Steady and Unsteady Flows

We have noted previously (see Velocity Field ) that velocity, pressure and other properties of fluid flow can be functions of time (apart from being functions of space). If a flow is such that the properties at every point in the flow do not depend upon time, it is called a steady flow. Mathematically speaking for steady flows,

$${\partial P \over {\partial t}}=0$$ (3.4)

where P is any property like pressure, velocity or density. Thus,

$$P~=~P(x,y,z)$$ (3.5)

Unsteady or non-steady flow is one where the properties do depend on time.

It is needless to say that any start up process is unsteady. Many examples can be given from everyday life- water flow out of a tap which has just been opened. This flow is unsteady to start with, but with time does become steady.

Some flows, though unsteady, become steady under certain frames of reference. These are called pseudosteady flows. On the other hand a flow such as the wake behind a bluff body is always unsteady.

Unsteady flows are undoubtedly difficult to calculate while with steady flows, we have one degree less complexity.

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney