A fluid enters a piping system with a specific enthalpy of $12\frac{J}{k}g$ and a volumetric flowrate of $12\mathrm{.}2\frac{m^3}{s}$ before reporting to a heat exchanger wherein it gives off $36\frac{J}{k}g$ of heat to a cold stream that flows counter currently to it$.$ After leaving the heat exchanger it is then compressed by a compressor which imparts $47\frac{J}{k}g$ of compression work on the stream before it rises $15m$ and then drops another $8\mathrm{.}3m$ and leaves the system with a specific enthalpy of $8\mathrm{.}31\frac{J}{k}g.$ The fluid leaves the system at $6\frac{m}{s}.$

$1\mathrm{.}1$ Determine the diameter of the pipe.

$1\mathrm{.}2$ What is the diameter of the pipe if the stream remains level after leaving the compressor?

$[20$ Marks$]$