The shallow-water equations are derived from equations of conservation of mass and conservation of linear momentum (the Navier–Stokes equations), which hold even when the assumptions of shallow-water break down, such as across a hydraulic jump. In the case of a horizontal bed, with negligible Coriolis forces, frictional and viscous forces, the shallow-water equations are: ∂ ∂ ( ρ ρ η η ) ∂ ∂ t + ∂ ∂ ( ρ ρ η η u ) ∂ ∂ x + ∂ ∂ ( ρ ρ η η v ) ∂ ∂ y = 0 , ∂ ∂ ( ρ ρ η η u ) ∂ ∂ t + ∂ ∂ ∂ ∂ x ( ρ ρ η η u 2 + 1 2 ρ ρ g η η 2 ) + ∂ ∂ ( ρ ρ η η u v ) ∂ ∂ y = 0 , ∂ ∂ ( ρ ρ η η v ) ∂ ∂ t + ∂ ∂ ∂ ∂ y ( ρ ρ η η v 2 + 1 2 ρ ρ g η η 2 ) + ∂ ∂ ( ρ ρ η η u v ) ∂ ∂ x = 0.