The hydraulic jump is a transitional slate from an upstream supercritical to downstream subcritical flow, and, for a given set of flow conditions, it has a fixed position length. The phenomenon of the hydraulic jump has been widely studied because of its frequent occurrence in nature, and because of its uses in many practical applications. In the present study the momentum principle is used to derive an equation expressed the hydraulic jump occurred in a short horizontal reach of a circular open channel. The derived equation indicates that the initial water depth and sequent water depth (conjugate depths) are functions of the critical water depth. In the present study the various elements of the hydraulic jump are expressed as dimensionless ratios, by dividing with the diameter of the circular channel. The procedure of dimensionless ratios described in the present paper can be used to determine the various elements of hydraulic jump in a circular channel when either both the discharge and the relative initial depth (or sequent depth) are known or the discharge and the relative dissipated energy are known. The methods of solution, analytical, graphical or by using tables are illustrated step by step in this paper.