text: The relationship between linear momentum and deformable fluid bodies is well explored, as are the Navier–Stokes equations for incompressible flow. However, exploring the relationships foundational to the Chézy formula can be helpful towards understanding the formula in full.
  To understand the Chézy similarity parameter, a simple   can help summarize the conservation of momentum of a control volume uniformly flowing through an open channel:
  Where the sum of forces on the contents of a control volume in the open channel is equal to the sum of the time rate of change of the linear momentum of the contents of the control volume, plus the net rate of flow of linear momentum through the control surface. The momentum principle may always be used for hydrodynamic force calculations.
  As long as uniform flow can be assumed, applying the linear momentum equation to a river channel flowing in one dimension means that momentum remains conserved and the forces are balanced in the direction of flow:
  Here, the hydrostatic pressure forces are F and F, the component (τPl) represents the shear force of friction acting on the control volume, and the component (ω sin θ) represents the gravitational force of the fluid's weight acting on the sloped channel bottom are held in balance in the flow direction. The free-body diagram below illustrates this equilibrium of forces in open channel flow with uniform flow conditions.
  Most open-channel flows are turbulent and characterized by very large Reynolds numbers. Due to the large Reynolds numbers characteristic in open channel flow, the channel shear stress proves to be proportional to the density and velocity of the flow. This can be illustrated in a series of advanced formulas which identify a shear stress similarity parameter characteristic of all turbulent open channels. Combining this parameter with channel components and the conservation of momentum in an open channel flow results with the Chézy formula that explains this relationship:  .
  Chézy's similarity parameter and formula explain how the velocity of water flowing through a channel has a relationship with the slope and sheer stress of the channel bottom, the hydraulic radius of flow, and the Chézy coefficient, which empirically incorporates several other parameters of the flowing water. This relationship is driven by the conservation of momentum present during uniform flow conditions.