Problem 5. Material Balance (50 points) An artificial kidney is a device that removes water and waste metabolites from blood. In one such device, the hollow fiber hemodialyzer, blood flows from an artery through the insides of a bundle of hollow cellulose acetate fibers, and dialyzing fluid, which consists of water and various dissolved salts, flows on the outside of the fibers. Water and waste metabolites-principally urea, creatinine, uric acid, and phosphate ions-pass through the fiber walls into the dialyzing fluid, and the purified blood is returned to a vein. A patient is undergoing dialysis, with the dialyzing fluid mass flow rate set to 4 times that of the entering arterial blood. At steady-state, the arterial and venous blood conditions are as follows: Arterial (enterino) Rlond Venous (exitino) Rland Flow Urea (H2NCONH2) Concentr: For this problem, assume that arterial blood, venous blood, dialyzing fluid, and dialysate contain only urea and water. Also assume that the densities of these streams are equal to that of water (1kg/L). a) Draw a labeled flowchart with the flow rates in g/min and the compositions in mass fraction. (Hint: Do you need to draw the internal details of the artificial kidney for the flowchart?) b) Based on the flowchart you made in (a), write Material Balance equations for total mass, urea, and water. c) Using the mass balance equations, determine the mass fraction of urea in the dialysate. What is its concentration in mg/mL ? (Ans: 0.048mg urea /mL ) e) Consider a particular patient whose arterial blood entering the dialysis machine has an initial urea level of 2.7mg urea /mL. We would like to decrease the patient's blood urea to 1.1mg/mL when it leaves the dialysis machine. If the total blood volume is 5.0 liters and the average rate of urea removal is that calculated in Part (d), how long must the patient be dialyzed, in hours? (Neglect the loss in total blood volume due to the removal of water in the dialyzer.) (Ans: 3.4h )