Many liquids are hard to compress (i.e., their volumes or densities
don't change much when you squeeze them), so that the density is
essentially a constant. For such an
*incompressible fluid*
the equation
of continuity simplifies to

so that the velocity field is a *solenoidal* vector.
This condition is analogous to the condition
which we encounter in electromagnetism--the magnetic field has
zero divergence.

Incompressible flows are much easier to treat theoretically than
compressible flows, so this is a very useful simplifying assumption.
You might worry about applying it to gases, but it turns out that
even there it often works well. In fact, if *U* is some characteristic
flow velocity, and *c* is the speed of sound in the fluid, then the
fluid can be treated as incompressible whenever . This
is often expressed in terms of the *Mach number* Ma, defined as

then if the fluid can be treated as incompressible. For instance, the speed of sound in air is 330 m/s (740 mi/h); therefore, fluid flow around people, cars, trains, as well as fluid flow in hurricanes and tornadoes, all satisfy the incompressibility condition. Air flow around commercial airliners ( ) violates this condition, as does supersonic flight.

Mon Aug 11 22:46:35 EDT 1997