Consider the hydraulic system in fig. 3. Develop a model for this system that can be used to find H1 and H2 as functions of time for any given variations in inputs. cylinder with a cross section A F1 = KVH1 H1 F2 = K2VH2 %3D r-H sphere with radius r HP H2 F2 Fig.3 Note that the cross section of the spherical tank varies with the level of its liquid, that is, its hydraulic capacitance is not constant. Flow U is the input to the system. Obtain the nonlinear equations that describe the behaviour of the system.