Consider a capillary completely filled with red blood cells $($RBCs$)$ as shown in the figure below. We wish to derive an expression for the effective viscosity $({}_{\text{e}\text{f}\text{f}})$ of the RBC suspension passing through this capillary compared with that of plasma $($of viscosity ${}_p)$ along passing through this capillary. You may assume that the small amount of fluid between two adjacent RBCs moves at the same velocity as that of the RBCs$.$

$($a$)$ Let the velocity of each RBC be given a $v,$ and let the average pressure gradient $(d\frac{P}{d}x$ driving the flow be $G.$ Can you find the velocity profile of the fluid in the gap $v2h$

$(b)$ Next $do$ a force balance $on$ the column $ofRBCs$ and find the velocity $vas$ a function $ofG.$

$In$ fact, after the derivation $of(a)$ and $(b),$ the relationship $of$ effective viscosity $of$ the $RBC$ and that $of$ the plasma could $be$ established afterwards given the condition $ofRBCs$ moves $at$ the same velocity $as$ that $of$ the fluid between the gap $of$ the $RBC$ and the capillary wall. $No$ derivation $is$ needed $at$ this question.