The Muskingum river routing equation, O2 = C0I2 + C1I1 + C2O1, was derived by substituting...

The Muskingum river routing equation, O2 = C0I2 + C1I1 + C2O1, was derived by substituting the storage equation Si = K[XIi + (1 − X)Oi], where S1 = K[XI1 + (1 − X)O1] and S2 = K[XI2 + (1 − X)O2 into the continuity equation and combining like terms. In these equations, I1,O1 and S1 are the inflow, outflow, and storage, respectively, at the beginning of the time period, and I2, O2, and S2 are, respectively, the corresponding values at the end of the time period. The terms and are the average inflow and outflow during the time period, and ΔS is the change in storage. Perform the described derivation and verify the equations for C0, Cl, and C2.