calling all engineers
 

This question bugs me every time I double check my gallon calculations.
First, as I understand it, the conversion factor for cubic feet to gallons
is cf x 7.5 (7.5 gallons in each square foot). Isn't that right? My very
math-savvy father says it is, and I have seen it in print. Now, what I
don't understand is this: A five gallon water jug is much bigger than one
square foot. You could set a 12 inch square block right down in to one of
those, if it was open at the big end. How can this factor be correct? I
just can't wrap my brain around it. Help me, please. If you are a lurker,
and you can explain it to me, feel free to email me. Or, just come up out
of lurkdom - we'd all love to meet you.

Thanks,

Ann

Ann in Houston wrote:

A five gallon water jug is much bigger than one
square foot.

You mean, "cubic" foot. And it isn't. I just did a rough calculation
(using a sheet of 8.5"x11" paper to measure a 5gal jug because i didn't
have a ruler or tape measure).

The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)
--
derek

"Derek Broughton" wrote in message
...
Ann in Houston wrote:

A five gallon water jug is much bigger than one
square foot.

You mean, "cubic" foot.
oops! sorry - I did mean cubic.

snip


The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)
--
derek

Well, okay. I can't argue the facts since you went to the trouble to measure
it. It sure seemed close, though. I know that the water bottle also is
sort of cone shaped at the bottom. Do your calculations treat the bottle as
a full cylinder, or did you stop at the top of the neck? That could make a
real difference too. Thanks for being intrigued enough to check it out.

Here is another one:

1) A liter of water is one kilogram by definition.
2) One kilogram is 2.2 pounds.
3) A quart is 2 pounds.

4) Hence, a liter is 1.1 quarts.

Conversion charts say that a liter is 1.0566882607957349 quarts. Why
the difference?









The above includes many approximations. The real values are.

1) A liter of water is one kilogram by definition at 4C and 1 atmosphere
of pressure. But at 20C a liter of water is 0.9982 kilograms.
2) One kilogram is 2.2046 pounds.
3) A quart is 2 pounds approximately. Actually at 4C a quart of water
is 2.086 pounds. At 20C a quart of water is 2.082 pounds.

4) Hence, at 4C a liter is 1.0567 quarts and at 20C a liter is 1.0567
quarts. So the common measures we take for granted are about 5 % off.

"Stephen M. Henning" wrote:
3) A quart is 2 pounds approximately. Actually at 4C a quart of water
is 2.086 pounds. At 20C a quart of water is 2.082 pounds.

But "A pint's 1.04 pounds the world around" just doesn't have the same ring to
it :-)

"Stephen M. Henning" wrote:
3) A quart is 2 pounds approximately. Actually at 4C a quart of water
is 2.086 pounds. At 20C a quart of water is 2.082 pounds.

But "A pint's 1.04 pounds the world around" just doesn't have the same ring to
it :-)

On or about Thu, 18 Nov 2004 18:51:03 GMT, "Ann in Houston"
wrote something like:

This question bugs me every time I double check my gallon calculations.

How can this factor be correct?

You play the lottery, don't you?
--
Crashj

Crashj wrote:
On or about Thu, 18 Nov 2004 18:51:03 GMT, "Ann in Houston"
wrote something like:

This question bugs me every time I double check my gallon calculations.

How can this factor be correct?

You play the lottery, don't you?

That was uncalled for.

"Crashj" wrote in message
...
On or about Thu, 18 Nov 2004 18:51:03 GMT, "Ann in Houston"
wrote something like:

This question bugs me every time I double check my gallon calculations.

How can this factor be correct?

You play the lottery, don't you?
--
Crashj

Why? Because I'm stubborn? or math challenged? I accept the factor as
correct, but I was wishing I could picture it better. And, no, my very math
competent husband is the designated lottery player in the house. I get too
disappointed and its just too stupid.

Ann in Houston wrote:

The jug is 10" in diameter and 14" tall. The volume of a cube is
Length*height*width=1728 cubic inches for a 1' cube. The volume of a
cylinder is Pi*Radius*Radius*height= Pi*5*5*14=1100 cubic inches. Not
surprisingly; smaller than a 12" cube. :-)


Well, okay. I can't argue the facts since you went to the trouble to
measure
it. It sure seemed close, though. I know that the water bottle also is
sort of cone shaped at the bottom. Do your calculations treat the bottle
as
a full cylinder, or did you stop at the top of the neck? That could make
a real difference too. Thanks for being intrigued enough to check it out.

I treated it as an exact cylinder - if I wanted to figure out the difference
due to curvature, I'd actually have emptied the contents into a proper
measuring container, as otherwise I'd have to take into account the
curvature on the bottom, the tapering on the top, the size of the neck (at
least, the one I used had some water in the neck), and the thickness of the
plastic (which looks like it probably isn't even uniform). It's a lot
easier to make assumptions :-) (besides which, since I couldn't get an
exact measurement, it was all rough anyway). In fact, either our water
supplier is cheating us, or the jug is actually a little bigger than my
calculation, because it should really be about 1150 cu.in. for a 5 (US)
gallon container.
--
derek

Ann in Houston wrote:

Do your calculations treat the bottle
as
a full cylinder, or did you stop at the top of the neck? That could
make
a real difference too. Thanks for being intrigued enough to check it
out.

