One, Two and Three Dimensional Fluid Flows

In fluid mechanics, there are various classifications of fluid flows such as steady and unsteady flows, laminar or turbulent flows, or compressible or incompressible flows. One of these classifications is the one or two-dimensional fluid flow. Here we explain how to assume fluid flows according to the number of dimensions. 

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What is Three-Dimensional Fluid Flow?

Firstly, we determine fluid flows according to the number of dimensions where the flow characteristics change. In general, we use cylindrical or cartesian coordinate systems. In their coordinate systems, there are three elements to show an object in 3D space. 

If we show a fluid flow with three dimensions in these coordinate systems, we characterize the fluid flow by three-dimensional. Most of the fluid flow regimes are three-dimensional in general. For example, we characterize fluid flow around a wind turbine by three-dimensional fluid flow in which all the fluid characteristics change in every direction of the coordinate system. 

One dimensional flow.
Image Source: Theteche.com.

What is Two-Dimensional Flow?

Two-dimensional flow is the type of flow where we make the flow characterization with the two elements of coordinate systems. There are some examples where the fluid flow that we can describe in two dimensions. For example, we can model fully developed fluid flow in a pipe in two dimensions. Because of the general flow that we can show by the dimension where we show along the pipe and the cross-section of the pipe. We do not require the cross-section in the second view. Because the flow characteristics are the same in this direction. 

What is One-Dimensional Flow?

In one-dimensional flow regimes, there is no need for the second and third dimensions in general. For example, we can model the same fully developed fluid flow in a pipe in a one-dimensional fluid flow model in a cylindrical coordinate system. Only the flow direction can be given in the cylindrical coordinate systems. 

Conclusion

These are the general classification of the fluid flows according to their number of dimensions. In general, the dimensions of the flow depending on the selection of a correct coordinate system and the correct assumption by the engineer. 

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