Problem 11.1. Terminal Settling Velocity

Determine the terminal settling velocity in water at 20°C of two particles both with density 2.0 gm/cc one particle with a radius of 1 pro. and the other with a radius of 0.1 pro. (Note, the viscosity of water at 20°C is 0.01 poise (gm/cm/sec) and its density is 1.0 gm/cc). 

Solution Using the preceding equation for the terminal settling velocity for laminar flow, 

In both cases the Rejmolds number is much less than 1, so that Stokes s law is valid. The difference in settling velocity between 0.1 and 1.0 pm particles is drastic and is the reason for segregation of particles in a ceramic suspensions. By inspection of this equation, differences in the terminal settling velocity can be due to either density or size differences between the two types of spherical particles. The effects of particle shape asymmetry are considered next. 

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To solve this problem, we will use the equations in Table 8.4 to determine the maximum drying time, r, for the various rate determining steps. In these equations the surface temperature of the water is not known. This problem shows a way in which the surface temperature can be determined. Using the terminal settling velocity, V, ... 

The terminal settling velocity of a spherical particle having a diameter of 0.6 mm is 0.11 m/s. Assuming the specific gravity of the particle is 2.65, at what temperature of water was the particle settling Assume the settling is type 1 and use the value of the drag coefficient in Problem 5.7. 

Since the actual terminal settling velocity is assumed to be one-half of the Stokes law velocity (according to the problem statement). 

To calculate the terminal settling velocity of the particle, the K value (see Problem FPD.4) must be used to determine the appropriate range of the fluid-particle dynamic laws. K is obtained from... 

When a suspension is introduced into the inclined lamella settler, the feed suspension may be characterized by means of its solids volume fraction and its particle size density function fjO p)- The corresponding quantities for the overflow and underflow streams are ji,/i(rp) (rp). Often such problems are analyzed instead using the solids volume fraction and the particle settling (terminal) velocity density function /[t/pzt), where the particle settling velocity Upzt in the Stokes law range is related to the particle radius tp by relation (6.3.1) ... 

Determine the size of the smallest sphere of SG = 3 that will settle in applesauce with properties given in Problem 19, assuming that it is best described by the Bingham plastic model [Eq. (11-49)]. Find the terminal velocity of the sphere that has a diameter twice this size. 

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