Types of Flood Routing
Flood Reservoir Routing
Flood routing is the process of determining the reservoir stage, storage volume of the outflow hydrograph corresponding to a known hydrograph of inflow into the reservoir, this is called Reservoir Routing. For this, the capacity curve of the reservoir, i.e. ‘storage vs pool elevation’, and ‘outflow rate vs pool elevation’, curves are required. Storage volumes for different pool elevations are determined by the planimeter of the contour map of the reservoir site. For examples, the volume of water stored (V) between two successive contours having areas A1 and A2 (planimeter) and the contour interval d, is given by-
Cone Formula, V= d (A1 + A2 + √A1A2)/3
Prismoidal Formula, = V= d (A1 + A2 + 4Am)/6
Where Am= (A1+A2)/2, i.e., area midway between the two successive contours. The Prismoidal formula is more accurate. The outflow rates are determined by computing the discharge through the sluices and the spillway discharge for different water surface elevations of the reservoir. (i.e., pool elevation):
Discharge through sluices, Qsl = CdA√2gh
Discharge over spillway crest, Qsp = CLH3/2
Outflow from the reservoir O = Qsl + Qsp
Where, h= height of water surface of reservoir above the centre of sluice
H= height of water surface of reservoir above the crest of spillway
Cd= coefficient of discharge for the sluice
C= coefficient of spillway
A= area of sluice opening
L= Length of spillway
The problem in flood routing is to determine the relation between the inflow, the outflow and the storage as a function of time. The problem can be solved by applying the hydrologic equation
I= O + ΔS
Where, I= inflow rate
O= outflow rate
ΔS= incremental storage, at any instant
Taking a small interval of time, t (called the routing period and designating the initial and final conditions by subscripts by 1 and 2 between the interval, written as,
[(I1 + I2)/2]t – [(O1 + O2)/2]t = S2-S1
The routing period, t selected should be sufficiently short such that the hydrograph during the interval 1-2 can be assumed as a straight line, i.e., Imean = (I1+I2)/2
Stream Flow Routing
In a stream channel (river) a flood wave may be reduced in magnitude and lengthened in travel time, i.e., attenuated, by storage in the reach between two sections. The storage in the reach may be divided into two parts-prism storage and wedge storage since the water surface is not uniform during the floods.
The volume that would be stored in the reach if the flow were uniform throughout, i.e., below a line parallel to the stream bed, is called ‘prism storage’ and the volume stored between this line and the actual water surface profile due to outflow being different from inflow into the reach is called ‘wedge storage’. During rising stages, the wedge storage volume into consideration before the outflow actually increases, while during failing stages inflow drops more rapidly than outflow, the wedge storage becoming negative.
In the case of streamflow routing, the solution of the storage equation is more complicated, than in the case of reservoir routing, since the wedge storage is involved. While the storage in a reach depends on both the inflow and outflow, prism storage on the outflow alone and the wedge storage depends on the difference (I-O). A common method of streamflow routing is the Muskingum method (McCarthy, 1938), where the storage is expressed as a function of both inflow and outflow in the reach as
S= K (xI + (1-x) O)
Where, K and x are called the Muskingum coefficients (since the equation was first developed by the U.S. Army Corps of Engineers in connection with the flood control schemes in the Muskingum River Basin, Ohio), K is a storage constant having the dimension of time and x is a dimensional constant for the reach of the river. In natural river channels, x ranges from 0.1 to 0.3.
After determining the values of K and x, the outflow O from the reach may be obtained by combining and simplifying the two equations,
[(I1 + I2)/2]t – [(O1 + O2)/2]t = S2-S1
And
S2-S1= K[x(I2-I1) + (1-x) (O2-O1)]
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