If we have $8000ft$ of $4\mathrm{.}26$ ID drillpipe and $200ft$ of $83$ collars, how many strokes does it take to move new mud to the bottom of the drillpipe?

Say the well diameter is $12$ inches, and the mud is $10$ ppg$.$ If we mix new mud at $10\mathrm{.}5$ ppg and pump in $100$ strokes,

a$.$ Where is the interface between the old and new mud? $($annulus$?$ Pipe? Exactly what depth..$)$

b$.$ What is the pressure at the bottom of the well now?

c$.$ What was it before we pumped in the new mud?