Using the Newton method and appropriate computer software, analyze the pipe network in Figure P4.4.13 if $H_A = 190$ ft, $H_E = 160$ ft, $H_G = 200$ ft, $Q_B = 6.0$ cfs, $Q_C = 6.0$ cfs, $Q_D = 6$ cfs, and $Q_F = 12.0$ cfs. Suppose the $K = 1.0 \text{ sec}^2/\text{ft}^5$ for pipes 1, 7, and 8 and $3.0 \text{ sec}^2/\text{ft}^5$ for the other pipes. Use initial estimates of $Q_1 = 10$ cfs, $Q_2 = 1.0$ cfs, $Q_3 = 2.0$ cfs, $Q_4 = 1.0$ cfs, $Q_5 = 10$ cfs, $Q_6 = 4.0$ cfs, $Q_7 = 10.0$ cfs, and $Q_8 = 10.0$ cfs.