2. Liquid flow out of a spherical tank discharging through a valve can be described approximately by the following nonlinear differential equation: dtdh=(Dh)h1(qiCvh) where h is the liquid level, D is the diameter of the tank, qi is the volumetric flow rate of liquid into the tank, and Cv is a constant. (a) Derive a linearized model (in deviation variables). (15%) (b) Develop a transfer function relating the liquid level to the volumetric flow rate of liquid into the tank. Give the final expression in terms of the standard form of the first-order transfer function. (10\%)