Terminal velocity, equation defining

By combining Eq. (44) and the recommended drag coefficient correlations in Table 8 or drag coefficient equations proposed by Turton and Levenspiel (1986), Eq. (34), and Haider and Levenspiel (1989), Eq. (35), the terminal velocity can be calculated. Haider and Levenspiel further suggested an approximate method for direct evaluation of the terminal velocity by defining a dimensionless particle size, d, and a dimensionless particle velocity, U, by... 

Diffuser jet throw, L, is a parameter commonly used in air diffuser sizing defined as the distance from the diffuser face to the jet cross-section where the centerline velocity equals a terminal velocity (v is often assumed to be 0.25 rn/s). Therefore, the throw (L) can be determined by velocity decay equations with v. equal to the terminal velocity ... 

In motion from a centrifugal force, the velocity depends on the radius, and the acceleration is not constant if the partide is in motion with respect to the fluid. In many practical uses of centrifugal force, however, du/dt is small in comparison with the other two terms in Eq. (7.32), and if du/dt is neglected, a terminal velocity at any given radius can be defined by the equation... 

While electrical breakdown constraints set the lower limit for IMS gas pressure, there also is the upper limit. At some point, the density of gas molecules makes their colhsions with an ion a many-body rather than binary interaction. Eventually, the dynamics becomes governed by laws of viscous fiiction appropriate for hquids. In that regime, the terminal velocity of ions is stiU proportional to E at low E, and mobihty is defined by Equation 1.8. However, formahsms such as Equation 1.10 that relate K to ion structure cease to apply, and becomes independent of gas pressure. ... 

Suppose the particle is subject to a gravitational force, = mg -vp, where g is the gravitation constant, v is tire partial specific volume of the solute particle, and p is the density of the solvent. The particle will move in the solution at a rate determined by the gravitational force and the frictional resistance. It will accelerate until the two forces balance and a terminal average velocity is attained. The instantaneous velocity will continue to fluctuate due to the random force, but a well-defined average terminal velocity is observed. The form of Equation 5.44 appropriate for this situation is ... 

Calculation of the terminal velocity of a porous sphere is useful and important in applications in water treatment where settling velocities of a floe or an aggregate are estimated. It is also important in estimation of terminal velocities of clusters in fluidized bed applications. The terminal velocity of a porous sphere can be quite different from that of an impermeable sphere. Theoretical studies of settling velocity of porous spheres were conducted by Sutherland and Tan (1970), Ooms et al. (1970), Neale et al. (1973), Epstein and Neale (1974), and Matsumoto and Suganuma (1977). The terminal velocity of porous spheres was also experimentally measured by Masliyah and Polikar (1980). In the limiting case of a very low Reynolds number, Neale et al. (1973) arrived at the following equation for the ratio of the resistance experienced by a porous (or permeable) sphere to an equivalent impermeable sphere. An equivalent impermeable sphere is defined to be a sphere having the same diameter and bulk density of the permeable sphere. 

Whereas the equations of Newitt et al. (1955) and Wilson (1942) focused on the terminal velocity, the work of Durand and Condolios (1952) focused on the drag coefficient for sand and gravel. Zandi and Govatos (1967) and Zandi (1971) extended the work of Durand to other solids and to different mixtures. They defined an index number as... 

Stokes law is applicable when the Reynolds number is very low (less than 2) in such cases, the terminal velocity would be defined as (Equation 3.In)... 

Dukler Theory The preceding expressions for condensation are based on the classical Nusselt theoiy. It is generally known and conceded that the film coefficients for steam and organic vapors calculated by the Nusselt theory are conservatively low. Dukler [Chem. Eng. Prog., 55, 62 (1959)] developed equations for velocity and temperature distribution in thin films on vertical walls based on expressions of Deissler (NACA Tech. Notes 2129, 1950 2138, 1952 3145, 1959) for the eddy viscosity and thermal conductivity near the solid boundaiy. According to the Dukler theoiy, three fixed factors must be known to estabhsh the value of the average film coefficient the terminal Reynolds number, the Prandtl number of the condensed phase, and a dimensionless group defined as follows ... 

In these equations, a is the specific interfacial area for a significant degree of surface aeration (m2/m3), I is the agitator power per unit volume of vessel (W/m3), pL is the liquid density, o is the surface tension (N/m), us is the superficial gas velocity (m/s), u0 is the terminal bubble-rise velocity (m/s), N is the impeller speed (Hz), d, is the impeller diameter (m), dt is the tank diameter (m), pi is the liquid viscosity (Ns/m2) and d0 is the Sauter mean bubble diameter defined in Chapter 1, Section 1.2.4. 

There are several definitions of respirable dust (Lippmann, 1970). In 1952 the British Medical Research Council (BMRC) defined the respirable fraction in terms of the terminal settling velocity (free-falling speed) by the equation... 

The kinetic energy of the particles is defined by Equation 3.30, where the particle velocity Up is a function of the terminal settling velocity u depending itself on the settling regime, as explained in Section 3.5.5.4. Iterations are, therefore, needed. Assuming applicability of Equation 3.32 to calculate Up it is found that the value of the particle Reynolds number Rep surpasses the limit of 0.4, so a second approach using Equation 3.33 is done, that is. 

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