A ventricular assist device $($VAD$)$ is an implantable electrically powered pump which can enhance the pumping capacity of the heart. Blood enters the VAD at $105$ kPa and $37\mathrm{.}0$C through a duct of diameter $7\mathrm{.}0$ mm$.$ It exits at $121$ kPa and $37\mathrm{.}1$C through a duct of diameter $9\mathrm{.}5$ mm$.$ The device operates in steady state and the flow rate is $0\mathrm{.}03$ kg$/$s$.$ In normal operation, the outlet of the device is located $20$ mm lower than the inlet. Heat transfer through the walls of the device is negligible. For the purposes of this question, assume that blood has the same thermophysical properties as water. $($a$)$ Calculate the speed of blood flow at the inlet and outlet. $[4]($b$)$ Determine the rise in enthalpy of the blood from the inlet to the outlet. $[5]($c$)$ Calculate the power required by the device. $[11]($d$)$ What fraction of the input power is converted into each of the following forms: $$ Heat $$ internal energy $$ enthalpy $$ gravitational potential energy $$ kinetic energy