verall results obtained and give your conclusions.

A water distribution system consisting of two centrifugal pumps in two parallel flow channels is to be designed. The total flow rate V is the sum of the flow rates Vl and V2 in the two paths. Therefore,V = Vl + V2Also, the characteristics of the two pumps are given in terms of the pressure difference P asP = P1 – A (Vl)2 P = P2 – B (V2)2where P1 and P2 are the maximum pressures generated (for no flow conditions) and A, B are constants. The energy balance, considering elevation change H and the friction losses, givesP = H + C (V)2Take the base, or design, values of the parameters P1, P2, H, A, B, and C as 450, 680, 125, 8, 15 and 5.2, respectively, in SI units.For these base values, compute the flow rates and the pressure difference P, using the Newton-Raphson and the modified Gauss-Seidel (successive substitution) methods. Elimination may be used to reduce the number of equations to 2 for Newton’s method and to 1 (root solving) for the other method. You may use under-relaxation to achieve convergence in the second case.Using either of the above two methods, calculate the pressure P and the total flow rate V if the design variables P1, P2, A, B and C are varied by up to 25% from their base values. In each case, vary only one variable at a time, keeping the others constant at the design, or base, values. Tabulate the results.Determine the conditions when (a) maximum flow rate and (b) minimum pressure arise. In practical systems, we want the highest flow rate at the lowest pressure. Since the two do not generally occur under the same conditions, optimization is needed.From the numerical results generated for V at different P1 and P2, obtain best fits to characterize your results, in terms of V (P1) and V (P2), employing second-order polynomial functions for curve fitting. Plot the curve fit, along with the calculated data points.The cost M of the system is given byM = 3.5 (P1 + P2) + 14000 C / (A+ B)For the solution that minimizes the cost (from inspection of this equation using given ranges of the parameters), calculate the total flow rate. Compare this solution with the one that maximizes the flow rate from your earlier results. Try to find an optimum solution that would yield a high flow rate at a low cost.Discuss the overall results obtained and give your conclusions.