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axelb

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- TL;DR Summary
- My derivation of the Reynolds number doesn't match the typical Re equation

I'm a HS student so please dumb it down. I'm looking into the Reynolds number of a sphere sinking in a fluid, and I want to determine whether my results meet creeping flow or not Re<<1, here's what I got. **sorry if I misused the prefix, I'm not sure whether it's highschool or undergraduate**

Inertial drag force = 0.5 * 0.47(CoefficientOfDragSphere) * rho(DensityOfLiquid) * pi r^2(CrossSectionalAreaSphere) * velocity^2

Viscous drag force = 6

Reynolds Number is the ratio between inertial and viscous drag forces so after simplifying it should be = (0.47(Cd) * rho(DensityOfLiquid) * velocity * r) / (12 * mu)

So then how did the equation of Reynolds number = (rho(DensityOfLiquid) * velocity * 2r) / (mu) come to be?

What happened to the 0.47, 12 and why did r multiply by 2?

What am I missing, the equations look similar but not quite, is there some sort of "super math" that I'm missing, or are my equations misused? And is my equation of Re correct? Could it be represented this way for what I want to do? Or should I just use the standard equation, and why?

Thanks,

- a confused HS student trying to write a physics essay

Inertial drag force = 0.5 * 0.47(CoefficientOfDragSphere) * rho(DensityOfLiquid) * pi r^2(CrossSectionalAreaSphere) * velocity^2

Viscous drag force = 6

*pi*r(ConstantKForSpheres) * mu * velocityReynolds Number is the ratio between inertial and viscous drag forces so after simplifying it should be = (0.47(Cd) * rho(DensityOfLiquid) * velocity * r) / (12 * mu)

So then how did the equation of Reynolds number = (rho(DensityOfLiquid) * velocity * 2r) / (mu) come to be?

What happened to the 0.47, 12 and why did r multiply by 2?

What am I missing, the equations look similar but not quite, is there some sort of "super math" that I'm missing, or are my equations misused? And is my equation of Re correct? Could it be represented this way for what I want to do? Or should I just use the standard equation, and why?

Thanks,

- a confused HS student trying to write a physics essay