Hatrack River Writers Workshop Post New Topic  Post A Reply
my profile login | register | search | faq | forum home

  next oldest topic   next newest topic
» Hatrack River Writers Workshop » Forums » Open Discussions About Writing » Math help

   
Author Topic: Math help
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
I need to know if my calculations are as off as I suspect. I am looking for the amount of gallons of water falls from a cloud when the yield is two inches for a two square mile area.
The answer I am getting is in the hundreds of billions. For some reason that seems like a bit too much.

Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Make sure to check me, because I'm not great at this stuff, but I get about 69,514,971.


square inches in a square mile = 4,014,489,600
http://wiki.answers.com/Q/How_many_square_inches_are_in_a_square_mile

x 2 miles

x 2 inches

Divided by square inches in a gallon = 231
http://wiki.answers.com/Q/How_many_square_inches_in_a_gallon


Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
Thanks Betsy but I believe when you calculate 2 square miles it isn't...

4,014,489,600 inches

times 2

I believe 2 square miles is an area of four miles, therefore the area is exponetionally increased so the equation may be...

4,014,489,600 inches squared

Which also means that the 2 inches of depth would cube the problem.

My figures reach 500 billionish gallons which sounds like a very lot. Anyone out there can let me know where and if I got this wrong?


Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
BenM
Member
Member # 8329

 - posted      Profile for BenM   Email BenM         Edit/Delete Post   Reply With Quote 
I'd have expected a square area of two miles on each side to be four square miles. Ie, two miles squared = four square miles.

The confusion perhaps stemming from your original question, in which you asked regarding an area of two square miles?

http://en.wikipedia.org/wiki/Square_mile

[editing to add, since I didn't cotton on to the other part of your question and want to avoid a double-post]
2 inches of depth would cube the problem
No, depth is one dimension, so you only multiply in that one dimension, ie 1 inch becomes 2, so the volume is multiplied by two.

may be.../4,014,489,600 inches squared
There's 4,014,489,600 "square inches" in a "square mile". The square inches is a unit of measurement - if you were to square it again you'd end up with some strange 4-dimensional unit of measurement. Instead, you want to end up with cubic inches, by adding 1 extra dimension.

Since a depth of 1 inch means multiplying by x1, then a 1 inch depth gives 4,014,489,600 cubic inches per square mile. Multiply by 2 for 2 inch depth (since, logically, there is twice the volume)

Then multiply by the number of square miles (2 or 4, depending on what you work out), and you've got the number of cubic inches. Again using Betsy's figures, divide by 231 for gallons, and the biggest number you're going to arrive at with these figures is 139 million gallons.

[This message has been edited by BenM (edited June 29, 2009).]


Posts: 920 | Registered: Nov 2008  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
Thanks Ben but one problem that I have with Wikipedias answer of 231 square inches to a gallon is it can't be correct. A square inch has no depth. A gallon is a three dimensional measurement. Should I assume the correct answer to be 231 cubic inches instead?

Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
BenM
Member
Member # 8329

 - posted      Profile for BenM   Email BenM         Edit/Delete Post   Reply With Quote 
Ah I see - yes, that must have been a typo. There are 231 cubic inches in a gallon.

(see also this google query)


Posts: 920 | Registered: Nov 2008  |  IP: Logged | Report this post to a Moderator
Kathleen Dalton Woodbury
Administrator
Member # 59

 - posted      Profile for Kathleen Dalton Woodbury   Email Kathleen Dalton Woodbury         Edit/Delete Post   Reply With Quote 
Yes, 231 cubic inches to a gallon.
Posts: 8541 | Registered: A Long Time Ago!  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Ahhh...Now I'm remembering why I always ditched math class. All those little rules that come back to bite you in the ***.

Way to save the day, BenM.


Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
Thanks Ben and Betsy.

140 million gallons of water sounds like a lot but plausible.

500 billion gallons of water sounds like Lake Michigan. A bit much to fall from a rain cloud.


Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
micmcd
Member
Member # 7977

 - posted      Profile for micmcd   Email micmcd         Edit/Delete Post   Reply With Quote 
With respect to the # gallons in Lake Michigan: according to an arbitrarily unreliable source (the internets) there are 1.3 * 10^15 gallons of water in Lake Michigan.

So, 500 billion is:
500,000,000,000 (if you're American)
500,000,000,000,000 (if you're European... and either-or if you're Canadian)

1.3*10^15 is
130,000,000,000,000

So snapper is either way under or way over, depending on where he is from. The profile says Michigan, so I'm leaning towards the former.

As a way of comparison to the calculation, 140 million... well:
140,000,000
It's six orders of magnitude smaller than a Great Lake, if that helps.


[This message has been edited by micmcd (edited July 01, 2009).]

[This message has been edited by micmcd (edited July 01, 2009).]

[This message has been edited by micmcd (edited July 01, 2009).]


Posts: 500 | Registered: May 2008  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
Thank you very much.

