where: k is consistence coefficient r is pipe radius l is pipe length s is radial position measure from centre of the pipe $$P is pressure drop. $3$ P $134$ s $43$ ux $42$kl$$ r$31$r$($i$)$ Using the above equation write down the equation for centre line velocity in terms of rheological parameters of the fluid and dimensions of the pipe. $[3$ MARKS$]($ii$)$ Derive an equation for volumetric flow rate of the fluid. $[6$ MARKS$]($iii$)$ Write down the equation relating the mean velocity of flow to centreline velocity. $[6$ MARKS$]$