Calculating Terminal Velocity in a Fluid

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SUMMARY

The discussion focuses on calculating the terminal velocity of a 1.5-mm-diameter steel ball bearing dropped into SAE 30 oil. Key parameters include the oil's density (917 kg/m³) and viscosity (0.26 kg/(m·s)). The relevant equations discussed are the drag force equations and the Reynolds number, which is essential for determining the coefficient of drag. The user seeks clarification on combining equations and understanding the forces acting on the ball bearing to find the terminal velocity accurately.

PREREQUISITES
  • Understanding of fluid dynamics principles, particularly drag force calculations.
  • Familiarity with the concept of Reynolds number and its significance in fluid flow.
  • Knowledge of the properties of fluids, including density and viscosity.
  • Basic algebra skills for manipulating equations and solving for variables.
NEXT STEPS
  • Study the derivation and application of the drag force equations in fluid dynamics.
  • Learn how to calculate Reynolds number and its implications for different flow regimes.
  • Explore the relationship between terminal velocity and the forces acting on objects in fluids.
  • Investigate the differences between various drag force equations and their applicable scenarios.
USEFUL FOR

Students in physics or engineering courses, particularly those focusing on fluid mechanics, as well as professionals involved in fluid dynamics simulations and calculations.

jldavid
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Homework Statement


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!


Homework Equations



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)

The Attempt at a Solution



When I combine all the equations, the v's cancel out. Is there a different equation I should be using?
 
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jldavid said:
When I combine all the equations, the v's cancel out. Is there a different equation I should be using?

Could you clarify this comment? Why do you "combine all the equations"?

The terminal velocity is attained when the net force on the ball in the fluid is zero. What are the forces on the ball bearing? Incidentally, you have two different drag force laws there: what situations do they correspond to and which is applicable to this problem?
 

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