I am just trying to figure out how much rain falls would fall on a roughly two-mile square area if the yield was 2 inches for a sci-fi story that I am writing. I don't want to have a ridiculous figure, plausibility is very important in a hard sci-fi story.


Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
DWD
Member
Member # 8649

 - posted      Profile for DWD   Email DWD         Edit/Delete Post   Reply With Quote 
If I'm understanding correctly, another way to ask this is "How many gallons of water would fill a rectangular container that is 1 mile long by 2 miles wide by 2 inches deep?"

If so, the answer is 69,514,971.4286 gallons.

There's a calculator here that will give you the answer in all sorts of measures (even teaspoons: 17,795,832,685.7).

One mile = 63,360 inches, so the inputs are

63,360 inches length
126,720 inches width
2 inches height

BTW, .004328 gallons of water will fit in a 1-inch cube.

So I think Betsy is the winner.

[This message has been edited by DWD (edited July 01, 2009).]


Posts: 88 | Registered: Jun 2009  |  IP: Logged | Report this post to a Moderator
DWD
Member
Member # 8649

 - posted      Profile for DWD   Email DWD         Edit/Delete Post   Reply With Quote 
Oh, and, in case we're actually talking about "miles square" and not "square miles" (2 miles square is 4 square miles), then the answer is 139,029,942.857, as BenM calculated.

If I say "Two inches of rain fell over a two-square-mile area," though, that's a 1 mile X 2 mile rectangle, not a 2 X 2 mile square.

[This message has been edited by DWD (edited July 01, 2009).]


Posts: 88 | Registered: Jun 2009  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Thanks, sweetie!

I'd love to take the crown, but I can't promise anyone that I wouldn't have done the same calculation if snapper had put "two miles squared" instead of "two square miles." I like to think I would have, but like I said...I was home watching One Life to Live through most of high school.

Shall we make BenM the winner?


Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Jinx. (I think a three minute difference still counts in the posting world.)
Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
DWD
Member
Member # 8649

 - posted      Profile for DWD   Email DWD         Edit/Delete Post   Reply With Quote 
LOL
Posts: 88 | Registered: Jun 2009  |  IP: Logged | Report this post to a Moderator
DWD
Member
Member # 8649

 - posted      Profile for DWD   Email DWD         Edit/Delete Post   Reply With Quote 
But wait: We may not be done here!!! Snapper, by "yield" did you mean total rainfall or runoff?
Posts: 88 | Registered: Jun 2009  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
Total run off and the calculation was a rectangle that was

2 miles long by 2 miles wide by 2 inches high

140 million gallons is close enough for me.


Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
DWD
Member
Member # 8649

 - posted      Profile for DWD   Email DWD         Edit/Delete Post   Reply With Quote 
Can you tell I'm trying to avoid writing? I seem to have hit nothing but endless dialogue today. Very tiring to me.

Was just thinking the actual runoff would be less depending on the prior level of saturation of the soil, soil retention capacity (soil type), evaporative loss back into the air, etc. Geez--I'll shut up and get back to work now, because I have no idea how you'd calculate that, and you could probably care less.

But for some reason it seems really, really interesting to me right now.

"Oh? How interesting?"

He thought for a moment. "About as interesting, I'd say, as anything I've ever looked at when trying to avoid doing something else."

... Um... sorry. Wrong window.


Posts: 88 | Registered: Jun 2009  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Oh my god, tell me about it. I keep clicking refresh on the MATH THREAD. Same for my email and facebook. I don't even like facebook. Geez.

Only, I just finished my dialog and have to do all that other stupid stuff. I hate transitions from one scene to another.



Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
BenM
Member
Member # 8329

 - posted      Profile for BenM   Email BenM         Edit/Delete Post   Reply With Quote 
I keep reading the thread but trying to avoid posting (unsuccessfully this time) as it's a confirmation that I'm procrastinating.

In interesting trivia:
In meteorological measurement, 2 inches of rainfall is the same amount of rainfall regardless of whether it falls over 2 square miles or 2 square feet or into a cup.
Hurricane Katrina dropped 15 inches of rainfall at one location, and 2 inches of rainfall in 20 other states.


Posts: 920 | Registered: Nov 2008  |  IP: Logged | Report this post to a Moderator
snapper
Member
Member # 7299

 - posted      Profile for snapper   Email snapper         Edit/Delete Post   Reply With Quote 
(okay, snap. Give'm what they want)

You know the evaporating rate and drainage equation may come in handy. Let me see...

My story involves a machine that evaporates sea water at an excelerated rate with a microwave beam on a blimp from a thousand feet. I am concerned that a microwave will lose its effectiveness at such a height.
Another problem I have is the blimp is used as sort of a magnet for water vapor. 140 million gallons of water is a lot. As a gas it is weightless but still has mass. If there wasn't any factors moving the cloud wouldn't be any problem but wind is always present. So at what windspeed would it be impossible to drive a cloud if the wind is blowing in a direction that runs counter to the way the blimp wants to go? 30 mph? 10? 2?


