1. Flood Routing

2. Introduction
Flow Routing is a procedure to estimate downstream hydrograph from upstream hydrograph (Figure 1). Since flow routing has been widely used in flood estimations, flow routing is usually called flood routing.

3. Introduction
The routed hydrograph is delayed by a time lag (translation) and is attenuated. Flow routing is divided into river flow routing and reservoir flow routing.

4. Basic Equations From the conservation of mass, water balance for a system in Figure 2 can be expressed as where I is upstream inflow , O is downstream outflow, S is the storage (reservoir or a river reach).

5. In practical calculation, it is more convenient to use a finite difference form of Eq(1) for a Δt duration. The mean values for the inflow and outflow are used instead of the instantaneous value. To estimate the downstream outflow, it is also necessary to get the storage function that links the input and output. S= f(I,O) (3) It is then possible to solve the outflow from Eq (2) and (3).

6. Flood Routing
River Flow Routing (The Muskingum Method) The storage function in a river reach is linked with both inflow and outflow. where K is the storage time constant for the reach, X is a weighing factor ( between 0~ 0.5, usually around 0.2).

7. Flood Routing
From the water balance equation Simplify it to get the Muskingum equation

8. Flood Routing
Where: It is important to check if If not, some adjustments to the parameters are needed. If there are rounding errors, adjust the largest C value first

9. Flood Routing
Ex6: Estimate the downstream hydrograph using the Muskingum method with K=3hr and X=0.3. The time interval is 3 hours. The upstream hydrograph is as follows:

10. Flood Routing
Ex7: A stream has a uniform flow of 10 m3/s. a flood in which the discharge increases linearly from 10 m3/s to a peak of 70 m3/s in 6 hours and then decreases linearly to a value of 10 m3/s in 24 hours from the peak arrives at a reach. Route the flood through the reach in which k=8 h, and x=0. estimate the peak flow at the town and the time at which the peak flow will occur.

11. Flood Routing
Reservoir Flow Routing For a flood going through a reservoir, the water level in the reservoir is assumed as horizontal. The storage function would be linked with the reservoir water level.

12. Flood Routing
Since the storage below the spillway crest plays no role in the flow routing process, only the storage above the crest is considered.

13. Flood Routing
The discharge over the spillway crest is a function of h. where C is the discharge coefficient, b is the width of the spillway crest.

14. Ex8:A triangular-shaped inflow hydrograph is routed through a reservoir assuming it is completely full at the beginning of the storm. The spillway crest is 20 m wide and has a coefficient of 2.7. The reservoir area is 0.5 km2 and has vertical sides. What are the discharge over the spillway crest and estimate the Δt ?