Fluid Dynamics
In fluid dynamics, the continuity equation states that, in any steady state process, the rate at which mass enters a system is equal to the rate at which mass leaves the system.
The differential form of the continuity equation is:
where
- ρ is fluid density,
- t is time,
- u is the flow velocity vector field.
If ρ is a constant, as in the case of incompressible flow, the mass continuity equation simplifies to a volume continuity equation:
which means that the divergence of velocity field is zero everywhere. Physically, this is equivalent to saying that the local volume dilation rate is zero.
Further, the Navier-Stokes equations form a vector continuity equation describing the conservation of linear momentum.
Read more about this topic: Continuity Equation
Famous quotes containing the words fluid and/or dynamics:
“On and on eternally
Shall your altered fluid run,
Bud and bloom and go to seed;
But your singing days are done;”
—Edna St. Vincent Millay (1892–1950)
“Anytime we react to behavior in our children that we dislike in ourselves, we need to proceed with extreme caution. The dynamics of everyday family life also have a way of repeating themselves.”
—Cathy Rindner Tempelsman (20th century)