The stringent nature of the incompressible flow equations means that specific mathematical techniques have been devised to solve them.

The equation of state is an important input into the flow equations.

To use the data from the phones, the researchers and graduate students on the project had to develop new methods of solving the flow equations.

When applied in the flow equations, they should be valid independent of the particular value of ε.

Then the flow equations become, for an incompressible steady flow:

However in general the Ricci flow equations lead to singularities of the metric after a finite time.

The calculation of the pressure drop along the individual pipes of a gas network requires use of the flow equations.

The exact flow equation for has a one-loop structure.

As the sliding scale is lowered, the flowing action evolves in the theory space according to the functional flow equation.

Therefore, to calculate net forces on bodies (such as wings) we should use viscous flow equations.