Many regular fluid dynamics equations are used in astrophysical fluid dynamics. Some of these equations are:
* Continuity equations
* The Navier–Stokes equations
* Euler's equations
Conservation of mass
The continuity equation is an extension of conservation of mass to fluid flow. Consider a fluid flowing through a fixed volume tank having one inlet and one outlet. If the flow is steady (no accumulation of fluid within the tank), then the rate of fluid flow at entry must be equal to the rate of fluid flow at the exit for mass conservation. If, at an entry (or exit) having a cross-sectional area  m, a fluid parcel travels a distance  in time , then the volume flow rate ( ms) is given by: 
but since  is the fluid velocity ( ms) we can write:
The mass flow rate ( kgs) is given by the product of density and volume flow rate
Because of conservation of mass, between two points in a flowing fluid we can write . This is equivalent to:
If the fluid is incompressible, () then:
This result can be applied to many areas in astrophysical fluid dynamics, such as neutron stars.