A polymeric fluid $($rho$=1000[($kg$)//$m$^(3)],$mu$=100[$cP$])$ is flowing through a vertically oriented cylindrical pipe with diameter D$=0\mathrm{.}1[$m$].($a$)$ Derive the analytical formula for the average potential energy delivered through the pipe per unit length of pipe and calculate the numerical value in units of $[$J$//$kg$]($b$)$ Now the fluid flow is in steady state and gives the loss coefficient K$\_($L$)=6\mathrm{.}4$ per unit length of pipe. What is the mean fluid velocity and the frictional loss per unit length? Derive the analytical formula and calculate the numerical values $($velocity $=[$m$//$s$],$ frictional loss $=[$J$//$kg$])$