Modeling the Liquid Height and Temperature in a Well-Mixed, Heated Tank in Python 

[che-4071-hw-1]
Part C:
A heated tank with cross-sectional area of 1 m2 drains through a hole at the bottom of area 0.05 m2. The system has been operating at steady steady with a water flowing in at 1 m3/s at 350 K with an applied heating power of 20 MW.
1. Derive the differential equations, then isolate the derivative terms to enable numerical solution via scipy.integrate.solve_ivp.
2. Derive expressions for the initial steady state height and temperature of the water in the tank.
3. At t=0, the inlet temperature drops to 340 K, and the heating power (Q) and inlet flow (qin) begin oscillating: Q=20e6 + 10e6 * sin(t/20) and qin=1 + 0.1*sin(t/100) for t in seconds. Calculate and plot the temperature and height of the water in tank from 0 to 2000 seconds.