ORIGINAL CONTRIBUTION An Empirical Formula for Design Flood Estimation of Un-Gauged Catchments in Brahmani Basin, Odisha Joygopal Jena 1 • Swetalina Nath 2 Received: 4 October 2018 / Accepted: 30 September 2019 Ó The Institution of Engineers (India) 2019 Abstract Several statistical methods, viz. flood frequency analysis and hydro-meteorological methods (i.e., unit hydrograph approach) are available for estimation of design flood in un-gauged catchments. Till today, the empirical formulae are relevant as the latest methods require adequate field observation and collection of suffi- cient data. The available formulae such as Dicken’s for- mula, Ryves formula and Inglis formula are applicable, respectively, to Northern India, Western India and South- ern India. But no such empirical formula is available for eastern India, especially for Odisha region, for which designers depend on the established formulae for other regions. This necessitated developing an empirical formula for computation of design flood for this zone. An empirical formula is developed for computation of design flood of un-gauged catchments in Brahmani Basin of Odisha and presented in this paper. Relation between the peak dis- charges of the unit hydrograph and the design discharges of individual sub-basins is established. Eight sub-basins are considered for this study. The derived formula is validated through upper and lower envelope curves for probable maximum flood for Mahanadi and adjoining river basins, recommended by Central Water Commission. This would provide guideline in planning any future water resources projects in Brahmani basin. The study would form a part of final work of derivation of a general equation applicable to the State/Eastern zone of India. Keywords Design flood Á Empirical formulae Á Brahmani basin Á Un-gauged catchment Introduction Several statistical methods, viz. flood frequency analysis and hydro-meteorological methods (i.e., unit hydrograph approach) are available for estimation of design flood in un-gauged catchments. These methods require sufficient field observations and data collection. Therefore, in the absence of the data, the empirical formulae developed for other zones of India are used in Odisha state. Almost in all the formulae, the flood peak ‘Q p ’ is expressed as a function of the drainage area ‘A,’ i.e., Q P = f(A). Good number of works are available for different regions of India. Dicken’s formula (1865) is mainly used in central and northern India. Ryves formula (1884) originally developed for the Tamil Nadu region is used in parts of Tamil Nadu, Kar- nataka and Andhra Pradesh. Inglis formula (1930) devel- oped based on flood data of catchment in Western Ghats is applicable to Maharashtra. Ali Nawab Jung Bahadur for- mula was developed for old Hyderabad state. But no specific formula is developed for estimation of design flood for water resources projects in Odisha/eastern zone of India. Besides 3000 small dams, Odisha state has 163 large dams out of which 63 were constructed prior to eighties. The design flood for most of the water resources projects constructed up to late seventies was estimated based on Dicken’s formula, where the value of the constant ‘C’ varies widely. Therefore, unit hydrograph method is rec- ommended for estimation of the design flood. It is & Joygopal Jena jenajoygopal@gmail.com Swetalina Nath swetalinace@cet.edu.in 1 Department of Civil Engineering, GITA, Bhubaneswar 752054, India 2 College of Engineering and Technology (CET), Bhubaneswar, India 123 J. Inst. Eng. India Ser. A https://doi.org/10.1007/s40030-019-00402-x