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A flow that is not a function of time is called steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Time dependent flow is known as unsteady (also called transient [8]). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference.
the flow must be steady, that is, the flow parameters (velocity, density, etc.) at any point cannot change with time, the flow must be incompressible—even though pressure varies, the density must remain constant along a streamline; friction by viscous forces must be negligible.
In a steady flow of an inviscid fluid without external forces, the center of curvature of the streamline lies in the direction of decreasing radial pressure. Although this relationship between the pressure field and flow curvature is very useful, it doesn't have a name in the English-language scientific literature. [25]
The equations governing the Hagen–Poiseuille flow can be derived directly from the Navier–Stokes momentum equations in 3D cylindrical coordinates (r,θ,x) by making the following set of assumptions: The flow is steady ( ∂... / ∂t = 0). The radial and azimuthal components of the fluid velocity are zero ( u r = u θ = 0).
A steady state flow process requires conditions at all points in an apparatus remain constant as time changes. There must be no accumulation of mass or energy over the time period of interest. The same mass flow rate will remain constant in the flow path through each element of the system. [3]
While the fluid mechanics of the original flow are unsteady when >, the new flow, called Taylor–Couette flow, with the Taylor vortices present, is actually steady until the flow reaches a large Reynolds number, at which point the flow transitions to unsteady "wavy vortex" flow, presumably indicating the presence of non-axisymmetric instabilities.
The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. [ 1 ] [ 2 ] This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.
An example of convection. Though the flow may be steady (time-independent), the fluid decelerates as it moves down the diverging duct (assuming incompressible or subsonic compressible flow), hence there is an acceleration happening over position.