Calculating Wind Speed Needed To Keep Hailstones Aloft

[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!

 

[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.

 

[ScienceGirl502]

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

 

[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.

 

[ScienceGirl502]

i have an answer D = 1.40

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

is my answer for D
D = 1.40 grams/second?

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

 

[Tide]

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

 

[ScienceGirl502]

thank you SOOOOOOOOOO much!

 

[ScienceGirl502]

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

 

[Tide]

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

Exactly!

 

[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?



thanks!

 

[NateTG]

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

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?

 

[ScienceGirl502]

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?

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?

 

[NateTG]

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?

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?

 

[ScienceGirl502]

thank you!