b$)$ Two concentric hollow cylinder cores made of different materials have identical thickness, which is also equal to the central bore diameter. The specimens are used for single$-$phase $($crude oil$)$ flow experiments. For items $($ii$)-($iv$),$ justify any assumptions and explain your derivations.

$($i$)$ Draw an annotated diagram t$.$ show all system elements and data.

$($ii$)$ Derive the pressure at the interface of the two hollow cylinders as a function of known quantities; define all symbols used and S$.$I. units.

$($iii$)$ Derive an expression for the inward volumetric flow of liquid $($oil$)$ in the simplest form possible; explain briefly all steps followed therein.

$($iv$)$ If the two materials have very different permeabilities, how can we determine which possible core arrangement yields the highest inward volumetric flow? State and discuss the relevant equations.

$(4)$