QUESTION 1: Non-linear equations (15 MARKS] The Ergun equation shown below is used to describe the flow of a fluid through a packed bed. AP is the pressure drop, p is the density of the fluid, G, is the mass velocity (mass flowrate per cross-sectional area), D.is the diameter of the particles within the bed, is the fluid viscosity, L is the length of the bed, and is the void fraction of the bed. APP D, E? 1-E = 150 GT1- + 1.75 (D, G,/u) Given the parameter values below, use the appropriate numerical method to find the void fraction of the bed. D G = 1000 PD, GL 10 QUESTION 2: Interpolation (15 MARKS] The following data define the sea-level concentration of dissolved oxygen for fresh water as a function of temperature: TC 16 32 0 8 o, mg/1 14.621 11.834 24 8.418 40 6.413 9.870 7.305 Estimate 0(31) using Newton's interpolation polynomial. QUESTION 3: Interpolation (15 MARKS] The following data come from a table that was measured with high precision. Use the best numerical method to determine y at x=3.5 and x=14.2. Your solution should prove that your result is exact. X 0 6 9.2 12 1.8 5 16.415 5.375 8.2 2.015 Y 26 3.5 2.54 8 00