Drag Coeffecient and Reynolds Number. HELP!

  • #1

Homework Statement



From dimensional analysis it is found that the drag force F that a fluid (density ρ, viscosity μ) exerts on a sphere (diameter d) moving through a fluid at a velocity u is given by

cD = f(Re),

where
.
The table below gives the relationship between the drag coefficient cD and the Reynolds number Re for spheres.

Re 10-1 100 101 102 103 104 105
cD 240 26.5 4.10 1.07 0.46 0.40 0.41

A spherical steel ball falling through a large expanse of oil attained a terminal velocity of 3.7 m s-1. What was the diameter of the steel ball?
Data: density of steel = 7800 kg m-3, density of oil = 920 kg m-3, viscosity of oil = 0.23 Pa s.

Homework Equations



Obviously F=ma=ρV * a
Everything else is provided in the question except the sphere's diameter.

The Attempt at a Solution



I had a method of equating both equations to "D" (diameter) since it is the variable which we wish to solve for. However, my lecturer told me I would only find the correct solution using one of the data point, which means this method is not efficient and won't get me any points. HELP please.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
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4,866

Homework Statement





From dimensional analysis it is found that the drag force F that a fluid (density ρ, viscosity μ) exerts on a sphere (diameter d) moving through a fluid at a velocity u is given by

cD = f(Re),

where
.
The table below gives the relationship between the drag coefficient cD and the Reynolds number Re for spheres.

Re 10-1 100 101 102 103 104 105
cD 240 26.5 4.10 1.07 0.46 0.40 0.41

A spherical steel ball falling through a large expanse of oil attained a terminal velocity of 3.7 m s-1. What was the diameter of the steel ball?
Data: density of steel = 7800 kg m-3, density of oil = 920 kg m-3, viscosity of oil = 0.23 Pa s.

Homework Equations



Obviously F=ma=ρV * a
Everything else is provided in the question except the sphere's diameter.

The Attempt at a Solution



I had a method of equating both equations to "D" (diameter) since it is the variable which we wish to solve for. However, my lecturer told me I would only find the correct solution using one of the data point, which means this method is not efficient and won't get me any points. HELP please.

Homework Statement





Homework Equations





The Attempt at a Solution


The sphere attaining a terminal velocity means that it is not accelerating, and a = 0. There are three forces acting on the sphere that are in equilibrium when the terminal velocity is attained. What are these three forces?
 

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