2.28. WP The following empirical equation correlates the values of variables in a system in which solid particles are suspended in a flowing gas: k,d,y 1/3 d,ир 1/2 2.00 + 0.600 D Both (u/pD) and (d,up/µ) are dimensionless groups; k, is a coefficient that expresses the rate at which a particular species transfers from the gas to the solid particles; and the coefficients 2.00 and o.600 are dimensionless constants obtained by fitting experimental data covering a wide range of values of the equation variables. The value of k, is needed to design a catalytic reactor. Since this coefficient is difficult to determine directly, values of the other variables are measured or estimated and k, is calculated from the given correlation. The variable values are as follows: d, 5.00 mm 0.100 (dimensionless) D 0.100 cm² /s 1.00 × 10-5 N ·s/m2 -3 3 1.00 x 10¬° g/cm' 10.0 m/s и a. What is the estimated value of k,? (Give its value and units.) Answer b. Why might the true value of k, in the reactor be significantly different from the value estimated in Part (a)? (Give several possible reasons.) c. Create a spreadsheet in which up to five sets of values of the given variables (d, through u) are entered in columns and the corresponding values of k, are calculated. Test your program using the following variable sets: (i) the values given above; (ii) as above, only double the particle diameter d, (making it 10.00 mm); (iii) as above, only double the diffusivity D; (iv) as above, only double the viscosity u; (v) as above, only double the velocity u. Report all five calculated values of k. 2.29. WP A seed crystal of diameter D (mm) is placed in a solution of dissolved salt, and new crystals are observed to nucleate (form) at a constant rate r (crystals/min). Experiments with seed crystals of different sizes show that the rate of nucleation varies with the seed crystal diameter as r(crystals/min) 200D – 10D² (Din mm) a. What are the units of the constants 200 and 10? (Assume the given equation is valid and therefore dimensionally homogeneous.) b. Calculate the crystal nucleation rate in crystals/s corresponding to a crystal diameter of o.050 inch. c. Derive a formula for r(crystals/s) in terms of D(inches). (See Example 2.6-1.) Check the formula using the result of Part (b).