3. The liquid storage tank shown in fig. Q3 receives a volumetric flow rate of qo and supplies two outlet streams. A pump removes liquid from the lower outlet at a constant flow rate of 11 m³/h. For turbulent flow, the flow rate from the upper outlet is given by q₁ = k√Ah, where Ah is the liquid level above the valve. qo(t) h(t) Ah 91(t) 2 m Fig. Q3 92 At steady-state the liquid level is 6 m and the feed flow rate is 15 m³/h. The cross-sectional area of the tank is 4 m². (a) Perform an unsteady state balance and linearise the ODE. Then obtain the transfer function relating the change in the tank level, h(t), to changes in the feed flow rate, qo(t). (b) The feed flow rate suddenly drops to 12 m³/h. Find the new steady-state liquid level and estimate the time required for 50% of this change to occur.