$(10pts)$ A coolant $($specific gravity $=1\mathrm{.}2)$ is pumped through a heat

exchanger and control valve at a nominal $($desired$)$ flow rate of $q_d=0\mathrm{.}6$

$\frac{m^3}{m}in.$ The total pressure drop over this heat exchanger system

$($including piping and fittings$)$ is constant at $450$ kPa $.$ The pressure drop

over the system without the control valve, $P_s,$ is proportional to the

flow rate squared. Its nominal value at the desired flow rate is $P_{sd}=$

$200$ kPa $.$ The control valve is to be designed so that the nominal flow

rate is $\frac{2}{3}$ of the maximum flow rate when the valve is completely open.

Based on this information, what value of the valve coefficient $C_v$ should

be specified?