Drag Force Equation: Sphere vs 1/2pv^2C_dA

[xphysics]

Homework Statement

Hi, i have a peculiar question after watching MIT lecture:http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-12/

What is the difference between the equation representing the drag force for a sphere: C(sub1)rv+C(sub2)r^(2)v^(2) and this drag force equation: (1/2)pv^(2)C(sub d)A

Homework Equations

The Attempt at a Solution

 

[lightgrav]

viscous resistance is proportional to velocity (1st term), drag resistance is proportional to v² (2nd term).
at very slow speeds, the viscous term is larger ... at high speeds, the drag term dominates.

 

[xphysics]

But why are there 2 different equation? Why didn't prof. WL just use the drag force one?Sent from my iPhone using Physics Forums

 

[haruspex]

But why are there 2 different equation? Why didn't prof. WL just use the drag force one?

It is very well explained in the lecture that C₁rv+C₂r²v² is the general equation, but if you are in a regime where one of those terms is very much larger than the other then you can omit the smaller term. If that doesn't answer your question, please specify the section of the video (minutes from start) that's puzzling you.

 

[xphysics]

I completely understand the lecture it's just that the equation represents the total resistive force on the object and I have a question on how is that equation(from the lecture) is different from the drag equation(google it) since they both shows the resistive force(if I'm correct)

 

[haruspex]

I completely understand the lecture it's just that the equation represents the total resistive force on the object and I have a question on how is that equation(from the lecture) is different from the drag equation(google it) since they both shows the resistive force(if I'm correct)

Perhaps you're not reading the fine print. E.g. http://en.wikipedia.org/wiki/Drag_equation:

The formula is accurate only under certain conditions: the objects must have a blunt form factor and the fluid must have a large enough Reynolds number to produce turbulence behind the object.

http://en.wikipedia.org/wiki/Drag_%28physics%29:

The drag coefficient depends on the shape of the object and on the Reynolds number:

where the Reynolds number depends on the speed (linearly). I.e. the linear term of the full equation has been hidden inside the drag coefficient.

At low Reynolds number, the drag coefficient is asymptotically proportional to the inverse of the Reynolds number, which means that the drag is proportional to the speed.