Q$2.$ Capillary viscometer $($re$-$exam $2022)$

A capillary viscometer with a radius $R$ of $472m$ and a length $L$ of $5cm$ of has been used to

measure the whole blood viscosity at $25\mathrm{.}5C.$ The figure indicates the flow rate $Q$ as a function of

the pressure gradient $\frac{P}{L}$ for a Hematocrit value of $0\mathrm{.}355.$

$4p$ a$)$ Determine the viscosity $$ in $cP$ and wall shearing

rate ${}_w^{}$ in $\frac{1}{s}$ for the measurements with the

lowest and highest flowrate. Note that ${}_w^{}$ can be

estimated using ${}_w^{}=\frac{4V_{\text{a}\text{v}\text{g}}}{R}$

$[1$p$]$ b$)$ Indicate whether the fluid is Newtonian or Non$-$

Newtonian and if it's viscosity is within normal

range for blood.

$[2$p$]$ c$)$ Estimate the force required to overcome the

yield shear stress, thereby initiating the flow.

$[3$p$]$ d$)$ Determine the pressure gradient in $\frac{mm{H}_{2}O}{cm}$ if the

Hematocrit value of blood would be $0\mathrm{.}400.$

Consider this for the measurement at the highest

flowrate.

If you did not find an answer for the viscosity at

the highest flowrate at a$),$ assume a viscosity of

$3\mathrm{.}3cP$ at a Hematocrit value of $0\mathrm{.}355.$