Terminal Velocity Steel Ball Bearing in Oil

In summary, the conversation is about finding the terminal velocity of a 1.5-mm-diameter steel ball bearing dropped into a tank of SAE 30 oil with a density of 917kg/m^3 and a viscosity of 0.26kg/(m*s). The equations for force of drag, coefficient of drag, and Reynolds number are discussed, but the person is stuck because the velocity cancels out and they are unsure of which equation to use. They are seeking help in finding the correct equation to solve for the terminal velocity.
  • #1
jldavid
3
0
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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  • #2
What have you tried so far?

Where are you stuck?
 
  • #3
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?
 

1. What is the concept of terminal velocity?

The concept of terminal velocity refers to the maximum speed that an object can reach when it is falling through a fluid, such as air or oil. This is due to the balance between the force of gravity pulling the object down and the resistance of the fluid pushing against it.

2. How does a steel ball bearing behave in oil?

A steel ball bearing in oil will experience a similar concept of terminal velocity as described above. As the ball bearing falls through the oil, it will reach a point where the force of gravity pulling it down is equal to the resistance of the oil pushing against it. At this point, the ball bearing will reach its maximum speed, or terminal velocity, and will continue falling at a constant speed.

3. Why is it important to study the terminal velocity of steel ball bearings in oil?

It is important to study the terminal velocity of steel ball bearings in oil because it can provide insight into the behavior and properties of fluids. This information can then be applied to various industries, such as aerospace and automotive, to improve the design and functionality of products.

4. How does the viscosity of the oil affect the terminal velocity of the steel ball bearing?

The viscosity, or thickness, of the oil will affect the terminal velocity of the steel ball bearing. A higher viscosity oil will provide more resistance to the falling ball bearing, causing it to reach its terminal velocity at a slower speed. On the other hand, a lower viscosity oil will offer less resistance, resulting in a faster terminal velocity for the ball bearing.

5. Can the terminal velocity of a steel ball bearing in oil be altered?

Yes, the terminal velocity of a steel ball bearing in oil can be altered by changing certain factors. The size, shape, and weight of the ball bearing can all impact its terminal velocity. Additionally, altering the viscosity or temperature of the oil can also affect the terminal velocity. By adjusting these variables, the terminal velocity of the ball bearing can be manipulated for various purposes.

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