Above what speed does a 3.1-mm-diameter ball bearing in 20∘C water experience quadratic drag?

College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Above what speed does a 3.1-mm-diameter ball bearing in 20∘C water experience quadratic drag?

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Step 1

Drag force acting on an object is always directed in the opposite direction of the velocity of the object.

If ρ is the density of water, v is the velocity of the ball, A is the ball's front area which is interacts with the water then the formula to calculate the quadratic drag is given by

FD=12CDρAv2 where CDis the drag coefficient.

Again the relationship between the drag coefficient and Reynolds number is given by

CD=24Re where Re is the Reynold's number.

Again the formula to calculate the Reynold's number is given by

Re=ρ×v×Dμ where D is the diameter of the ball and μ is the dynamic viscosity.

Note: At 20C the value of μ for water is 0.00089 Ns/m2, density of water at 20C is ~1000 kg/m3

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