The basis of unit hydrograph is that if two identical rainfalls occur on a drainage basin having identical conditions prior to the rains, the hydrograph of run-off from the two storms would be expect to be same.
In actual conditions two identical storms are rare to occur.
Most of the practical storms vary in duration, amount, and distribution of rainfall.
A unit hydrograph is a hydrograph of a rainfall of a specified duration and areal pattern, resulting in a run-off of 1 cm.
In other words, the total volume of water contained in this run-off hydrograph will be equal to 1 cm depth of water on the catchment.
Various storms of varying intensities and having different volumes of run-off, but a particular unit duration, will have the same shape of their run-off hydrographs.
Different unit hydrographs for different unit duration can be prepare.
A particular unit hydrograph when once prepare for a particular unit duration can be utilised for evaluating the run-off hydrographs of other storms of the like durations
The number of unit hydrographs for a given basin is theoretically infinite, since there may be one for every possible rainfall duration, and for every possible distribution pattern in the basin.
Practically only a certain limited number of hydrographs can be used for a given basin.