1. Consider the process illustrated in this diagram: P1 40 psig (constant) P2 = 0 psig (constant) Heat exchanger Control valve Pump APhe-30 psi at 200 gal/min ??,-10 psi at 200 gal/min The process fluid has a density of ? 9 lbm / gal. Assume that the pressure drop across the heat exchanger Ahe is proportional to the volume flow rate squared, V2, with ? Phe-0 at V-0 and with ? Phe-30 psi at V-200 gal/min. The total difference in pressure between P and P2 is 40 psig, regardless of the flow rate. Consider three different options for the valve (valves 1, 2, and 3). These valves have different designs resulting in different volume Flow rates at the same value of the valve position, L. All three valves are designed so that the ??,-10 psi when the flow rate V-200 gal / min. The designs have the following behavior: gal lbm psig min V 250 where F is as follows ??. o Valve 1: F-L5 o Valve 2: F-L o Valve 3: F-AP ??, L-1 Use MATLAB to plot the flow rate through the system for different values of the valve position (0 the valve designs. L