Posts: 3072 | Registered: Dec 2007  |  IP: Logged | Report this post to a Moderator
BenM
Member
Member # 8329

 - posted      Profile for BenM   Email BenM         Edit/Delete Post   Reply With Quote 
I think my brain just exploded.
Posts: 920 | Registered: Nov 2008  |  IP: Logged | Report this post to a Moderator
Betsy Hammer
Member
Member # 8139

 - posted      Profile for Betsy Hammer   Email Betsy Hammer         Edit/Delete Post   Reply With Quote 
Seriously. I was just staying to chat.
Posts: 316 | Registered: Aug 2008  |  IP: Logged | Report this post to a Moderator
rstegman
Member
Member # 3233

 - posted      Profile for rstegman   Email rstegman         Edit/Delete Post   Reply With Quote 
quote:
snapper
Member posted July 01, 2009 09:58 PM
--------------------------------------------------------------------------------
(okay, snap. Give'm what they want)
You know the evaporating rate and drainage equation may come in handy. Let me see...

My story involves a machine that evaporates sea water at an excelerated rate with a microwave beam on a blimp from a thousand feet. I am concerned that a microwave will lose its effectiveness at such a height.
Another problem I have is the blimp is used as sort of a magnet for water vapor. 140 million gallons of water is a lot. As a gas it is weightless but still has mass. If there wasn't any factors moving the cloud wouldn't be any problem but wind is always present. So at what windspeed would it be impossible to drive a cloud if the wind is blowing in a direction that runs counter to the way the blimp wants to go? 30 mph? 10? 2?


I did a google and landed on this site
http://ask.reference.com/related/Blimp+Speed?qsrc=2892&l=dir&o=10601
It says the top speed is 35 mpg, though one can go a lot faster.
The technology involved may allow a lot faster speeds. Consider using jets instead of props. One might use a duragable instead if you want good speeds.

Are they seeding existing clouds or adding moisture to the air to create clouds? the general humidity levels will make a difference.
Also the land will have an effect. A large water source such as the great lakes or the everglades will add to the moisture and then cause rain there. Hills and mountains will cause the air to go up condense and rain down.
Two inches of rain will not stay put. In the everglades, the water moves at a half mile a day.
As mentioned before, evaporation and seeping into the land will effect the final result.
The land structure will also have an effect. the rain will flow downhill. That usually results in ditches, channels and rivers, along with lakes.
The rate of rainfall makes a diference too. Over a whole day will have a different effect than in an hour.
where the rain falls makes a difference. Over the entire area will have a different effect than at the base of the mountains.

Just some things to think about.


Posts: 1005 | Registered: Feb 2006  |  IP: Logged | Report this post to a Moderator
sjsampson
Member
Member # 8075

 - posted      Profile for sjsampson   Email sjsampson         Edit/Delete Post   Reply With Quote 
I don't know what kind of cloud your blimp is trying to control, so...

I'm assuming since you have a blimp and a cloud it's not nimbostratus.

A single thunderstorm can drop about 125 million gallons of water
http://www.osen.org/Technologies/Lightning/tabid/194/Default.aspx
As a meteorologist, I would have a hard time believing your blimp could control a thunderstorm. Storm dynamics being what they are, I'm not sure with all the environmental factors if I'd believe your blimp could even control a smaller rain cloud, but I'll pretend for now.

So I'll assume you are creating a smaller cumulonimbus. And here are some things to keep in mind:

Clouds are not only gas. Are you in the tropics? If so, you'd have a warm cloud with water droplets. If not, you'd have ice.

There is no proof that cloud seeding works. Having said that, in order to generate a cloud and rain you would need a source of condensation nuclei.

You won't be able to create a cloud without a source of vertical motion. I don't know the specifics of your blimp, but I don't think your blimp "magnet" alone is enough for that. Your water/ice particles need to collide in order to form precip.


quote:
So at what windspeed would it be impossible to drive a cloud if the wind is blowing in a direction that runs counter to the way the blimp wants to go? 30 mph? 10? 2?

I think you need to consider the role your wind is playing in the generation of this cloud before you can even hope to attempt to answer this question.



Posts: 133 | Registered: Jul 2008  |  IP: Logged | Report this post to a Moderator
   

Quick Reply
Message:

HTML is not enabled.
UBB Code™ is enabled.
UBB Code™ Images not permitted.
Instant Graemlins
   


Post New Topic  Post A Reply Close Topic   Feature Topic   Move Topic   Delete Topic next oldest topic   next newest topic
 - Printer-friendly view of this topic
Hop To:


Contact Us | Hatrack River Home Page

Copyright © 2008 Hatrack River Enterprises Inc. All rights reserved.
Reproduction in whole or in part without permission is prohibited.


Powered by Infopop Corporation
UBB.classic™ 6.7.2