Von Karman coefficient

Suspended load reduced the value of the Von Karman constant. Values of Aj. between 0.314 and 0.342 were measured (by comparison with 0.4 for full pipes). The reduction of the Von Karman coefficient indicated a reduced level of mixing and a tendency by the sediments to suppress turbulence. 

FIGURE 6-5 Variation of the equivalent roughness, Von Karman coefficient, and with the weight concentration of the sand-water mixture. (From Vanoni, 1946, by permission of ASCE.)... 

Iron sand is flowing in a rectangular open channel that is 300 mm wide x 120 mm high at a speed of 3 m/s. Assume the Von Karman coefficient K= 0.33. The average particle size is 0.3 mm. Using Einstein s approaches, it is assumed that the reference layer a is to be twice the particle size diameter. The flume is one-third full (i.e., = 40 mm). The slurry... 

Experimental constant Von Karman coefficient Length of conduit... 

Figure 6.5 Distinct differences in transport behavior between pools of surface and bottom floes over several tidal cycles, as determined by R0 values, in the ACE Basin (USA). Hatched areas are times of maximum current speed. ws = sediment settling velocity, 0 = proportionality coefficient between eddy viscosity and diffusivity, k = von Karman s constant, and n = frictional velocity. (From Milligan et al., 2001, with permission.)...

One way of seeing this explicitly is to consider the Schrodinger equation modified for a periodic lattice with Born-von Karman periodic boundary conditions assuming a wavefunction ij/(r) = Eqcq exp(iq r) and a potential U(r) which has the periodicity of the lattice U(r) = 2,GUG exp(/G r), where the Fourier58 coefficients UG are given by UG = JCeiiG(r) exp (—zG r) dr, the Schrodinger equation is rewritten as... 

Schacham equation, 94 von Karman equation, 95 Froth flotation, 636,638 equipment, 645 performance, 638 Fuel cells, 646 characteristics, 655, 656 Fugacity coefficient, 372... 

In Figure 10.8 we have plotted the variation of the ratios of mass transfer coefficients 12/ 11 k i/k22 for an acetone-benzene-helium system considered in Example 11.5.3. The Chilton-Colburn analogy predicts that these ratios would be independent of Re, as shown by the horizontal lines in Figure 10.8. The von Karman turbulent model, on the other hand, predicts that the influence of coupling should decrease with increase in Re. The latter trend is in accord with our physical intuition. Depending on the driving forces for mass transfer, the Chilton-Colburn and the von Karman turbulent models could predict different directions of transfer of acetone (see, e.g., Krishna, 1982). 

Figure 10.8. Ratio /C12A115 which are elements of the zero-flux matrix of mass transfer coefficients [/c], as a function of the gas-phase Reynolds number. Mass transfer between a gaseous mixture of acetone (l)-benzene (2)-helium (3) and a liquid film containing acetone and benzene. Calculations by Krishna (1982) based on the von Karman turbulent film model and the Chilton-Colburn analogy.

Estimate the rates of condensation using the Von Karman model for calculating the mass transfer coefficients. 

Formulas (1.6.1) and (1.6.2) have formed the basis of most theoretical investigations on the determination of the average fluid velocity and the drag coefficient in the stabilized region of turbulent flow in a circular tube (and a plane channel of width 2a). The corresponding results obtained on the basis of Prandtl s relation (1.1.21) and von Karman s relation (1.1.22) for the turbulent viscosity can be found in [276,427]. In what follows, major attention will be paid to empirical and semiempirical formulas that approximate numerous experimental data quite well. 

For the turbulent boundary layer on a flat plate, von Karman s friction law with modified numerical coefficients [212,289],... 

The simplest way to close equations (3.1.37) is to use the hypothesis that the turbulent Prandtl number for the examined process is a constant quantity. Then it readily follows from Eq. (3.1.39) that the turbulent diffusion coefficient is proportional to the turbulent viscosity >t = i /Pr,. By using the expression for vx borrowed from the corresponding hydrodynamic model, one can obtain the desired value of Dt. In particular, following Prandtl s or von Karman s model, one can use formula (1.1.21) or (1.1.22) for vx. 

This form of equation originated with von Karman however, the coefficients appearing here are slightly different because they are based on more recent data. 

Researchers extensively use the Bom-von Karman theory in order to estimate the strength of interatomic bonding [47]. This traditional method is to make a formal expansion of energy of a vibrating crystal in a series and to treat the expansion coefficients as force constants. The main assumptions of this theory are as follows. 

The coefficients 0ap in (12.14), which represent the second derivatives of the potential energy with respect to the atomic displacements determined at the equilibrium points, are called atomic force constants. By definition, they have an ex-pUcit physical meaning. The coefficient 4>afi(lk I k ) is equal to the minus force which acts on the atom (Ik) in the direction a, when the other atom (Vk ) deviates per unit distance in the direction /3. The Born-von Karman model implies that all other atoms stay at their equihbrium positions. 

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