2 . Qin, m/s Surface area A, m? Thir metres Qout, m/s Consider an open-topped spherical tank through which water flows. Denote the radius of this tank by R (in metres), and let the liquid level h be relative to the level of the base of the tank as shown above. (a) Show (using Pythagoras) that the surface area A is given by: A = r.{R2 - (R-1)} and integrate this with respect to h from h = 0, to show that the volume of liquid in a sphere that is partially filled to a level h is V = n. {R.42 - } (b) Write the differential equation for the dynamic volume balance over this tank, and convert this to a differential equation for dh/dt. (c) Linearise the differential equation of the process from (b) around a steady state level of 1 metre, to get a differential equation for doh/dt. Let the radius R be 4 metres