The storage equation has been given as and the continuity equation as
Si= KxIi + (1 - x)Oi]
And the continuity equation as
= + ∆S / ∆t
Given that  and  are the average inflow and outflow within the time period and ∆S is the change in the storage, derive the Muskingum river routing equation:
O2 = C0I2 + C1I1 + C2O1,
Where I2 and O2 refer to the inflow and outflow at the end of the time period and I1 and O1 refer to those values at the beginning of the time period. Verify the equations for Co, C1, and C2 given in Section 4.2.