Terminal Velocity Steel Ball Bearing in Oil

AI Thread Summary
To determine the terminal velocity of a 1.5-mm-diameter steel ball bearing in SAE 30 oil, the relevant equations involve the forces of drag and gravity. The drag force can be expressed using the drag coefficient, fluid density, and the sphere's cross-sectional area. The Reynolds number is crucial for calculating the drag coefficient, but the user is struggling with the algebra as the velocity variable cancels out in their calculations. Suggestions for alternative approaches or equations to solve for terminal velocity are requested. Clarification on the correct method to integrate these equations is needed to find the terminal velocity accurately.
jldavid
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A 1.5-mm-diameter steel ball bearing (7830 kg/m^3) is dropped into a tank of SAE 30 oil. What is its terminal velocity?

The density of oil is 917kg/m^3, and the viscosity of oil is 0.26kg/(m*s).

Help is much appreciated!
 
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What have you tried so far?

Where are you stuck?
 
Force of drag = 1/2 * (density of fluid) * (area of sphere) * v^2 * (coefficient of drag)
Force of drag = 3 * pi * (coefficient of fluid) * (diameter of obj) * v

Coefficient of drag = 24 / (Reynolds number)

Reynolds number = (density of fluid * velocity of fluid * chracteristic length)/(viscosity of fluid)

When I combine the equations, v cancels out so I cannot solve for it. Is there another equation I should be using?
 

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