This is an equation of motion for a [[Newtonian fluid]] that is a type of [[conservation law]] which describes the conservation of a quantity that flows through a given region - this may be [[mass]] for a literal fluid substance, but the equation appears throughout physics for other quantities. Here we present it in the most general way first by presenting how it emerges in [In fluid mechanics](Continuity%20equation.md#In%20fluid%20mechanics) # The continuity equation for fluid mechanics # The continuity equation for spacetime The continuity equation is also valid for [Newtonian fluids](Newtonian%20fluid) in [3+1 dimensional spacetime](Spacetime.md) where it derives from the [Stress-energy tensor](Stress-energy%20tensor.md) [equation of motion](Stress-energy%20tensor.md#Equation%20of%20motion) where we find that $T^{00}_{\;\;\;,\,0}+T^{0j}_{\;\;\;,\,j}=\frac{\partial \rho}{\partial t}+\nabla\cdot (\rho\mathbf{v})=0$ # The continuity equation for other areas of physics * In [Electromagnetism (index)](Electromagnetism%20(index).md) the [Continuity equation](Continuity%20equation.md) describes [charge conservation](Charge%20conservation.md). #Mechanics #Mechanics/ClassicalFields