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Name:  Jeffrey F.
Status:  student
Age:  20s
Location: N/A
Country: N/A
Date: 2000-2001


Question:
My question concerns the force equation for air resistances, specifically, the quadratic drag equation: F=.5DrCV^2


Replies:
I developed a derivation for this equation by using the concepts presented in the development of the ideal gas laws relating pressure to the motion of the gas molecules bouncing off the container walls. However, it seemed to me that it was necessary to ignore the translational motion of the air molecules when calculating the impulse experienced by an object due to the change in momentum of the air molecules. Only when ignoring the translation motion of the air molecules does my equation integrate into the above equation.

Is the translational motion associated with the air molecules ignored in that equation? If so, how can it even be valid? When dealing with fluids on the molecular level, it is important to separate translational motion of the fluid from the random vibrations of individual molecules. The 400 m/s motion of a nitrogen molecule due to its temperature is a random vibration. Consider air without significant wind. There are just as many air molecules moving north as south, and just as fast. So long as the moving object is much slower than the vibrational speed of the molecules, the effects of vibrational motion will balance.

Any variation due viscosity is within the initial constant, C. It is not actually a constant. "C" can be anywhere from 0.4 to 1 in common situations. A slightly more viscous fluid will have a slightly higher value of C. The major effect of temperature is within the density. A higher temperature results in a lower density. The "constant" also accounts for effects such as shape of the moving object. For a given situation, however, C will be fairly constant so long as the object speed doesn't vary a great deal.

I am aware that the equation will provide a good approximation of drag when the fluid is moving slowly compared to the speed of the object.

My concern is that the motion of the air is usually much faster than the speed of an object traveling through it. At about 26 degrees Celsius, A Nitrogen molecule travels somewhere in the ball park of 400 m/s. I feel that the equation is not adequate because it does not seem to incorporate the notion that the speed of the fluid is very high. The equation also seems to ignore the viscosity of air itself.

I feel that the dynamics of a fluids are still a mystery, an I am just looking for a little insight.

It is important to realize that many equations used in science are approximations. The drag force is useful when the object moving through the air is moving much faster than the air itself. When in a fluid with a large current, a scientist must view the motion relative to the fluid. True drag is more complicated, depending on factors such as aerodynamics and temperature. The drag equation is a very good approximation if the fluid is not moving too fast or is not too thick. The equation can not be used with honey as the fluid.

Kenneth Mellendorf



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