Contents preface (VII) introduction 1—37

2.7.4.3. Instantaneous Unit Hydrograph (IUH)
As the duration D of unit hydrograph is reduced, the intensity of rainfall excess i.e., 1/D increases, and the unit hydrograph becomes more skewed with its peak occurring earlier, Fig. 2.26. The fictitious case of unit hydrograph of zero duration is known as instantaneous unit hydrograph which represents the direct runoff from the catchment due to an instantaneous precipitation of the rainfall excess volume of 1 cm.

HYDROLOGY

77

		A	ERH
		B
3	/s	C	C
m	D
		in		A
		Discharge
				Unit hydrograph
		D
			B
			Time in hours

Fig. 2.26 Unit hydrographs of different durations
2.7.4.4. Synthetic Unit Hydrograph
Unit hydrographs can be derived only if suitable records of data for the catchment are available. Many of the catchments, especially the remote ones, remain ungauged. To derive unit hydrographs for such basins, one requires suitable empirical relations of regional validity which relate basin characteristics and the salient features of resulting hydrographs. Such relations usually pertain to time to peak, peak flow and time base of the unit hydrograph. Unit hydrographs derived in this manner are known as synthetic unit hydrograph. Dimensionless unit hydrographs (Q/Q_p versus t/t_pk) based on a study of large number of unit hydrographs are also used to derive synthetic unit hydrograph.
2.7.4.5. Use and Limitations of Unit Hydrograph
Unit hydrograph is useful for (i ) the development of flood hydrographs for extreme rainfalls for use in the design of hydraulic structures, (ii) extension of flood-flow records based on rainfall data, and (iii) development of flood forecasting and warning system based on rainfall.
In very large catchment basins, storms may not meet the conditions of constant intensity within effective storm duration and uniform areal distribution. Therefore, each storm may give different direct runoff hydrograph under, otherwise, identical conditions. Therefore, unit hydrograph is considered applicable for catchments having area less than about 5000 km² (9). Very large catchments are usually divided into smaller sub-basins and the hydrographs of these sub-basins are processed to obtain composite hydrgraph at the basin outlet.
The application of unit hydrograph also requires that the catchment area should not be smaller than about 200 ha as for such small basins there are other factors which may affect the rainfall-runoff relation and the derived unit hydrograph may not be accurate enough.
Example 2.7 The following Table lists the ordinates of a runoff hydrograph in response to a rainfall of 21.90 mm during the first two hours, 43.90 mm in the next two hours, and 30.90 mm during the last two hours of the rainfall which lasted for six hours on July 19, 1995 in

78 IRRIGATION AND WATER RESOURCES ENGINEERING
Warasgaon catchment basin whose area is 133.1 km² (Source: M.Tech. Dissertation on ‘‘Rainfall—runoff modelling of Mutha river system’’ by S.R. Vhatkar submitted at the Department of Hydrology, University of Rookee in 1996).

Time (hr)	0	2	4	6	8	10	12	14	16	18
Discharge (m^3/s)	0	171	393	522	297	133	51	10	10	10

Obtain the following : (a) φ-index

(b) unit hydrograph and its duration (say, T hours) (c) time of concentration, T_c
Thereafter, derive the following :
(i) Unit hydrographs for 2T and 3T hours
(ii) T-hr unit hydrograph from the derived 2T-hr unit hydrograph
Solution: On plotting the runoff hydrograph, Fig. 2.27 (a), one notices that the stream flow stabilizes at 10 m³/s. This must be on account of the base flow contribution.

Discharge(cumecs)

600

500

400

300

200

100

0

0

Runoff hydrograph

Base flow line

5 10 15 20
Time ( hrs )

Fig. 2.27 (a) Runoff hydrograph and base flow (Example 2.7)
Therefore, treating the base flow as 10 m³ /s at time t = 14 hrs, the base flow line is obtained by assuming linear variation between t = 0 and t = 14 hrs. The values of the base flow (Col. 3 of Table A for this example) have been subtracted from the corresponding values of the runoff hydrograph (Col. 2 of Table A) to obtain the ordinates of the direct runoff hydrograph (Col. 4 of Table A).

HYDROLOGY									79