A dialysis unit is being designed. It will consist of a large number of small hollow fibers arranged in parallel. Blood will flow inside the fibers, each of which is 30 cm long. It is desired that the hold-up volume (the volume of blood needed to fill all the fibers) should be no more than 80 ml, and that the total pressure drop across the fibers should be no more than 105 dyne/cm2 at a total flow rate of 50 ml/s. If the blood viscosity is 3.5 cP and the density of the blood is 1.05 g/cm3, how many fibers should be used, and of what diameter should they be, so as to meet the design conditions