Differential Relations to Fluid Flow

in #steemstem6 years ago

The Acceleration Vector For a Particle

The purpose of the following is to determine the acceleration of a particle over time in a flow field based on its 3 dimensional vector.


Image from the National Committee for Fluid Mechanics: Illustrate the Eulerian

Find the total Acceleration For Vector V:

V = 3ti + xzj + ty^2
part 1.jpg

Part 1 & Part 2

Find the partial derivatives (w.r.t. x, y ,z, & t) of the convective terms of the combined acceleration vector.
part 2.jpg

Part 3

Combine all four terms into the single , "total" or "substantial" derivative.
Part 3.jpg

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lol, Yeah does my head in too. Needless to say it is hard to keep followers, I will have some stuff, if you are interested in boats, from time to time. Oh thanks for leaving a comment and a vote too, i need all I can get. :)