A toxic liquid stream is flowing via two stirred tanks in series. In each tank, the outlet flow rate from the tank is proportional to tank volume (V_{i} = K_{i}V_{i}), where Vi is the tank volume and Vi is the outlet flow rate from the tank. For tank 1, which consists of a capacity of 15 m^{3}, the constant K_{1}= 0.3. For tank 2, which consists a capacity of 5 m^{3}, the constant K_{2} = 0.67. Initially, the liquid flow into tank 1 is V_{0} = 2.0 m^{3}/min and the system is operating at steady state.
Q1. Find out the quantities of liquid in each tank at this initial steady state. Since of a flow controller failure, the liquid flow rate into tank 1 is suddenly doubled to VN = 4 m^{3}/min. The operator identifies this disturbance exactly 5 minutes after change takes place and returns the inlet flow to tank 1 back to its original flow rate of 2 m^{3}/min.
Q2. Determine the volume of liquid in each tank would have been if the system would have been permitted to reach a new steady state at a flow of V_{n} = 4 m^{3}/min?
Q3. Did the operator identify the process disturbance soon enough to prevent any damage to or danger in the vicinity of method?