For the handling of a very toxic liquid in a tank with a diameter of 5 and height range of 0 to 10ft, it is desired to install a level sensor which is non-contact. A radar gauge is recommended. The level indicator is to be integrated into a control loop which includes a flow rate manipulator (valve) for the exit stream to keep the level constant. The system has to be accurate for level control within one inch. Develop a mathematical model of the process. Propose a control scheme and include all peripherals.