In a tangential flow ultrafiltration unit, a protein of MW = 3 x 10⁵ Da is separated from the fermentation broth by a single tube filtration unit. The tube has a diameter d = 2 cm and a length L = 50 cm. The low rate of the system is Q = 2 L/min. The flow regime is turbulent, f=0.0005, and C4 = 2 [atm*s²/cm²]. The inlet pressure is P_I = 2 atm. The pressure gauge at the permeate outlet (P_f) is 1 atm . Protein concentrations in the solution and in the gel film are C_B = 30 mg/l and C_G = 100 g/l, respectively.

1. Determine the exit pressure (P₀).
2. Determine the transmembrane pressure drop (P_m).
3. If the mass transfer coefficient (k) for protein flux is k = 5 cm/s, determine the flux of liquid through the membrane (J).
4. If the resistance of the filter is R_M = 0.002 atm.cm²s/cm³, determine the cake resistance, R_G.