The purpose of this question is to investigate the implications of Fig. 3.16. Specifically, we wish to determine how the feed reservoir hematocrit changes as a function of time in the experiment shown in Fig. 3.14. Suppose that at time zero the total blood volume in the feed reservoir is V₀, and that the feed reservoir hematocrit is H_F,0. Further, suppose that blood is pumped from the feed reservoir through a capillary at a constant volumetric flow rate Q.

(a) Show that the feed reservoir hematocrit changes with time, t, according to the equation

where H_R is the tube relative hematocrit. Hint: start from the statement

where V_RBC is the volume of red cells in the feed reservoir, and V_p is the volume of plasma in the reservoir.

(b) Integration of the above equation shows that the hematocrit eventually approaches 100% in the feed reservoir. Why does this not occur in the circulatory system: that is, why does the red cell count not increase to something close to 100% at the entrance to the capillaries? You do not need to use any mathematics; a description in words (plus a simple sketch if you prefer) will do the job.
 
 

dHy dr Q Hy Vo - Qr (1-H) (3.54)