In deriving the equation for the hydraulic jump in a rectangular channel in terms of conjugate depths and initial Froude number

Explanation:

Continuity Equation: This equation is always used to describe the conservation of mass in fluid flow. For a hydraulic jump in a rectangular channel, the continuity equation ensures that the flow rate before the jump equals the flow rate after the jump. This is mathematically expressed as:

Q=A_1​V_1​=A_2​V

Momentum Equation: This is crucial for analyzing the forces involved in a hydraulic jump, as it relates to the change in momentum across the jump. The momentum equation in terms of depth and velocity is used to relate the initial and sequent depths of the hydraulic jump. The specific force or momentum flux function is given by:

These two equations are the fundamental tools needed to derive the relationship between the initial and sequent depths of a hydraulic jump and the initial Froude number in a rectangular channel.