lag. Peak flow attenuation. Recession limb. Rising limb. Outflow at x+ D x. c D t. time t. time t+ D t. x. Flood Routing definitions. Q(t). Inflow at x. t p. time. Flood Routing methods. Hydraulic Uses both dynamic and continuity equations
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Peak flow attenuation
Outflow at x+Dx
xFlood Routing definitions
Inflow at x
xKinematic Wave Equation
Continuity with no lateral inflow yields:
For quasi-uniform flow:
Substitute and separate variables to get wave eq.
where c = dQ/dA is wave celerity
Flow Q4 unknown
1Continuity Around the Nucleus
and get Q4=f(Q1 , Q2 , Q3)
Setting b = 0.5 yields
Convert the Wave equation to a Diffusion equation
Diffusion coefficient is related to channel conveyanceDeriving the Diffusion equation
Non-centered finite difference scheme creates a numerical error
f(a,b,D)=0 leads to multiple sets of (a,b) coordinates for any value of D.Determine weighting coefficients
Condition for numerical stability is
orLimits for Dx and Dt
For b = 0.5
For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N = 2,3,4...
From parts 2 & 3Limits for Dx and Dt
For b = 0.5
For very long channels, route hydrograph over multiple sub-reaches of length Dx=Length/N, N=2,3,4...
For very short channels, use routing time-step equal to sub-multiple of hydrology time step, dt=Dt/N, N=2,3,4...
Details of last conduit design are displayed
Changes to Dx or Dt reported for information
User can change computed X or K valuesMIDUSS 98 Route Command