Expanding the derivatives in the above using the product rule, the non-conservative form of the shallow-water equations is obtained. Since velocities are not subject to a fundamental conservation equation, the non-conservative forms do not hold across a shock or hydraulic jump. Also included are the appropriate terms for Coriolis, frictional and viscous forces, to obtain (for constant fluid density): ∂ ∂ h ∂ ∂ t + ∂ ∂ ∂ ∂ x ( ( H + h ) u ) + ∂ ∂ ∂ ∂ y ( ( H + h ) v ) = 0 , ∂ ∂ u ∂ ∂ t + u ∂ ∂ u ∂ ∂ x + v ∂ ∂ u ∂ ∂ y − − f v = − − g ∂ ∂ h ∂ ∂ x − − k u + ν ν ( ∂ ∂ 2 u ∂ ∂ x 2 + ∂ ∂ 2 u ∂ ∂ y 2 ) , ∂ ∂ v ∂ ∂ t + u ∂ ∂ v ∂ ∂ x + v ∂ ∂ v ∂ ∂ y + f u = − − g ∂ ∂ h ∂ ∂ y − − k v + ν ν ( ∂ ∂ 2 v ∂ ∂ x 2 + ∂ ∂ 2 v ∂ ∂ y 2 ) ,