Flow Routing Flashcards
What is flow routing?
A procedure used to estimate a downstream hydrograph from an upstream hydrograph
What is the key assumption in flow routing?
What equations represent this?
Conservation of mass
I - 0 = dS/dt
(I1 + I2) /2 - (O1 + O2) /2 = (S2 - S1) /dt
Define the parameters in the storage function of a river equation
K = storage time constant (hours)
X = weighting factor
Why is a weighting factor required in the storage function of a river equation?
Because flood does not take up whole river section
What must we do to check the base parameters for the river storage equation? How can we ensure this condition is met?
Check that C0 + C1 + C2 = 1
Use fractions to avoid complication
What is method of finding a downstream hydrograph?
- Use Muskingum method (S equation in equation sheet)
- Find base parameters
- Check C0+C1+C2=1
- Use a table to compute outputs using S equation where t, I and O are all columns
- O1 = I1 - Plot O against time
If there are no downstream records how is K and X found?
K is estimated from travel time in the reach based off the river bed and cross section
X is assumed as 0.2
If there are downstream records how is X and K derived?
- Find S from the records using:
S = SUM(Imean - Omean) cumulative through time - Trial different X guesses finding XI+(1-X)O
- Plot S against (XI+(1-X)O)
- X solution is X guess which has narrowest loop
- K = dt x slope gradient
For a flood going through a reservoir, what is the storage a function of?
How is this function found?
S = f(h)
where S is only the storage above the crest and h is the depth of water above the crest
Found from a topographic map
What is the equation for the discharge over a reservoir spillway?
O = Cbh^1.5
C is discharge coefficient
b is width of spillway
h is depth of water above crest
What is dt in the reservoir flow routing equation?
dt = duration of inflow rising limb / 5
How is a reservoir’s outflow found from an inflow hydrograph?
- Find dt from duration of inflow rising limb/5 in seconds!
- Find discharge function from O = Cbh^1.5
- Rearrange for h
- Define the storage function from S=Ah
- Combine S and h functions
- Sub into water balance flow routing equation and rearrange so O2 is on RHS
- Create a graph of RHS over O using different O values to create a curve
- Work out LS one by one using inflow data
- LS = RS so O can be measured off graph
What are the 2 components of flow routing?
Attenuation and translation
