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Velocity representation

Fig. E2.5b Schematic representation velocity shear rate and shear stress profiles of a Newtonian fluid between parallel plates. Fig. E2.5b Schematic representation velocity shear rate and shear stress profiles of a Newtonian fluid between parallel plates.
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]

Pig. 22. Schematic representation of typical pressure drop as a function of superficial gas velocity, expressed in terms of G = /9q tiQ, in packed columns. O, Dry packing , low Hquid flow rate I, higher Hquid flow rate. The points do not correspond to actual experimental data, but represent examples. [Pg.39]

Fig. 2. Representation of longitudinal modes ia a laser. Where line A = cj2D, c is the velocity of light, and D is the distance between the laser mirrors. Fig. 2. Representation of longitudinal modes ia a laser. Where line A = cj2D, c is the velocity of light, and D is the distance between the laser mirrors.
Studies of individual bubbles rising in a two-dimensional gas—Hquid—soHd reactor provide detailed representations of bubble-wake interactions and projections of their impact on performance (Fig. 9). The details of flow, in this case bubble shapes, associated wake stmctures, and resultant bubble rise velocities and wake dynamics are important in characteri2ing reactor performance (26). [Pg.512]

We assume that in (4.38) and (4.39), all velocities are measured with respect to the same coordinate system (at rest in the laboratory) and the particle velocity is normal to the shock front. When a plane shock wave propagates from one material into another the pressure (stress) and particle velocity across the interface are continuous. Therefore, the pressure-particle velocity plane representation proves a convenient framework from which to describe the plane Impact of a gun- or explosive-accelerated flyer plate with a sample target. Also of importance (and discussed below) is the interaction of plane shock waves with a free surface or higher- or lower-impedance media. [Pg.84]

Figure lb gives a graphical representation of the steps involved in the leap-frog propagation. The current velocity v , which is necessary for calculating the kinetic energy, can be calculated as... [Pg.46]

The potential (Eq. 10.24) and stream (Eq. 10.25) functions for the point sink provide a simple theoretical representation of the velocity variations near real suction openings. Close to the origin the velocity for the point sink approaches infinity and deviates considerably from the actual fluid velocities. However, at distances greater than approximately one diameter from the finite opening, the velocities given by the sink model are reasonable approximations of the true values. [Pg.837]

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. [Pg.115]

Used in conjunction with zero-to-peak (PK) terms, velocity is the best representation of the true energy generated by a machine when relative or bearing cap-data are used. (Note Most vibration monitoring programs rely on data acquired from machine housing or bearing caps.) In most cases, peak velocity values are used with vibration data between 0 and 1000 Hz. These data are acquired with microprocessor-based, frequency-domain systems. [Pg.675]

The representation of the results from slow strain-rate tests may be through the usual ductility parameters such as reduction in area, the maximum load achieved, the crack velocity or even the time to failure, although as with all tests, metallographic or fractographic examination, whilst not readily quantifiable, should also be involved. Since stress-corrosion failures are usually associated with relatively little plastic deformation, the ductility... [Pg.1366]

We have thus the following representation of the phenomenon (Fig. 6-10) on the arc AB the motion is slow at the point B the representative point ceases to follow the curve F(x) and its horizontal velocity becomes very large, bringing it to the point C at which a slow motion begins on the arc CD, followed by another jump DC, and so on. [Pg.338]

In the Universal Velocity Profile , the laminar sub-iayer extends to values of y+ = 5 and the turbulent zone starts at y+ = 30 and the range 5 < y+ < 30, the buffer layer, is covered by a second linear relation between and In, y+. What is the maximum difference between the values of u+, in the range 5 < y4 < 30, using the two methods of representation of the velocity profile ... [Pg.863]

Fig. 14. 3D representation of the H-atom velocity flux contour, d a/dvd(cos6). The contours are constructed directly from a total of 33 slices of the Doppler-selected TOF measurements. [Pg.28]

Fig. 21. The product D-atom velocity-flux contour map, d Fig. 21. The product D-atom velocity-flux contour map, d <j/dv d(cos0), in a 3D isometric representation. Each contour is constructed directly from a total of 28 slices of the Doppler-selected TOF measurements, as exemplified in Fig. 20. For clarity, a coarse grid size is used here. The zero degree is defined as the initial center-of-mass velocity of the HD beam from which the D-atom product is originated. Note the dominance of the HF(V = 2) co-product for all cases, yet the dramatic variations in angular distributions with a slight change in collision energy ( 0.1 kcal/moll).
Fig. 34. Schematic two-dimensional representation of the flow field which is generated by a force at the origin in the y-direction. The arrow length and directions symbolize the velocities of the solvent. (Reprinted with permission from [14]. Copyright 1992 Kluwer Academic Publishers, Dordrecht)... Fig. 34. Schematic two-dimensional representation of the flow field which is generated by a force at the origin in the y-direction. The arrow length and directions symbolize the velocities of the solvent. (Reprinted with permission from [14]. Copyright 1992 Kluwer Academic Publishers, Dordrecht)...

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See also in sourсe #XX -- [ Pg.164 , Pg.166 , Pg.168 ]




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