The general continuity equation, describing the conservation of mass, takes the form:where  is the fluid density and  is the divergence operator. Under the assumption of incompressible flow, with a constant control volume , this equation has the simple expression . However, it is possible that the cross-sectional area  can change with both time and space in the channel. If we start from the integral form of the continuity equation:it is possible to decompose the volume integral into a cross-section and length, which leads to the form:Under the assumption of incompressible, 1D flow, this equation becomes:By noting that  and defining the volumetric flow rate , the equation is reduced to:Finally, this leads to the continuity equation for incompressible, 1D open-channel flow: