Blood enters a hollow fiber unit hemodialysis that is used a

Blood enters a hollow fiber unit (hemodialysis) that is used as an artificial kidney. Theunit consists of 10,000 hollow fibers arranged in a shell and tube configuration. Blood flows from an artery in the patient’s arm through a tube and is uniformly distributed to the fibers via an arterial head space region at the entrance of the unit. The blood then leaves each fiber through the venous head space region of the unit and is returned to a vein in the patient’s arm. Each hollow fiber has an inside diameter of 220 m and a length of 25 cm. The fiber void volume with the shell of the unit is 50%. Assuming the maximum available pressure drop across the hollow fiber unit is 90 mmHg, estimate the total flow rate of blood through the hollow fiber unit.

Solution

Based on the information provided form the question , the total blood flow rate across the tube is caluculated.

1. Assuming the blood pressure across the fiber to be 90mm/hg

2. viscosity of the blood to be in general 40/100 =0.4 ,length =25cm

3. Assuming the radius =3.14*10^-7

so the Flow rate Q = delta pressure * pi *[radius]⁴

8*L* viscosity .

90*3.14 * {3.41*10^-7   = 90*3.14 *135.21/ 80 = 479.1 cubic meter/hr

8*25*0.4