Terminal velocity with Reynods# and Drag Coeff.

[joe3]

Hi guys I've been reading on the boards for a few days now and everyone here seems really helpful, so I've decided to come and ask for some guidence on a problem I've been having

Homework Statement

I have to find the terminal velocity of a smooth wooden ball.
rho(ball)=420 kg/m^3
rho(air)=1.1614kg/m^3
mu=1.846x10^-5 N-s/m^2
dia(ball)=.2m

Homework Equations

I am given a table of about 25 reynolds numbers and drag coeff values, i can post them if it is necessary

The Attempt at a Solution

My approach was to use the terminal velocity equation

mg=(.5)(rho of ball)(v)^2(A)(drag coeff)

to guess a value for the velocity, then calculate the drag coeff, then use my guessed velocity to calculate reynolds number using

Re=[(rho ball)(v)(dia ball)]/mu

Then my plan was to take my calculated reynolds number(which i hoped was the same as one of the reynolds numbers in my given table) and then take the corresponding drag coeff and see if it matched my calulated drag coeff, and if it i would know that the guess i made for the terminal velocity was correct. But i cannot get this approach to work, my calulated Re values are much larger than my table values. Any suggestions?

 

[PhanthomJay]

Hi guys I've been reading on the boards for a few days now and everyone here seems really helpful, so I've decided to come and ask for some guidence on a problem I've been having

Homework Statement

I have to find the terminal velocity of a smooth wooden ball.
rho(ball)=420 kg/m^3
rho(air)=1.1614kg/m^3
mu=1.846x10^-5 N-s/m^2
dia(ball)=.2m

Homework Equations

I am given a table of about 25 reynolds numbers and drag coeff values, i can post them if it is necessary

The Attempt at a Solution

My approach was to use the terminal velocity equation

mg=(.5)(rho of ball)(v)^2(A)(drag coeff)

to guess a value for the velocity, then calculate the drag coeff, then use my guessed velocity to calculate reynolds number using

Re=[(rho ball)(v)(dia ball)]/mu

Then my plan was to take my calculated reynolds number(which i hoped was the same as one of the reynolds numbers in my given table) and then take the corresponding drag coeff and see if it matched my calulated drag coeff, and if it i would know that the guess i made for the terminal velocity was correct. But i cannot get this approach to work, my calulated Re values are much larger than my table values. Any suggestions?

Your terminal velocity equation is incorrect. What densiy (and what area) should you be using?

 

[m2003]

Hello there! It's great to see you using the forums for help with your problem. It sounds like you're on the right track, but there may be some errors in your calculations. Let's break down the steps and see if we can identify where the issue might be.

First, let's double check your terminal velocity equation. It should be mg=(.5)(rho of air)(v)^2(A)(drag coeff), since the drag force is caused by the air, not the ball. Also, make sure you are using the correct values for the density of air and the area of the ball (pi * (diameter/2)^2).

Next, let's look at your approach for guessing the velocity. It's important to remember that the terminal velocity is the maximum velocity that the object will reach, so your guess should be a high value to start with. Also, make sure you are using consistent units throughout your calculations.

Now, for the Reynolds number. It seems like you are using the correct formula, but make sure you are using the correct values for the density and viscosity of air, and the diameter of the ball.

Finally, when comparing your calculated Reynolds number to the values in the table, make sure you are using the same units. It's also possible that your calculated value may not exactly match any of the values in the table, but it should be close.

If you're still having trouble, it may be helpful to post your calculations and the table of values so we can take a closer look. Keep in mind that the drag coefficient can vary depending on the shape and surface of the object, so it's possible that your calculated value may not match perfectly with any of the values in the table.

I hope this helps guide you in the right direction. Good luck with your problem!