1. A processing company recently just installed a surge tank (as shown in Figure 1) to smooth out flow to downstream processes that are caused by the fluctuations in flow from upstream processes. Qi(t), h(t), Q(t) refer to the inlet flow, tank level and outlet flow, respectively. Qi(t) h(t) Tank 1 Q(t) Figure 1: Liquid Surge Tank = The control objective for the tank is to ensure that the level is within a safe range and to prevent it from over flowing by restricting the incoming flow. a. Assuming Q(t) = 0.0433/ h(t) (:), A = 5000(cm), p= , 5000(cm), p = 1000(k), where A, p are the $ cross-sectional area of tank and density of liquid, respectively. Develop the model that can help to achieve the objective. b. At steady-state, Qi(t) = 0.05m/s. Determine the corresponding liquid level at steady-state. s