646 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS 10 t NRe i iii i / - I I I I Illl• p• [ I I I Illll I I I I [llll • '•_•J_111ill I I I II1111 '1111 ///Illill I I III1111 l',',', [ [ , ,l[,[I i II [ Illl':[l, I]ll ] I I II1[[ ! I I I II[1 IlIl I --I-- I I II111 I I I IIIl[ I1[I I I I I I[[11 I IIIII I 111] I [ I IIIIII I I I III[]1 111I I 11111111 I I IIIt111 •- •olvo for • • 0 3 • 0 4 Figure 7. A factor rs. Reynolds number in the ]aminar ttow region (10 Nae 9, X 10 3) iiiiii iiiiii ' iiiii iiiii Ilii i I i i ii ii i i i El , ,,,,, l Ill,, I I '" ,, ,,, II!t Ill ! I I Ill I I Illl I I Ill I I Ill I III IIIIII I IIIII 11111 III1! IIII IIIIII IIIIII 11ill IIIII IIII IIIIII II1111 11111 IIIII IIII i i i i ii ] I 1 I II I I III iii!11 ........... ii... :::: iii i i iiii iiiii III IIII iii i i ii •11111 ..... III'" Ill -' HI'" lllll - 4- ........ l,ql, III '" "'" PROCEDURE: ,, II IIIIII II IIII II 1-Locate ERe IIII 111111 I III11 IIIII •sR i de fv I/ "B" at intercept 10 3 10 • I 0 • 10" NRe Figure 8. B factor rs. Reynolds number in the turbulent tto•v region (N• 9, X 10 3)

CONTINUOUS MIXING AND PROCESSING 647 Table I Dimensions and Pressure Drop K Factors for the Device of Several Sizes Noln. Pipe Size Housing Outside Dia. Inside Dia. Mod. Length • Schedule Inch (mm) Inch (mln) Feet (m) KoL K'o•, ro T 1/.• 40 0.84 21.34 0.62 15.75 0.51 0.16 6.00 0.075 1 40 1.32 33.53 1.05 26.67 0.90 0.27 5.79 0.069 I 80 1.32 33.53 0.96 24.38 0.85 0.26 5.57 0.062 2 40 2.38 60.45 2.07 52.58 1.71 0.52 5.70 0.068 2 80 2.38 60.45 1.94 49.28 1.67 0.51 5.54 0.062 4 40 4.50 114.30 4.03 102.36 3.37 1.03 5.08 0.058 4 80 4.50 114.30 3.83 97.28 3.18 0.97 5.16 0.060 10 40 10.75 273.05 10.02 254.51 7.79 2.37 5.07 0.060 12 40 12.75 323.85 11.94 303.28 9.66 2.94 4.88 0.056 40.7 36.3 31.4 35.1 31.6 26.9 28.2 27.8 24.8 One module consists of 6 mixer elements. If NRE 10, K = KoL If 10 Nm•: 2000, K = (K'oL X A) + Ko• If NR• 2000, K = Ko•, x B (6) (7) (s) Some values of Kote, K'oL, and Ko•, are listed in Table I and values of A and B are obtained from Figs. 7 and 8. Once the pressure drop is obtained in the device, the required theoretical horsepower can be readily calculated from the equation: Theoretical Hp = 0.262 AP,• ß Q (9) where AP•s•u = pressure drop in the device (psi) Q = volumetric flow rate (fta/sec) The following two examples illustrate respectively the calculation of the pressure drop and the theoretical horsepower required for a laminar and a turbulent flow. Example I-A NewtonJan fluid flows at 500 lb/hr in the Static Mixer unit of g-in. Schedule 40 size. Viscosity of the fluid is 100,000 cp and density is 60 lb/fl a . What is the pressure drop and the theoretical horsepower required in the device 6.84 ft in length which corresponds to 24 mixer elements as recom- mended for mixing viscous fluids? What is the thickness of striation? From Table I we have D = 2.07 in. KoL = 5.70 K'o• = 35.1 Ko•, = 35.1