$4-8.$ For a PWR with roughly cylindrical shape $(3\mathrm{.}8-$m diameter x $4\mathrm{.}1-$m height$)$:

a$.$ Calculate the geometric buckling neglecting extrapolation distance.

b$.$ Calculate k$\backslash$infty for a critical system where the migration area is $60$ cm$2.$

c$.$ Recalculate $($a$)$ and $($b$)$ assuming $\backslash$delta $+\backslash$delta t $=7\mathrm{.}5$ cm

$4-9$ A very large homogeneous reactor is to be built using a solution of $235$U$-$salt and water. Based on the following thermal parameters:

$\backslash$sigma f$25=585$ barns n$25=1021$ at$/$cm$3$

$\backslash$sigma c$25=99$ barns nsalt$=4$x$1021$ at$/$cm$3$

$\backslash$sigma csalt $=25$ barns

u $=2\mathrm{.}5$

$\backslash$sigma cH$2$O $=0$ barns

and using a four$-$factor$-$formula model with $=1\mathrm{.}03$

a$.$ Calculate $\backslash$eta and f$.$

b$.$ Estimate the value of p required for criticality.