Continuity equation

This equation is a differential equation which describes the conservative transport of some kind of quantity. As energy, momentum, mass, and other natural quantities are conserved, a huge variety of physics can be described with continuity equations. Continuity equation is the equation obeyed by any conserved, indestructible quantity like mass, electrical energy, electric charge, thermal energy, or quantum-mechanical probability, which is a statement that the rate of increase of quantity in any region equals the total current flowing into the region. It is called as equation of continuity. Continuity equation can be defined as the mean velocities at all the cross sections having equal areas are then equal, and if the areas are not equal, velocities are inversely proportional to areas of the respective cross sections. The equation of continuity is the statement of mass conversion. The Law of Conservation of Mass states that mass can be neither created nor destroyed. The equation of continuity states that for an incompressible fluid flowing in the tube of varying cross-section, the mass flow rate is same at every place in the tube. The mass flow rate is the rate at which mass flows past a given point, so it's the total mass flowing past divided by time interval. The equation of continuity can be given as follows:

 This equation is called as continuity equation for the steady 1-dimensional flow. For a steady flow through a control volume with several inlets and outlets, the net mass flow should be zero, where inflows are negative and outflows are positive. The continuity equation can also be stated in any steady state process as rate at which the mass enters a system is equal to the rate at which the mass leaves the system. In an electromagnetic theory, the continuity equation can be regarded as an empirical law expressing charge conservation which can be derived as a consequence of the Maxwell's equations. It states that the divergence of current density is equal to the negative rate of change of the charge density.

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