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## Drag (physics) derivations(See Huntley 1967)The drag equation may be derived to within a multiplicative constant by the method of dimensional analysis. If a moving fluid meets an object, it exerts a force on the object, according to a complicated (and not completely understood) law. We might suppose that the variables involved under some conditions to be the speed, density and viscosity of the fluid, the size of the body (expressed in terms of its frontal area ## Additional recommended knowledgeAlternatively, one can derive the dimensionless parameters via direct manipulation of the underlying differential equations. That this is so becomes obvious when the drag force This rather odd form of expression is used because it does not assume a one-to-one relationship. Here, There are many ways of combining the five arguments of and the drag coefficient, given by Thus the function of five variables may be replaced by another function of only two variables: where Because the only unknown in the above equation is or Thus the force is simply ρ Dimensional analysis thus makes a very complex problem (trying to determine the behavior of a function of five variables) a much simpler one: the determination of the drag as a function of only one variable, the Reynolds number. The analysis also gives other information for free, so to speak. We know that, other things being equal, the drag force will be proportional to the density of the fluid. This kind of information often proves to be extremely valuable, especially in the early stages of a research project. To empirically determine the Reynolds number dependence, instead of experimenting on huge bodies with fast-flowing fluids (such as real-size airplanes in wind-tunnels), one may just as well experiment on small models with slow-flowing, more viscous fluids, because these two systems are similar. |

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Drag_(physics)_derivations". A list of authors is available in Wikipedia. |