Question

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

Answer 1

The correct Answers is :0.32 or 0.34 Approx