It is possible to formulate equations describing three conservation laws for quantities that are useful in open-channel flow: mass, momentum, and energy. The governing equations result from considering the dynamics of the flow velocity vector field  with components . In Cartesian coordinates, these components correspond to the flow velocity in the x, y, and z axes respectively.
To simplify the final form of the equations, it is acceptable to make several assumptions:
# The flow is incompressible (this is not a good assumption for rapidly-varied flow)
# The Reynolds number is sufficiently large such that viscous diffusion can be neglected
# The flow is one-dimensional across the x-axis