I treated it as an exact cylinder - if I wanted to figure out the
difference
due to curvature, I'd actually have emptied the contents into a proper
measuring container, as otherwise I'd have to take into account the
curvature on the bottom, the tapering on the top, the size of the neck (at
least, the one I used had some water in the neck), and the thickness of
the
plastic (which looks like it probably isn't even uniform). It's a lot
easier to make assumptions :-) (besides which, since I couldn't get an
exact measurement, it was all rough anyway). In fact, either our water
supplier is cheating us, or the jug is actually a little bigger than my
calculation, because it should really be about 1150 cu.in. for a 5 (US)
gallon container.
--
derek

I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

"Andy Hill" wrote in message
...
Crashj wrote:
On or about Thu, 18 Nov 2004 18:51:03 GMT, "Ann in Houston"
wrote something like:

This question bugs me every time I double check my gallon calculations.

How can this factor be correct?

You play the lottery, don't you?

That was uncalled for.

I thought it sounded snide, but I had no reason not to give him the benefit
of the doubt. And anyway, I don't play the lottery, although a lot of people
do, who know better, but figure ten bucks every two months is no worse than
most people's vices.

"Ann in Houston" wrote:
I certainly wouldn't have bothered to figure out the neck and all. The real
question was whether or not 12 cubic inches could hold 7.5 gallons. I
appreciate you doing it the way you did.

nitpick on
It's 1728 cubic inches (12*12*12 - a cube 12 inches in all three dimensions),
not 12 cubic inches.
nitpick off

Now, anyone want to talk about koi or something? ;-)

"Snooze" wrote in message
. com...


1 cubic foot is 7.48065 gallons. So 7.5 is a close enough estimate for our
needs. I think you misunderstand what 1 cubic foot is. Picture a box that
is
1 foot wide, 1 foot deep and 1 foot high. That is 1 cubic foot.

You can also think of 1 cubic foot as a box that is 12 inches wide, 12
inches deep and 12 inches high. That would give you 1728 cubic inches.
Because a water jug is not a perfect cylinder, with out making tedious
measurements and calculations, it would be difficult to calculate the
exact
volume on paper.

Ok, guys, I know that not all newsreaders perform equally, so I won't
belabor the "read the thread" point, but we have established that I typed
one thing while I was thinking another. Derek smoothly pointed out, just in
case I was actually confused, that I must have meant "cubic", even though I
typed "square". And, in my answer, I confirmed that I did indeed understand
the difference. So, please no more assumptions that I am one power short of
volume measurement. Also, I realize now, that 12 cubic inches can refer to
a single row of 12 cubes of one cubic inch each. My mistake was to cube
the 12 in my head, but not in my typing. Sorry for the sloppy description
of my thought processes. The whole point I was trying to make and clarify
for myself is that if you took seven and a half gallon jugs and poured them
into a container, they would fill a "lot" of space, and that "box" that is
12 inches in each direction didn't seem, in my mind, to be big enough to
hold it all. Does this not resonate with anyone, here? I have had several
people react in disbelief when they were present as I was working out the
volume of possible pond configurations, and they heard for the first time
how many gallons of water were in a cubic foot.

Perhaps an easy way to satisfy your curiosity, would be to take a 1 cubic
foot box, fill it with rice, then slowly pour the rice from the box into
the
5 gallon jug. You will see that when the jug is full, you still have about
1/3rd the rice still in the box. I hope that this was able to improve your
mental image.

If I knew where to get a water-tight box like that, I would try it, just to
see. I don't want to go get a bunch of rice or sand. I have plenty of
water. I do appreciate your understanding that this is just a curiosity
issue on my part. I think crash thought I wasn't willing to use the
conversion factor because it was hard for me to picture in my head.




PS before engineers were able to calculate the volume of awkward shapes,
such as the interior of a car on a computer, one of the techniques they
used, was to pour foam peanuts in from a hole in the roof, and keep track
of
how many bags of foam peanuts it took to fill the inside. Otherwise they
had
to make estimates by making many measurements and calculations of smaller
chunks of the car, and adding up all those chunks.

Can't resist: was each bag of peanuts shaped like a cubic foot? Still,
that's pretty interesting. I wonder what they did before we had foam
peanuts. Rice would be hard to clean out of a car.

I think they do some rounding off. The 7.5 number I mentioned earlier is an
approximation. I think people doing sensitive measurements use a different
chart.
"Stephen M. Henning" wrote in message
...
Here is another one:

1) A liter of water is one kilogram by definition.
2) One kilogram is 2.2 pounds.
3) A quart is 2 pounds.

4) Hence, a liter is 1.1 quarts.

Conversion charts say that a liter is 1.0566882607957349 quarts. Why
the difference?









The above includes many approximations. The real values are.

1) A liter of water is one kilogram by definition at 4C and 1 atmosphere
of pressure. But at 20C a liter of water is 0.9982 kilograms.
2) One kilogram is 2.2046 pounds.
3) A quart is 2 pounds approximately. Actually at 4C a quart of water
is 2.086 pounds. At 20C a quart of water is 2.082 pounds.

4) Hence, at 4C a liter is 1.0567 quarts and at 20C a liter is 1.0567
quarts. So the common measures we take for granted are about 5 % off.