When an alluvial stream is partially/fully obstructed by a bridge pier, scour takes place in the vicinity of the pier. Estimation of this scour depth is a major concern of bridge engineers. The underestimation of scour depth leads to unsafe design, while an overestimation leads to uneconomical design. Therefore, estimation of anticipated maximum scour depth for given design discharge is essential. Scour at bridge piers is mainly affected by pier, flow and sediment characteristics. On the basis of field investigations, many investigators have suggested criteria for assessing maximum scour depth around bridge pier in alluvial bed. These studies are mainly regarding scour around bridge piers at normal flow conditions. Adequate information in connection with scour at bridge pier at different depth of flow, piers size and sediment size is not available. From the observation, we found that scour depth goes on increasing with increase in pier diameter.Out of these, the effects of pier size and shape, and of the approach flow angle on scour depth are fairly well understood. The effects of flow depth and sediment non-uniformity on scour depth have been also studied in detail. In this paper, a method has been presented to estimate the time variation of scour depth with uniform and nonuniform sediments. The procedure has been developed for computing the time variation of scour depth which is based on the dimensional analysis, and considering the horse-shoe vortex system to be the main scouring agent.