Derive and solve a model of an insulated water tank with a changing level (i.e., changing tank volume).

There is only one in ow stream with a flow rate of 1 kg/sec for t < 0 and 0.9 kg/sec for t  0.

The out flow rate depends upon the level, H, within the tank and is given by m_out = k_v √H where k_v = 0:8kg=(m^0:5s). The tank is tted with an electric heater that inputs Q = 100kW (constant), and the cross-sectional area of the tank is 1:1m2. Derive both the mass and energy balances, determine the steady state conditions at t < 0, and determine via numerical simulation the impact of the changing in flow rate at t ≥ 0.