A spherical tanik is used for storing the water supply for a local municipality. It is suspended in a supporting structure so it sits high enough off the ground to provide adequate supply pressure. Water is directed to a distribution point on the ground through a vertical drainpipe. The tank has a radius R and the drain plpe is of length L and inner diameter D that is attached to the botlom of the tank. The tank has an air vent at the top and is completely filled at t=0 with a liquid that has density . There is a gate valve connected on the tank botiom that is connected to the drainpipe. When operated, the valve is either fully closed or fully open. When fully open, the pressure drop through the valve is negligble when compared to the hydrostatic head in the tank. (a) Make a diagram of the physical arrangement and add labels that show the problem variables. (b) Derive an equation that shows the instantaneous mass of liquid in the tank at any time t in terms of the tank radius R and instantaneous liquid height h(t) where the height at the zero plane is located at the botlom of the tank. (c) Assuming that the fluid in the drainpipe is described by the HagenPoiseulle equation, derive a differential equation based on a mass balance(s) that shows how dh/dt can be expressed in terms of the tank radius R, the drainpipe length L, the fluld density , the fluid viscosity , the gravitational constant g, and the instantaneous fluid height h(t). (d) Integrate the above equation to obtain an expression for the efflux time in terms of the above variables. (e) Set up an Excel spreadsheet that defines the problem parameters. For simplicity, assume the fluid is water at 25C. Initially, you can assume