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

Correct Answer: 0.32

The correct Answers is :0.32 or 0.34 Approx