Fluid Flow Field

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A Fluid Flow Field is a physical field associated with a region around a flowing fluid.

  • Context:
  • Example(s):
    • The flow of a fluid can be considered as a constant vector field. Mathematically the field can be represented as [math]\displaystyle{ V=\hat{i}+\hat{j} }[/math].Here [math]\displaystyle{ i }[/math] and [math]\displaystyle{ j }[/math] are the unit vectors along x-axis and y-axis respectively. This is a constant vector field where each vector is of magnitude [math]\displaystyle{ \sqrt{2} }[/math] and direction [math]\displaystyle{ 45^o }[/math]angle with respect to x-axis.
    • Rotational field: A fluid flow field is said to be rotational if every particle of the fluid rotates at a particular velocity. An example of a 2D rotational field mathematically can be [math]\displaystyle{ \vec{V}(x,y) = -y\hat{i}+x\hat{j} }[/math] such that [math]\displaystyle{ x^2 +y^2=1 }[/math]. Here all the vectors are of unit magnitude and all possible direction but the starting point of a vector is the point on the circle [math]\displaystyle{ x^2 +y^2=1 }[/math].
    • Velocity field: The fluid flow field can be a velocity field if velocity of fluid particles are distributed in a given region R.Mathematically a velocity field can be represented as [math]\displaystyle{ \vec{V}(x,y,z,t) = u(x,y,z,t)\hat{i}+v(x,y,z,t)\hat{j}+w(x,y,z,t)\hat{k} }[/math] where x,y and z are the three co-ordinates of the 3D-Space and t is the time.
  • Counter-Example(s):
  • See: Hydrodynamic Stability, Dermal Denticle, Kammback, Spoiler (Aeronautics), Fluid Mechanics, Fluid, Liquid, Gas, Aerodynamics, Hydrodynamics.


References

2015


  • (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Fluid_dynamics#Steady_vs_unsteady_flow Retrieved:2015-11-30.
    • When all the time derivatives of a flow field vanish, the flow is considered steady flow. Steady-state flow refers to the condition where the fluid properties at a point in the system do not change over time. Otherwise, flow is called unsteady (also called transient [1]). Whether a particular flow is steady or unsteady, can depend on the chosen frame of reference. For instance, laminar flow over a sphere is steady in the frame of reference that is stationary with respect to the sphere. In a frame of reference that is stationary with respect to a background flow, the flow is unsteady. Turbulent flows are unsteady by definition. A turbulent flow can, however, be statistically stationary. According to Pope: [2]

      This roughly means that all statistical properties are constant in time. Often, the mean field is the object of interest, and this is constant too in a statistically stationary flow.

      Steady flows are often more tractable than otherwise similar unsteady flows. The governing equations of a steady problem have one dimension fewer (time) than the governing equations of the same problem without taking advantage of the steadiness of the flow field.

  1. Transient state or unsteady state?
  2. See Pope (2000), page 75.

1989

1987

  • (Brown, 1987) ⇒ Stephen R. Brown. (1987). “Fluid Flow through Rock Joints: The Effect of Surface Roughness.” In: Journal of Geophysical Research: Solid Earth (1978–2012) 92, no. B2