7]. The rate of energy dissipation between the flight lands and the barrel wall is given by Eq. 7.82. This dissipation is considered to be the same as that for barrel rotation, and it is provided in the literature [9]. [Pg.306]

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