Flood route the given input hydrograph through a linear reservoir (S = KQ), given K = 2.5 hr and ∆t = 1 hr. Solve one step beyond the peak outflow by developing a simple relation for computing outflow Q2, as a function of Q1, and inflows I1 and I2. Assume storage and outflow are initially zero. Use the fact that S = K(xI + (1 - x)Q) and I - Q = ∆S/∆t.
Time (hr)Inflow (cfs)
0......................0
1...................100
2...................250
3...................400
4...................350
5...................300
6...................200
7...................100
8......................50
9......................0
The Muskingum eqn is Q2 = C0I2 + C1I1 + C2Q1.
C0 = - Kx + 0.5 ∆t / D
C1 = Kx + 0.5 ∆t / D
C2 = K - Kx - 0.5 ∆t / D
D = - K - Kx + 0.5 ∆t