Problem Set 1  H  Rutgers University BME 14:125:201

PROBLEM SET 1
SOLUTIONS
Problem 1:
You need to prepare blood for a transfusion. You have the following three processed blood packs available:
Pack A – Enriched in red blood cells (RBCs)
Contents: 2.5 wt% white blood cells (WBCs); 50.0 wt% isotonic fluid; the rest is RBCs.
Pack B – Enriched in serum proteins
Contents: 50.0 wt% serum proteins; 1.0 wt% WBCs; 18.0 wt% isotonic fluid; the rest is RBCs
Pack C – Isotonic fluid
Contents: 100.0 wt% isotonic fluid
All three packs must be mixed in the correct proportions to generate blood for a transfusion pack. The transfusion pack
needs to have the following composition: 2.0 wt% WBCs and 12.6 wt% serum proteins. How much of each processed
blood pack do you need to mix to get 100 g of reconstituted blood for a transfusion pack?
Problem 2:
Within the bloodstream, the concentration of a metabolite is 100
parts per million (1mg/kg = 1 part per million = 1 ppm). Assume
that 1000 mg of metabolite is to be used as a tracer; it is injected
over 5 min and the downstream concentration is measured to be
4000 ppm. What is the mass flow rate of blood in the vessel,
assuming good mixing occurs? Estimate the volumetric flow rate
of blood based on the answer.
Problem 3:
You have designed a centrifuge system to separate
cells from a solution. A mixture of water and cells
enters the centrifuge system at a rate 1000 L/h and
contains 500 mg cells/L. You can assume that the
density is that of water (1 g/cm3). The inlet stream or
feed (F), is separated to a cell-free supernatant (S),
and a pellet (P) consisting of a solution containing
water and cells. The mass fraction of cells in the pellet
is 0.75. Using the data in the figure, calculate the mass
flow rates mP (g/hr) and mS (g/hr).