Q$4($a$)$ What are normal and shear stresses? Please give an example for each of them.

$($b$)$ One way of treating occlusion of blood vessels due to blood clots is to introduce

enzymes to assist in the dissolution of the clot Assume that this enzyme$-$catalyzed

reaction is a first$-$order reaction with a reaction constant $k,$ the cylindrical blood vessel

has an original diameter $d,$ and a clot thickness $h.$ The enzyme is injected into the

vessel at a flow rate of $Q$ and a concentration of $c$ by a pressure difference $P.$ The

density and viscosity of blood are $$ and $$ respectively. Use dimensional analysis to

express the dissolution time as a function of the variables in the problem.

$($c$)$ Consider the following enzymatic reactions

$E+2S_{{}_{k_{-1}}}^{longrightarro{w}^{k_1}}E{S}_2{k}_{2}E+P$

i$)$ Derive the enzyme kinetics using the Michaelis$-$Menten approach.

ii$)$ Derive the enzyme kinetics using the Briggs$-$Haldane approach.

iii$)$ Compare and contrast your answers in i$)$ and ii$)$