# Wind speed question

1. Sep 26, 2004

### ScienceGirl502

i have calculated volume and weight from different size hailstones.
i now have to calculate the wind speed needed to keep a hailstone of each size aloft.
i am stuck on which equation to use...
should i solve using
D = 1/2(C*rho*A*v^2) ?

for rho do i plug in the density of air or of each hailstone?

i can only get as far as plugging in values for
(drag coefficient) C=.5 and A for each respective hailstone.

thanks!

2. Sep 26, 2004

### Tide

That would be the density of air but I don't see how the wind will keep a hailstone aloft unless the wind is directed upward.

3. Sep 26, 2004

### ScienceGirl502

we were given a hint: your calculations will involve the weight of the hailstone and the upward force of wind on the hailstone.

4. Sep 26, 2004

### Tide

Okay, so it's an updraft!

You can calcuate the drag force on the hailstone and compare it with the weight of the hailstone.

5. Sep 26, 2004

### ScienceGirl502

i have an answer D = 1.40

the units that don't cancel out are gram/sec

D = 1.40 grams/second?

i can't find a unit for D anywhere...is this acceptable?

6. Sep 26, 2004

### Tide

Use
$$mg = \frac {1}{2} C \rho A v^2$$
to find the speed. The units should work out.

7. Sep 26, 2004

### ScienceGirl502

thank you SOOOOOOOOOO much!

8. Sep 27, 2004

### ScienceGirl502

would that answer be the wind speed of the terminal velocity of the hailstone?
thanks!

9. Sep 27, 2004

### Tide

Exactly!

10. Sep 27, 2004

### ScienceGirl502

this is really confusing...the 1st question was "for each size hailstone, calculate the wind speed needed to keep a hailstone of that size aloft...hint--your calculations will involve the weight of the hailstone and the upward force of wind on the hailstone."

and then a few questions later it asks: "hailstones typically reach terminal velocity before they hit the ground. Find the terminal velocity of the hailstones. hint--finding the terminal velocity of the stones is easy if you've completed the 1st question"

is it possible that these questions are asking for the same thing?

:uhh:

thanks!

11. Sep 27, 2004

### NateTG

Perhaps the two are related. Does a hailstrone at terminal velocity have net acceleration? Is there a net force acting on it? What about a hailstone that is held aloft?

12. Sep 27, 2004

### ScienceGirl502

i think i solved for terminal velocity with the equation that tide gave me.

the first question should be solved by Fdrag = -1/2 CpAv^2 to get the air drag.

right?

13. Sep 27, 2004

### NateTG

Yes, but you should be able to see similarities between the two problems.

Perhaps you could consider the terminal velocity problem from the hailstone's reference frame?

14. Sep 27, 2004

thank you!