Question

Consider the surge drum in the figure. Initially the system is at steady-state with a hold-up V̄ $= 5 m³,$ which is 50% of full tank capacity, $V_{full},$ and volumetric flow rates F̄_in = F̄_out $= 1 m³/h.$ The high hold-up alarm limit $V_{high} = 0.8 \times V_{full}$ while the low hold-up alarm limit $V_{low} = 0.2 \times V_{full}.$ A proportional (P-only) controller manipulates the outflow to regulate the hold-up V as $F_{out} = K_{c}(V−V̄) +$ F̄_out. At t=0, $F_{in}$ increases as a step from $1 m³/h$ to $2 m³/h.$ Assume linear control valves and instantaneous valve dynamics. Let $K_{c,min}$ be the minimum controller gain that ensures V never exceeds $V_{high}.$ The value of $K_{c,min},$ in $h⁻¹,$ rounded off to 2 decimal places, is _________

Official answer: 0.32 to 0.34