Contents preface (VII) introduction 1—37

17.2. FLOOD ROUTING
The change in storage ∆s of a reservoir depends on the difference between the amount of inflow and outflow and can be expressed by the equation,

∆s = Qi∆t – Qo∆t

(17.1)

where, ∆s is the change in storage during time interval ∆t, and Q_i and Q_o are, respectively, the average rates of inflow and outflow during the time interval ∆t. The rate of inflow at any time is obtained from the inflow flood hydrograph selected for the purpose (Fig. 17.1). The rate of outflow (which should, strictly speaking, include outflow from the river outlets, irrigation outlets, and power turbines) is obtained from the outflow discharge versus reservoir water surface elevation curve (Fig. 17.2). Similarly, the storage is obtained by the reservoir storage versus reservoir water surface elevation curve (Fig. 17.3). While the inflow flood hydrogrpah and the storage curve would remain fixed for a given project site, the spillway discharge curve would depend not only on the size and type of the spillway but also on the manner in which the spillway and outlets, in some cases, are operated to regulate the outflow. If one could establish simple mathematical expression for these three curves, a solution of flood routing

564 IRRIGATION AND WATER RESOURCES ENGINEERING

Reservoirlevel,m

		3000
				Inflow
				hydrograph
3	/s	2000
m
		in			Outflow
		Discharge	1000
		hydrograph

0	2	4	6	8	10
0

Time in hours

Fig. 17.1 Typical hydrographs of inflow and outflow floods
108

106

104
3/2

Q_o = 220 H

102

100

0			1000	2000	3000
					3
					Outflow rate, m /s
	Fig. 17.2 Spillway discharge versus reservoir level
	108
m	106
level,		104
Reservoir
	102
	100
	100	150	200	250
					6
			Reservoir storage, 10 cu.m.

Fig. 17.3 Reservoir level versus reservoir capacity

SPILLWAYS

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could be obtained simply by mathematical integration. This, however, is not possible and one has to use one of the several techniques of flood routing ranging from purely arithmetical method to an entirely graphical solution. One such simple arithmetical trial and error method makes the flood routing computations (Table 17.1) in the following manner:

(i) Select a suitable time interval ∆t (Col. 2),
(ii) Obtain inflow rates for different times from the inflow hydrograph (Fig. 17.1) and enter these values in Col. 3.
(iii) Average inflow rates for time interval ∆t are entered in Col. 4.
(iv) Determine the amount of inflow volume in time and enter the value in Col. 5. (v) Assume a trial reservoir water surface elevation (Col. 6).

(vi) Obtain the rate of outflow from Fig. 17.2 for the assumed trial reservoir water sur-face elevation and enter its value in Col. 7.

(vii) Obtain the average rate of outflow for the time interval under consideration and enter this value in Col. 8.
(viii) Obtain the amount of outflow volume in time ∆t and enter the value in Col. 9.
(ix) Obtain the change in storage ∆s by subtracting outflow volume from inflow volume (Col. 10).
(x) Add ∆s of Col. 10 to the total reservoir storage at the beginning of the time interval (Col. 11).
(xi) Determine the reservoir water surface elevation using Fig. 17.3 and enter the same in Col. 12.
(xii) Compare the reservoir water surface elevation (Col. 12) with the trial reservoir wa-ter surface elevation (Col. 6). If they do not match within specified accuracy, say 3 cm, make another trial and repeat until the agreement is reached.
Based on the above procedure, flood routing computations have been carried out for the curves of Figs. 17.1-17.3 as shown in Table 17.1. Using the values of the outflow rate (Col. 7), the outflow hydrograph can be prepared as shown in Fig. 17.1. Obviously, the volume indicated by the area between the inflow and outflow hydrographs would be the surcharge storage.
Another method of routing a flood is a graphical method which is also known as inflow-storage-discharge curves method or, simply, ISD method. Equation (17.1) can, alternatively, be written as

s	– s	n	=	^Qi , n ^+ ^Qi , n+ 1	∆t −	^Qo, n ^+ ^Qo , n+1	∆t	(17.2)
n+1		2	2

in which, Q_i,n and Q_o,n represent, respectively, the inflow and outflow discharge rates at the beginning of the n^th time step (or, at the end of (n – 1)^th time step) of duration ∆t during which the reservoir storage volume changed by (s_n+1 – s_n). Equation (17.2) is rewritten as

F 2sn+ 1

+ Q

I

= d

Q

+ Q

+

F

2sn

− Q

I

(17.3)

G

∆t

o , n+ 1J

i , n

i , n+ 1 i

G

∆t

o , n J

H

K

H

K

For this method, one would require a graph	F 2sn	+ Q	I	versus outflow discharge rate
	G	∆t	o J
	H			K

Q_o , Fig. 17.4. This graph can be prepared by knowing the values of s and Q_o for different values of reservoir water surface elevation (Figs. 17.2 and 17.3) and suitably chosen time interval, ∆t. Procedure for computation of the outflow hydrograph is as follows :

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			Remarks
	Reservoir	level	at the	end of t	(m)
	Total	storage	at the	end of t	4 3(10m)