Fluid Flow Field

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

• Context:
  • It can be composed of fluid particles present in the fluid defined at each and every point at any instant of time.
  • It can be represented mathematically by a Vector Field (for flow parameters like velocity and pressure).
  • It can be specified by the velocities at different points in the region at different times.
  • It can range from being a 2D Vector Field, to being a 3D Vector Field to being a k-Dimensional Vector Field.
  • It can be a constant field, rotational field or velocity field.
  • It can range from being a Steady Fluid Flow Field to being an Unsteady Fluid Flow Field.
  • …
• 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):
  • an Electric Field.
  • a Magnetic Field.
• See: Hydrodynamic Stability, Dermal Denticle, Kammback, Spoiler (Aeronautics), Fluid Mechanics, Fluid, Liquid, Gas, Aerodynamics, Hydrodynamics.

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References

2015

• (Wikipedia, 2015) ⇒ http://en.wikipedia.org/wiki/Fluid_dynamics Retrieved:2015-11-30.
  • In physics, fluid dynamics is a subdiscipline of fluid mechanics that deals with fluid flow — the natural science of fluids (liquids and gases) in motion. It has several subdisciplines itself, including aerodynamics (the study of air and other gases in motion) and hydrodynamics (the study of fluids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and modelling fission weapon detonation. Some of its principles are even used in traffic engineering, where traffic is treated as a continuous fluid, and crowd dynamics.

    Fluid dynamics offers a systematic structure — which underlies these practical disciplines — that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fluid dynamics problem typically involves calculating various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and time.

    Before the twentieth century, hydrodynamics was synonymous with fluid dynamics. This is still reflected in names of some fluid dynamics topics, like magnetohydrodynamics and hydrodynamic stability, both of which can also be applied to gases.

• (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 ). 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:

    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.

1989

• (Helman & Hesselink, 1989) ⇒ James Helman, and Lanbertus Hesselink. (1989). “Representation and Display of Vector Field Topology in Fluid Flow Data Sets." Computer 8

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

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