Contents preface (VII) introduction 1—37

Data and computation of mass curve (Example 2.4)

Month	Mean monthly	Days in month	Monthly flow	Accumulated
	flow (m^3/s)		volume	volume
			(cumec-day)	(cumec-day)
January	60	31	1860	1860
February	50	29	1450	3310
March	40	31	1240	4550
April	28	30	840	5390
May	12	31	372	5762
June	20	30	600	6362
July	50	31	1550	7912
August	90	31	2790	10702
September	100	30	3000	13702
October	80	31	2480	16182
November	75	30	2250	18432
December	70	31	2170	20602

64 IRRIGATION AND WATER RESOURCES ENGINEERING
Solution: Actual number of days in a month (Col. 3 of the Table) are used for calculating monthly flow volume (Col. 4 of the Table). Mass curve of the accumulated flow versus time is shown plotted in Fig. 2.17. For the mass curve and demand rate, all months are assumed to be of equal duration i.e., 30.5 days. A demand line (with a slope of line PR) is drawn tangential to the mass flow curve at A. Another line parallel to this line is drawn so that it is tangential to the mass-flow curve at B. The vertical difference BC (= 2850 cumec-day) is the required storage for satisfying the demand rate of 50 m³/s.

cumec-day)

21

20

18

16

14

3

Demand - 50 m /s Storage - 2850 cumec-day

Accumulatedmassinflowvolume(1000

12

10

Demand line

8

6

C

2850

B
Mass flow curve

A _P

4
61 × 51
= 3050 cumec-day

2
		R
			61 days
			(2 months)
0	Jan Feb Mar Apr May June Jul Aug Sep Oct	Nov Dec

Fig. 2.17 Mass-flow curve and demand line for Example 2.4

HYDROLOGY

65

2.6.2.2. Flow-Duration Curve
Flow-duration curve (or discharge-frequency curve) of a stream is a graphical plot of stream discharge against the corresponding per cent of time the stream discharge was equalled or exceeded. The flow-duration curve, therefore, describes the variability of the stream flow and is useful for
(i) determining dependable flow which information is required for planning of water resources and hydropower projects,
(ii) designing a drainage system, and (iii) flood control studies.

For preparing a flow-duration curve, the stream flow data (individual values or range of values) are arranged in a descending order of stream discharges. If the number of such discharges is very large, one can use range of values as class intervals. Percentage probability P_p of any flow (or class value) magnitude Q being equalled or exceeded is given as

Pp =	m	× 100(%)	(2.20)
N + 1

in which m is the order number of the discharge (or class value) and N is the number of data points in the list. The discharge Q is plotted against P_p to yield flow-duration curve, as shown in Figs. 2.18 and 2.19. The ordinate Q at any percentage probability P_p represents the flow magnitude in an average year that can be expected to be equalled or exceeded P_p perc ent of time and is termed as P_p% dependable discharge (or flow). The discharge Q in the flow-duration curve could be either daily average or monthly (usually preferred) average.

3

Discharge,Q(m/s)

50

40

30				3
				Q75 = 15.5 m /s
20	3
	Pp for Q = 30 m /s
	31.5 %
10
0
0	20	40	60	80

P_p (%)

Fig. 2.18 Flow-duration curve for Example 2.5

66

3	/s)
	DischargeQ(m

IRRIGATION AND WATER RESOURCES ENGINEERING

140

120

100

80

60

40
20			3
			Q80 = 37 m /s
0
0	20	40	60	80	100
			p p (%)

Fig. 2.19 Flow-duration curve for Example 2.6
Example 2.5 The observed mean monthly flows of a stream for a water year (June 01 to May 31) are as given in the first two columns of the following Table. Plot the flow-duration curve and estimate the flow that can be expected 75% of the time in a year (i.e., 75% dependable flow, Q₇₅) and also the dependability (i.e., P_p) of the flow of magnitude 30 m³/s.

HYDROLOGY							67
Table : Data and computations for flow-duration curve (Example 2.5)
	Observed flow	Flow (Q) arranged			Pp
Month	Q (m^3/s)	in descending order,	Rank m	=	m	× 100
( N + 1)
			(m^3/s)				(%)
June	15	44	1		7.7
July	16	40	2		15.4
August	44	35	3		23.1
September	40	31	4		30.8
October	35	30	5		38.5
November	31	23	6		46.2
December	30	21	7		53.8
January	21	18	8		61.5
February	23	16	9		69.2
March	18	15	11		84.6
April	15	15	11		84.6
May	8	8	N = 12		92.3

Solution: The flow-duration curve (Q (col. 3) v/s P_p (col. 5)) is as shown in Fig. 2.18. From the curve, one can obtain
Q₇₅ = 15.5 m³/s
And the dependability (i.e., P_p) of the flow of magnitude 30 m³/s = 31.5%.

Example 2.6 Column 1 of the following Table gives the class interval of daily mean discharges (m³ /s) of a stream flow data. Columns 2, 3, 4, and 5 give the number of days for which the flow in the stream belonged to that class in four consecutive years. Estimate 80% dependable flows for the stream.