Diameter worked example

The separation between each particle in gas is immense, and usually thousands of times greater than the diameter of a single gas particle. In fact, more than 99 per cent of a gas s volume is empty space. The simple calculation in Worked Example 1.5 demonstrates this truth. 

Table 9 Worked example El calculation of mean particle diameter...

For a reactor operating with constant output, the criterion for optimal performance is for the cooling medium to have the highest possible temperature in the heat removal system. For a working example of the nonadiabatic reactor, there are 4631 cylindrical tubes with inner diameters of 7 mm packed with a catalyst and surrounded by a constantly boiling liquid at 703 K. Sulfur dioxide and air are fed into the reactor at a total pressure PT, in volume fractions of > s,, 2 =0.11 and >v,2 =0.10. The empirical expression oftakes into account diffusion and reaction kinetics, and we have... 

Worked example 5.1 — soil water and air contents, and bulk density A soil core of 5 cm diameter and 8 cm height contains 257 g of fresh soil. After drying the soil at 110°C, the soil weighed 196 g. Calculate (i) the gravimetric soil water content, (ii) the volumetric soil water content, (iii) the soil bulk density, (iv) the % pore space, (v) the % water-filled pore space, and (vi) the % air-filled pore space. 

Problem 3.4(b) (Worked Example) Suppose you now mold a 1-cm-diameter spherical ball of 1,4-polyisoprene and place it on a flat surface at 25 °C and find that the time for it to sag to 90% of its original height is 10 minutes. Now you place the polyisoprene in a rheometer at 25°C to measure its viscosity, but the viscosity is too high to measure accurately, so you raise the temperature to lOO C and measure a zero-shear viscosity of 10 P. Use this information and that in Problem 3.4(a) to determine the viscosity of the gel in Problem 3.4(a), given that the gel density is = 3g/cm ... 

Problem 6.1 (Worked Example) Estimate the zero-shear viscosity of a suspension of hard spheres 100 nm in diameter at a volume fraction of [Pg.318]

Problem 6.8 (Worked Example) Estimate the steady-state uniaxial viscosity of a suspension of 0.1% by volume of rod-like particles L = 6 yum long and d = 10 nm in diameter in a Newtonian oil of viscosity 100 P at an extension rate of 1 sec . ... 

Problem 6.9 (Worked Example) You need to know if silica particles 20 pm in diameter with density 2 g/cm are likely to settle in an aqueous dispersion containing 10 M NaCl and 10% by volume of small, well-dispersed, 200-um-diametcr polystyrene spheres, each with a charge-... 

Cascading Rotary Dryers In design mode, the required gas flow rate can be obtained from a heat and mass balance. Bed cross-sectional area is found from the scoping design calculation (a typical gas velocity is 3 m/s for cocurrent and 2 m/s for countercurrent units). Length is normally between 5 and 10 times drum diameter (an L/D value of 8 can be used for initial estimation) or can be calculated by using an incremental model (see worked example). 

Figure 3 illustrates that the polymerization rate is independent of resin diameter. During 30 min reactions, CALB immobilized on resins 1 to 4 gives turnover frequency (TOF) of e-CL of about 12 s" In contrast, our previous work of CALB immobilized on PMMA resins showed a large dependence of e-CL %-conversion on resin particle diameter. For example, in 30 minutes reaction time, as the particle size decreased from 560-710, 120, 75 and 35 pm, turnover frequency (TOF) of e-CL increased from 3.8 to 5.3, 7.5 and 11.2, respectively. However, by increasing the resin pore size from 300 (resin 4) to 1000 A (resin 5) for 35 pm beads, the TOF reached 28.2 s. As discussed above, increase in resin pore diameter also corresponds to an increase in %-area of beads at which CALB is found (37 to 88%). 

In this method, the pressure gradient across a packed bed of known voidage is measured as a function of flow rate. The diameter we calculate from the Carman-Kozeny equation is the arithmetic mean of the surface distribution (see Worked Example 6.1 in Chapter 6). 

The use of explosives in metalworking was initially employed in 1880 to make spittoons. Today, the missile and rocket industry use explosives to shape bulkheads, nosecones, and even large rocket sections. A small 50-g charge can do the work of a 1,000-t press shaping a thick metal plate 2-3 m in diameter. An example of a metal forming system is shown in Fig. 14.2. The dye is usually cheap material of concrete or plaster which can be evacuated. The sheet metal is held in place by a bed of water in which the explosive charge is detonated. The pressure and shock wave forces the metal into the evacuated mold in microseconds. 

Example 8.1.4 Sherwood and Holloway (1940) determined the mass-transfer behavior in O2 desorption from water from a series of Raschig rings of sizes 0.5", 1.0", 1.5" and 2" in a column of diameter 20" at 25 °C. Sherwood et al. (1975), have considered a particular example from this study for 2" Raschig rings, wherein, at superficial liquid and gas velocities of = 0.542 cm/s, (vi ) = 26.3 cm/s and a packed height of 15.5 cm, the values of Hocp and Notp were found to be 29.26 cm and 0.529, respectively. We employ this worked example from Sherwood et al. (1975) to illustrate the application of the axial dispersion analysis just provided. Determine the true values of Hd and Not for this case, given the Henry s law constant for O2 and water at 20 °C and 30 °C to be 4.01 X 10 and 4.75 x lO atm/mole fraction, respectively. You are given that (A.eft.r) = 0.0148 ft Vs. 

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