Manufacturers of cooling towers often present catalog data showing the outlet temperature as a function of...

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Manufacturers of cooling towers often present catalog data showing the outlet temperature as a function of the wet-bulb temperature (WBT) of the ambient air and the range. The range is the difference between the inlet and outlet temperatures of the cooling water. The objective is to express the outlet-water temperature t as a function of the WBT and the range R using Lagrange interpolation method, which can be extended to a function of two independent variables. For example, if z = f(x,y), the form can be chosen as z = - C11(x-x2) (x x3) (y - y2) (y - y3) + C12 (x x2) (x x3) (y y) (y - Y3) + C13 (x x2) (x x3) (y y) (y - y2) + C21 (x x1) (x x3) (y y2) (y - y3) + C22 (x x1) (x x3) (y y) (y - y3) + C23 (x x1) (x x3) (y y) (y - y2) +C31(x x1) (x x2) (y y2) (y Y3) + C32 (x x1) (x x2) (y y) (y - y3) - - - - + C33 (x x1) (x x2) (y y) (y - y2) Note: to represent the data in the Table below, z = the outlet-water temperature t; x = WBT, and y = R (Range). Air Wet-bulb temperature, C c11 c12 c13 c21 c22 c23 c31 c32 c33 Range, C 20 23 26 262 10 25.9 27.5 29.4 16 27.0 28.4 30.2 28.4 29.6 31.3 Determine the values of c11, c12, c13, c21, c22, c23, c31, c32, and c33. Determine the outlet-water temperature t C when WBT = 24 C and Range = 20 C. Manufacturers of cooling towers often present catalog data showing the outlet temperature as a function of the wet-bulb temperature (WBT) of the ambient air and the range. The range is the difference between the inlet and outlet temperatures of the cooling water. The objective is to express the outlet-water temperature t as a function of the WBT and the range R using Lagrange interpolation method, which can be extended to a function of two independent variables. For example, if z = f(x,y), the form can be chosen as z = - C11(x-x2) (x x3) (y - y2) (y - y3) + C12 (x x2) (x x3) (y y) (y - Y3) + C13 (x x2) (x x3) (y y) (y - y2) + C21 (x x1) (x x3) (y y2) (y - y3) + C22 (x x1) (x x3) (y y) (y - y3) + C23 (x x1) (x x3) (y y) (y - y2) +C31(x x1) (x x2) (y y2) (y Y3) + C32 (x x1) (x x2) (y y) (y - y3) - - - - + C33 (x x1) (x x2) (y y) (y - y2) Note: to represent the data in the Table below, z = the outlet-water temperature t; x = WBT, and y = R (Range). Air Wet-bulb temperature, C c11 c12 c13 c21 c22 c23 c31 c32 c33 Range, C 20 23 26 262 10 25.9 27.5 29.4 16 27.0 28.4 30.2 28.4 29.6 31.3 Determine the values of c11, c12, c13, c21, c22, c23, c31, c32, and c33. Determine the outlet-water temperature t C when WBT = 24 C and Range = 20 C.