Line sink

Line Sink The velocity induced by a line sink is purely radial and is given in cylindrical coordinates by... 

The analytical solution for an infinitely flanged slot can be obtained by assuming that the inlet is composed of elemental point sinks.The velocity field of an infinitely flanged slot can be obtained by assuming the velocity to be uniformly distributed across the opening. The contribution to the velocity potential at point (x, y) due to the elemental line sink of length and located at (0, Q is given by... 

FIGURE lO.iS Anafyti cal and line sink velocity contours for a flanged slot. 

Figure 10.16 shows the calculated velocity contours as a fraction of the average velocity in the channel (average face velocity). In addition, velocities ob- rained from the line sink model are plotted. It can be seen that, compared to the line sink model, the calculated contours are displaced somewhat in the positive direction, with the greatest relative difference near the exhaust opening and with decreasing relative difference as the dimensionless distance v/VX increases. 

FIGURE 10.16 Velocity contours for the upper half of a plain slot by analytical and line sink solutions. 

An adequate quantitative description of such a situation requires a two- or even three-dimensional approach. Today, a great variety of numerical models are available that allow us to solve such models almost routinely. However, from a didactic point of view numerical models are less suitable as illustrative examples than equations that can still be solved analytically. Therefore, an alternative approach is chosen. In order to keep the flow field quasi-one-dimensional, the single well is replaced by a dense array of wells located along the river at a fixed distance xw (Fig. 25.2c). Ultimately, the set of wells can be looked at as a line sink. This is certainly not the usual method to exploit aquifers Nonetheless, from a qualitative point of view a single well has properties very similar to the line sink. 

As illustrated in Fig. 5.2, the classic Jeffery-Hamel flow concerns two-dimensional radial flow in a wedge-shaped region between flat inclined walls. The flow may be directed radially outward (as illustrated) or radially inward. The flow is assumed to originate in a line source or terminate in a line sink. Velocity at the solid walls obeys a no-slip condition. In practice, there must be an entry region where the flow adjusts from the line source to the channel-confined flow with no-slip walls. The Jeffery-Hamel analysis applies to the channel after this initial adjustment is accomplished. 

Comparison of the various depreciation methods shows that the declining-balance and the sum-of-the-years-digits methods give similar results. In both cases, the depreciation costs are greater in the early-life years of the property than in the later years. Annual depreciation costs are constant when the straight-line, sinking-fund, or present-worth method is used. Because interest effects are included in the sinking-fund and present-worth methods, the annual decrease in asset value with these two methods is lower in the early-life years than in the... 

PC/ABS blends have better flow properties than PC, which means that the parts have fewer knit lines, sink marks as well as less molded-in stress. Molded parts offer excellent surface appearance and good paint adhesion. Up to 20% regrind may be used for all grades. 

If the best-fit line rises to the right, then the slope of the line is positive. A positive slope indicates that the dependent variable increases as the independent variable increases. If the best-fit line sinks to the right, then the slope of the line is negative. A negative slope indicates that the dependent variable decreases as the independent variable increases. In either case, the slope of the line is constant. 

The automotive indushy is an extremely competitive market for the injection molding industry. Automotive manufacturers are reducing the number of supphers which produce components for their vehicles. To stay competitive, injection molders need to be proactive in both technology and pricing. Interior trim is a very competitive market for the injection molding industry. Much of the interior of an automobile is comprised of plastic parts molded from many different materials. The variety of plastics used in interior trim makes it very difficult for the assembler to obtain color match between all components. Each type of base resin requires a different formulation of colorant to achieve the same finished color. This problem is further complicated by the addition of additives such as UV stabilizers, lubricants, fillers, etc. Other problems include molding faults such as flow lines, weld lines, sink, splay, and blush... 

In an introductory course on soil mechanics there is a limit to how far one can proceed. However, there are many more or less realistic problems which can be reduced to a single degree of spatial freedom onedimensional consolidation, flow of water towards a point sink or a line sink in a suitably infinite domain, stability of an infinite slope - these have already been mentioned. There are a number of examples of soil-structure interaction which can also be reduced to problems with a single degree of freedom. It is important to take whatever opportunities are provided by the skills and understanding that the students have developed to increase awareness of the interaction of soil and structural elements. It is not inevitable that the structural elements will always be significantly stitfer than the natural or man-made soils with which they interact (Muir Wood Nash 2000, Muir Wood 2004). 

Weld line Sink mark Dull finish Voids... 

The sink flow analysis, which assumes a purely extensional flow (i.e., no shear component), was presented by Metzner and Metzner (1970) to evaluate the extensional viscosity from orifice Apen measurements. For an axisymmetric contraction, the flow into the orifice is analogous to a point sink for a planar contraction flow, the analogy is with a line sink (Batchelor, 1967). In the case of axisymmetric contraction (Figure 7.8.1), the use of spherical coordinates and continuity gives the velocity components... 

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