Dimensionless momentum-depth relationship in open-channel flow

Momentum for one-dimensional flow in a channel can be given by the expression: For open channel flow calculations where momentum can be assumed to be conserved, such as in a hydraulic jump, we can equate the Momentum at an upstream location, M1, to that at a downstream location, M2, such that:

Dimensionless momentum-depth relationship in open-channel flow

Momentum for one-dimensional flow in a channel can be given by the expression: For open channel flow calculations where momentum can be assumed to be conserved, such as in a hydraulic jump, we can equate the Momentum at an upstream location, M1, to that at a downstream location, M2, such that: