I am running a simulation of fluid in a pipe.
The fluid in this pipe is "swirling" (instead of just moving in one direction, it's rotating as well. Like the Helix below.
The fluid is faster on the edges of the pipe. The z direction is the flow of the fluid. X and Y are the fluid flowing.
The Fluid on the edge is moving faster because of an external motor. This adds an extra velocity component to the fluid, particularly the portion of the fluid away from the center. In the plot below the tangential velocity vs. the radius is shown. In the plot you can see the velocity rising as it moves away from the center.
With this plot, I am trying to calculate the Kinetic Energy of the fluid, excluding pressure. Originally, I planned on putting these values into a matrix, summing them, then diving by the number of elements in the matrix. I am not sure if this the appropriate way to get the "overall velocity" to use to find kinetic energy.
What is the appropriate way to calculate the kinetic energy of this fluid?