Flatness ratio

Characterization of the particle shape is generally described by the deviation from sphericity, as in the case of ellipsoids where the ratio of the two radii is the measure of deviation. The surface and volume are important properties aflected by the overall shape of a particle. A more complicated relationship for particle characterization was described by Heywood, who introduced shape coefficients such as surface and volume coefficients and elongation and flatness ratios [42]. 

Heywood s Surface Coefficient, Flatness Ratio and Elongation Ratio... 

For flat spiral (pancake) coils, in which the ratio D /Dj varies for each turn, a different value of coefficient will be obtained for each turn a weighted average based on length per turn is used. 

Mass-Transfer Coefficient Denoted by /c, K, and so on, the mass-transfer coefficient is the ratio of the flux to a concentration (or composition) difference. These coefficients generally represent rates of transfer that are much greater than those that occur by diffusion alone, as a result of convection or turbulence at the interface where mass transfer occurs. There exist several principles that relate that coefficient to the diffusivity and other fluid properties and to the intensity of motion and geometry. Examples that are outlined later are the film theoiy, the surface renewal theoiy, and the penetration the-oiy, all of which pertain to ideahzed cases. For many situations of practical interest like investigating the flow inside tubes and over flat surfaces as well as measuring external flowthrough banks of tubes, in fixed beds of particles, and the like, correlations have been developed that follow the same forms as the above theories. Examples of these are provided in the subsequent section on mass-transfer coefficient correlations. 

The drag coefficients for disks (flat side perpendicular to the direction of motion) and for cylinders (infinite length with axis perpendicular to the direclion of motion) are given in Fig. 6-57 as a Function of Reynolds number. The effect of length-to-diameter ratio for cylinders in the Newton s law region is reported by Knudsen and Katz Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1958). 

A basic stirred tank design is shown in Fig. 23-30. Height to diameter ratio is H/D = 2 to 3. Heat transfer may be provided through a jacket or internal coils. Baffles prevent movement of the mass as a whole. A draft tube enhances vertical circulation. The vapor space is about 20 percent of the total volume. A hollow shaft and impeller increase gas circulation (as in Fig. 23-31). A splasher can be attached to the shaft at the hquid surface to improve entrainment of gas. A variety of impellers is in use. The pitched propeller moves the liquid axially, the flat blade moves it radially, and inclined blades move it both axially and radially. The anchor and some other designs are suited to viscous hquids. 

The phenomenon uneven distribution of current within the same conductor due to the inductive effect is known as the skin effect and results in an increased effective resistance of the conductor. The ratio of a.c. to d.c. resistance, R JR. is the measure of the skin effect and is known as the skin effect ratio . Figure 28.13(a) illustrates the skin elTect for various types and sizes of aluminium in flat sections. For easy reference, the skin effects in isolated round (solid or hollow) and channel conductors (in box form) are also shown in Figures 28.13(b) and (c) respectively. 

Now refer to Figure 28.13(a) to obtain the skin effect ratio Ffac/ffdc- Consider the cross-sectional curves for EIE-M grade of flat busbars at an operating temperature of 85°C for a cross-sectional area of 6.45 cm and determine the Ffac/ dc ratio on the skin effect curve having... 

A composite material consists of flat, thin metal plates of uniform thickness glued one to another with a thin, epoxy-resin layer (also of uniform thickness) to form a multi-decker-sandwich structure. Young s modulus of the metal is Ej, that of the epoxy resin is E2 (where E2 < Ej) and the volume fraction of metal is Vj. Find the ratio of the maximum composite modulus to the minimum composite modulus in terms of Ej, E2 and V. Which value of gives the largest ratio ... 

Fig ure 1-5. The typioally flat turboexpander effioienoy oharaoteristie with various flowrates is shown here. Effioienoy versus the velooity ratio v (ratio tip speed to spouting velooity) is also shown. (Source Atlas Copco.)... 

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