Numbers exponents

NUMBER EXPONENT S-COEF P-COEF D-COEF F-COEF ... 

Figure 5-16. Factors in Froude number exponent, n. By permission, Rushton, J. H., ef a/. [18].

Determine from experimental data the Reynolds number exponent for the s) stem, or use information in Figure 5-40 if the systems of Table 5-8 can be considered similar, use proper coefficients and solve for outside film coefficient, hg. 

Hubbard and Lightfoot (HI la) earlier reported a Sc,/3 dependence on the basis of measurements in which the Schmidt number was varied over a very large range. The data did not exclude a lower Reynolds number exponent than 0.88, and reaffirmed the value of the classical Chilton-Colburn equation for practical purposes. Recent measurements on smooth transfer surfaces in turbulent channel flow by Dawson and Trass (D8) also firmly suggest a Sc13 dependence and no explicit dependence of k+ on the friction coefficient, with Sh thus depending on Re0,875. The extensive data of Landau... 

The following section consists of 10 sets of miscellaneous math, including basic arithmetic questions and word problems with whole numbers. You will also see problems involving pre-algebra concepts such as negative numbers, exponents, and square roots (getting you ready for the algebra in Section 5). This section will provide a warm-up session before you move on to more difficult kinds of problems. 

In one respect Eq. (20) is satisfying. The exponents on the Reynolds and Prandtl numbers are roughly the same as those used for ordinary forced-convection heat transfer. The negative sign on the Prandtl-number exponent in Rohsenow s equation has seemed illogical to many scientists. The logical exponents found by Forster and Zuber... 

Different values of the constant and exponent r were used for different system geometries and operating conditions. Thus, for the turbine agitators at a Reynolds number less than 7400, was 0.00058 and r was 1.4. For the turbine agitators at a Reynolds number above 7400, was 0.62 and r was 0.62. For the propellers, over a range of Reynolds numbers from 3300 to 330,000, was 0.0043, and r was 1.0. In every case, the Schmidt number exponent s was 0.5. Although these equations fit the data fairly well, there is a scatter of the individual points. Hence, for any particular solid-liquid combination at constant temperature in a... 

Here n denotes "effective quantum number", exponent 5C, is an arbitrary positive number, r, t, y) are polar coordinates for a point with respect to the origin A in which the function (2,3) is centered. Apart from the first two terms that represent a normalizing factor, the function (2,3) is closely related to hydrogen-like orbitals. For the hydrogen Is orbital the function I q q 0 identical with Q q, if we assume Z Z/n, However, it should be recalled that in contrast to hydrogen-like orbitals STO s are not mutually orthogonal. Another essential difference is in the number of nodes. Hydrogen functions have (n -i - 1) nodes, whereas STO s are nodeless in their radial part. Alternatively, the STO may be expressed by means of Cartesian coordinates as follows... 

Two improved versions of Eq. (6.26), which incorporate the effect of variable properties by considering the wall temperature relative to the fluid bulk temperature, are given in Table 6.1, L being the length of the pipe. All properties for these correlations are evaluated at Tb. The Prandtl-number exponent of the first correlation and the ratio... 

Available empirical results show that the Reynolds number exponent m depends not only on rid and Hid but also on the nozzle geometry [83], Some experimental results illustrating the local Nusselt number dependence on the Reynolds and nozzle-to-surface spacing are given in Fig. 18.18. Numerous citations to extensive local heat transfer coefficient results showing the effects of Re and Hid can be found in Refs. 82-84. 

When spheres or other particles are in a packed bed, the mass and heat transfer coefficients are higher than for isolated particles exposed to the same superficial velocity. There is also more uncertainty in the coefficients, because published data show considerable scatter and significant differences in the Reynolds number exponents. Most of the published data are reported as /-factors, which are dimensionless groups that are functions of the Reynolds number ... 

Pure numbers, such as Avogadro s number, exponents, and the base of natural logarithms (e), have no dimensions. 

If a prime number exponent has two digits some blank space separates these from the following digits. In the last row for Pr... 

In view of the Schmidt number exponent (Sc° ) in Equation 6.24 being substantially different than those for the surface renewal (Sc 0 or boundary layer flow (Sc ) models, Hughmark (1980) introduced a new argument that the mechanism of solid-liquid mass transfer in a stirred vessel is not the same as described by the two models mentioned earlier. 

An exponent is a number written as a superscript following another number. Exponents are often called powers of numbers. The term power indicates how many times the number is used as a factor. In the number 10, 2 is the exponent, and the number means 10 squared, or 10 to the second power, or 10 X 10 = 100. Three other examples are... 

The Arrhenius number, exponent of the Arrhenius equation evaluated at Ts ... 

At first we will consider = 10 and work only with concentrations that can be expressed with whole-number exponents. In the next section, after you have become familiar with the mathematical procedures, concentrations will be written in the usual exponential notation form, including coefficients. 

Detector Characteristic width z Characteristic length i Numerical constant Jc" Reynolds Number exponent a... 

They generally suggest an increase of the Reynolds number exponent when using less wettable packings. This is well accounted for by Eq. 22 which predicts an exponent equal to 1-2/3 f i.e. increasing with Re. This role of wetting paramete ... 

Figure 16-7 shows correlations for the dependence of heat transfer on Reynolds number for a variety of such vessels. As the viscosity increases, dependency on Reynolds number, exponent a, shifts from to (Figure 16-7). A selection of correlations for vessels is given in Chapter 14. In the Reynolds number range 10 to 10, Todd (1988) correlated data for twin-screw extruders as follows ...

Fig. 5 Top Double-logarithmic plots of the bond valence divided by the scaling factor hm — If x 1/ vs. pbcp, where m (h-x) is the pcmod number of the cation (animi). (Top using softBV bond valence parameters, bottom using conventional txmd valence parameters). The respective values of the period number exponents are chosen to maximize the correlation coefficient for the linear regression over all data points (solid line), while maintaining a 1 2 ratio betweoi x and y. The inset of the top graph compares the observed Pbcp to values predicted fiom the correlation derived in the main graph...

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