process control

Question 1 Use Taylor method to linearize the following equations: 1.1. cos(x) expand to the third derivative (5) 1.2. f(x)=2x43x3+4x230x when x3, expand to the first derivative (15) [20 marks] Question 2 In late 2017, the Western Cape experienced severe water shortage; in this era there were plans for "Day Zero", a phrase that simply references "the day when the water level of the major dams supplying the city could fell below 13.5 percent". As a preventative measure Rand Water has employed you as lead process designer in the department of Water Conservation and Management, your first task as process designer is find ways to prevent "Day Zero" at in Gauteng. Your first task is to design a surge drum below: 2.1. On the diagram, draw the necessary controller to regulate the discharge and sensors to determine the system need to release the stored water in the drum. Use the correct symbols and give the correct name for the symbols. (10) 2.2. Derive an unsteady-state model relating the liquid level h to the input flow rate wi,w0(kg/h) and (kg/m3); where wi=a+bsin(ct) and at t=0, the amount of water in the drum is constant, therefore h(0)=h0 - (20)