Particle terminal velocity Reynolds number

JVRet particle terminal velocity Reynolds number, Eq. (15-39), [—]... 

A. Solid particles suspended in agitated vessel containing vertical baffles, continuous phase coefficient A = 2 + 0.6N tNS Replace vz [p with uT = terminal velocity. Calculate Stokes law terminal velocity c d lp,-pjg K 18 ic and correct 1 10 100 1,000 10,000 100,000 [S] Use log mean concentration difference. Modified Frossling equation = Vn "P ° Re (Reynolds number based on Stokes law.) V -vTdrP° A Re,r — (terminal velocity Reynolds number.) kl almost independent of dp. Harriott suggests different correction procedures. Range ki/k is 1.5 to 8.0. [74] [ 138] p. 220-222 [110] [74]... 

A wide range of particle terminal velocities for various Reynolds numbers have been investigated by Kunii and Levenspiel.43 They suggested that if the particles were assumed to be spherical and operated at low particle Reynolds number (Rep < 0.4), the Stokes equation was found to be acceptable (see Figure 17.4). Therefore, the terminal velocity Ut can be expressed as ... 

Solution The particle terminal velocity Upt and the particle Reynolds number Rep are obtained from Eq. (1.7) and Eq. (1.5), respectively, as... 

For plastic beads with pp = 500 kg/m3 falling in air at ambient conditions, estimate the range of variation of the shedding frequency of the particle wake when the particle Reynolds number, based on the particle terminal velocity, varies from 500 to 1,000. For this particle Reynolds number range, what is the corresponding range of variation for the particle sizes ... 

V,s = settling velocity for hindered uniform spherical particle, ft/s or m/s (terminal) c = volume fraction solids K = constant given by equation above Nrc = Reynolds number, Dp V,pf/ j. 

This expression for the terminal velocity (i.e., the constant velocity that the particle ultimately attains), is called Stokes law. When the Reynolds number is high, say usually greater than of the order of 800, the flow becomes turbulent flow and eddies form. It was Newton... 

Reynolds number based on the terminal velocity of the solid particles, dpUtpf//i... 

A spherical glass particle is allowed to settle freely in water. If the particle starts initially from rest and if the value of the Reynolds number with respect to the particle is 0.1 when it has attained its terminal falling velocity, calculate ... 

Consider two spherical particles 1 and 2 of the same diameter but of different densities settling freely in a fluid of density p in the streamline Reynolds number range Rep< 0.2. The ratio of the terminal settling velocities un/ut2 is given by equation 9.8 rewritten in the form... 

Experimental results generally confirm the validity of equation 5.80 over these ranges, with n 4.8 at low Reynolds numbers and 2.4 at high values. Equation 5.78 is to be preferred to equation 5.79 as the Galileo number can be calculated directly from the properties of the particles and of the fluid, whereas equation 5.79 necessitates the calculation of the terminal falling velocity u0. 

In Chapter 3, relations are given that permit the calculation of Re 0(uodp/p), the particle Reynolds number for a sphere at its terminal falling velocity n0, also as a function of Galileo number. Thus, it is possible to express Re mp in terms of Re 0 and u ,f in terms Of Uq. 

Previous correlations of the influence of z on terminal velocities (El, H4, Ml, SI, S6, T3, Ul) are limited to specific systems, fail to recognize the different regimes of fluid particles (see Chapter 2), or are difficult to apply. In the present section we consider both bubbles and drops, but confine our attention to those of intermediate size (see Chapter 7) where Eo < 40 and Re > 1. Only the data of Uno and Kintner (Ul), Strom and Kintner (S6) and Salami et ai (SI) are used since other workers either failed to use a range of column sizes for the same fluid-fluid systems, or it was impossible to obtain accurate values of the original data. This effectively limits the Reynolds number range to Re > 10 for the low M systems studied. 

The approach of representing the fluid and particle motion by their component frequencies is only valid if drag is a linear function of relative velocity and acceleration, i.e., if the particle Reynolds number is low. This is the reason for the restriction on small particles noted earlier. The terminal velocity of the particle relative to the fluid is superimposed on the turbulent fluctuations and is unaffected by turbulence if Re is low (see Chapter 11). 

Here is a function of Re, analogous to used for steady motion in Chapter 5, and may be evaluated using the correlations in Table 5.2. Since = 24Rexs for a spherical particle at its terminal velocity, Re s fixes the terminal Reynolds number Re via the correlations in Table 5.3. The relationship between Rex and Re s is shown by the uppermost curve in Fig. 11.11. In view of the complex dependence of A and Ah on Re and Re, Eq. (11-33) must be... 

Here, the particle Reynolds number is based on the slip velocity. If terminal velocity is used, then the above correlation gives the minimum value for the mass transfer coefficient. Minimum mass transfer coefficients further depend on the density difference between solid particles and solvent. For the typical case of water, the approximate values presented in Table 3.7 can be used (Harriot, 1962). 

Then, the actual mass transfer coefficients, which cover a hundred-fold range, are about 1.5 -8 times that predicted from the correlations for fixed particles if the terminal velocity is used to calculate the particle Reynolds number. McCabe gives the narrower range of 1.5 -5, for a wide range of particle sizes and agitation conditions (McCabe et. al., 1993). Using these values and Table 3.7, we can calculate the ranges of the actual mass transfer coefficients. 

Viscosity affects the various mechanisms of separation in accordance with the appropriate settling law. Tor instance, viscosity has no effect on terminal velocities in the range where Newton s law applies except as it affects the Reynolds Number which determines which settling law applies. Viscosity does affect the terminal velocity in both the Intermediate law range and Stokes law range as well as help determine the Reynolds Number. As the pressure increases or the temperature decreases the viscosity of the gas increases. Viscosity becomes a large factor in very small particle separation (Intermediate and Stokes law range). 

RS Particle Reynolds number at terminal falling velocity — —... 

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