Dimensionless Analysis Essay
Drag is the resistance experienced when a fluid comes in contact with an object and a force is found to be opposing the motion of flow.
Dimensionless analysis is a method for reducing the number and complexity of experimental variables that affect a given physical phenomena. It is a system in which we take all the variables relevant to the situation which we are faced with and try to compare them to one another. (White, 2011)
Buckingham PI Theorem
To do this method we list the parameters we think will be relevant to our equations. We then assign the correct MLTѲ units to each variable. The number of PI groups we end up with can be determined by taking the number of dimensionless groups away from the number of variables being used.
Reynolds Number:
One of the most important experimental contributions was made by Reynolds. Osborne Reynolds found that the type of flow is
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(Hamill, 1995)
When an ideal fluid with no viscosity flows past a body, it does not exert a force on it. However when a viscous fluid flows past a body that is either partly or totally immersed in it, the fluid exerts a force on the body in the direction of flow. This is known as the drag force. A good example is the force exerted on the piers of a bridge by the water flowing past. The same argument applies if the fluid is stationary and the body is moving: a force is needed to propel an aircraft through the atmosphere. The force needed depends upon many factors including the coefficient of drag, C¬D, and the cross sectional area of the body presented to the flow, A:
ΔP/(1/2 ρu^2
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