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+clear;

+clc;

+

+// Illustration 9.13

+// Page: 548

+

+printf('Illustration 9.13 -  Page: 548\n\n');

+

+// solution

+//*****Data*****//

+// w-water a-proteins

+T = 293; // [K]

+d = 2; // [diameter of tube, cm]

+dw = 1; // [g/cubic cm]

+uw = 0.01; // [cP]

+Da = 4*10^-7; // [Diffusivity of proteins, square cm/s]

+vo = 1.5*100; // [m/s]

+Qm = 250*10^-3/3600*100; // [water permeance, cm/s.atm]

+cR = 40; // [g/L]

+

+printf('Illustration 9.13(a) -  Page: 549\n\n');

+// Solution(a)

+

+v = 25*10^-3/3600*100; // [cm/s]

+

+Re = d*vo*dw/uw; // [Renoylds number]

+Sc = uw/(dw*Da); // [Schmidt number]

+Sh = 0.0048*Re^0.913*Sc^0.346; // [Sherwood number]

+ks = Sh*Da/d;

+// From equation 9.87

+cS = cR*exp(v/ks); // [g/L]

+

+// From figure 9.12

+pi1 = 2; // [osmotic pressure, atm]

+// For 100% rejection deltapi = pi1 because pi2 = 0

+// Therefore

+deltapi = pi1; // [atm]

+// From equation 9.83

+deltaP = deltapi+(v/Qm);

+printf("The required pressure differential to produce a water transmembrane volume flux of 25 L/square m.h when the membrane is clean is %f atm.\n\n",deltaP);

+

+

+printf('Illustration 9.13(b) -  Page: 549\n\n');

+// Solution(b)

+

+// Membrane permeance is reduced fivefold by fouling

+Qm = Qm/5; // [cm/s.atm]

+// Here deltaP remains same

+// Equations 9.83 and 9.87, and the osmotic pressure data of Figure 9.12 must be solved simultaneously by trial and error to calculate new values for these three variables.

+// The results are

+cS2 = 213; // [g/L]

+deltapi2 = 1.63; // [atm]

+v2 = 6.53*10^-4; // [cm/s]

+printf("The water flux if the applied pressure differential remains the same as calculated in part (a) is %f L/square m.hr.",v2*1000*10^-2*3600);