A transition is constructed to connect two trapezoidal channels with bottom slopes of 0.001 and 0.0004, respectively. The channels have the same cross-sectional shape, with a bottom width of 3 m, a side slope of z = 2, and Manning's coefficient n = 0. 02. The transition is 20 m long and is designed to carry a discharge of 20 m3/sec. Assume an energy Joss of 0.02 uniformly distributed through the transitional length. Determine the change in the bottom elevations at the two ends of the transition. Assume uniform (normal) depth before and after the transition and use appropriate computer software to assist you.