2-D Incompressible
Flow in which the divergence of the velocity is zero.
“In vector calculus , divergence is an operator that measures the magnitude of a vector field 's source or sink at a given point, in terms of a signed scalar.” From wikipedia page
“divergence”
An operator is a mapping of one vector space to another.
Basically incompressible flow would be a
FLUID WHOSE DENSITY IS RELATIVELY
CONSTANT THROUGHOUT ITSELF AND
CANNOT BE COMPRESSED!
Liquids cannot be compressed* and are basically constant density, therefore they are incompressible fluids.
Gaseous fluids are usually considered incompressible if they have a velocity 0.3 times the speed of sound.
*Everything is able to be compressed however slightly and therefore nothing is truly incompressible.
It’s impossible
But making the assumption a fluid is incompressible simplifies the equations about how the fluid flows
The equation for incompressible flow, where U is the velocity of the material
The continuity equation states that,
This can be shown through the derivative as
This can be expressed via the material derivative as
Since ρ > 0, we see that flow is incompressible if
density is constant through the material
“In fluid mechanics or more generally continuum mechanics, an incompressible flow is solid or fluid flow in which the divergence of velocity is zero.” Wikipedia page
“Incompressible flow”
An application of this is the otto cycle/ otto engine
An engine cycle that works through adiabatic compression.
Constant volume
Pressure buildup
Four stroke engine
1.Intake stroke
2.Compression
3.Power
4.Exhaust
Dad died when he was 8
Went to live with his Granduncle, Emiland
Gauthey
He enrolled in École des Ponts et Chaussées
Eventually succeeded his granduncle as
Inspector General for Corps des Ponts et
Chaussées
These equations are used to describe the motion of fluids
The various problems are used to figure out the velocity of a fluid, not the position
These equations come from the application of
Newton’s Second Law to the motion of fluids
Most often written for Newtonian Fluids
Assume that temperature, velocity, pressure, density are all differentiable
Derived from principles of energy, conservation of mass and momentum
These are continuations of the Euler equations, more focused on fluid
Bibliography
"An introduction to theoretical fluid mechanics." SciTech Book News 1 Dec.
2009: 11-14. Print.
"Divergence - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia . N.p., n.d. Web. 27 July 2010.
<http://en.wikipedia.org/wiki/Divergence>.
"Incompressible flow." Galileo . N.p., n.d. Web. 27 July 2010.
<http://galileo.phys.virginia.edu/classes/311/notes/fluids1/node6.htm
l>.
"Incompressible flow - Wikipedia, the free encyclopedia." Wikipedia, the free encyclopedia . N.p., n.d. Web. 27 July 2010.
<http://en.wikipedia.org/wiki/Incompressible_flow>.
Numerical Simulations of Incompressible Flows . .: World Scientific Pub Co
Inc, 2003. Print.
PANTON, RONALD L.. INCOMPRESSIBLE FLOW . 2ND ed. New York:
John Wiley And Sons Ltd, 2005. Print.
