An inch of rain on an acre of land= a million gallons??

[AskNott]

I work with a guy who also farms. Another farmer told him that an inch of rainfall on an acre of ground amounted to a million gallons of water. He was skeptical. So am I, because of the nice round number. Niether of us knew how to disprove the million. Do you?

Specifically, if an inch of rain falls on an acre of land, how much water fell?

[DanBlather]

1 acre inch = 27,154.284888 gallon [US, liquid]

See: http://www.onlineconversion.com/volume.htm

[Kamandi]

One acre = 6,272,627 square inches.

One inch of rainfall on one acre = 6,272,627 cubic inches of rain

There are 231 cubic inches in a US gallon.

6,272,627 / 231 = 27,154 gallons (not including rounding errors).

Not exactly a million.

[DanBlather]

1 acre inch = 27,154.284888 gallon [US, liquid]

See: http://www.onlineconversion.com/volume.htm

[bibliophage]

So close, Kamandi. There are 6,272,640 square inches in an acre (exactly). Your error of 13 square inches is completely unacceptable. Reminds me of an old joke at the expense of engineers (“Two times two is 4.02, plus or minus .01)”.

It takes almost 37 inches inches over an acre (37 acre-inches or a little more than three acre-feet) to make a million gallons.

[mangeorge]

Maybe that farmer meant on the south forty. Pretty close.
Peace,
mangeorge

[g8rguy]

[major and probably unfortunate hijack]
What an unusual number (6,272,640, that is). I suppose I shouldn’t ask, the English system being notoriously odd as it is, but why isn’t that a nice number of square feet? I mean, if I map out an acre of land in a square, I get a square with about 208.71 feet on a side. Why not a nice round number like 200, or 210?
[/major and probably unfortunate hijack]

[Duckster]

*Originally posted by g8rguy *
[major and probably unfortunate hijack]
What an unusual number (6,272,640, that is). I suppose I shouldn’t ask, the English system being notoriously odd as it is, but why isn’t that a nice number of square feet? I mean, if I map out an acre of land in a square, I get a square with about 208.71 feet on a side. Why not a nice round number like 200, or 210?
[/major and probably unfortunate hijack]

The acre, by the way, was originally an English unit of measurement that described the area that a yoke of oxen could plow in a day. It originally differed in size from one area to the next, but was ultimately fixed at 4,840 square yards, or 160 square chains (its current size).

Source: http://www.infoplease.com/askeds/9-26-99askeds.html

So the historical origins of an acre are not scientific and exact, but homespun practical. Hence, an acre measurement is not a nice round number. After all, my yoked oxen plow more than your yoked oxen.

[g8rguy]

sigh And this is why I get along so much better with the metric system, I suppose. Thanks much, Duckster.

[Colibri]

*Originally posted by g8rguy *
**[major and probably unfortunate hijack]
What an unusual number (6,272,640, that is). I suppose I shouldn’t ask, the English system being notoriously odd as it is, but why isn’t that a nice number of square feet? I mean, if I map out an acre of land in a square, I get a square with about 208.71 feet on a side. Why not a nice round number like 200, or 210?
[/major and probably unfortunate hijack] **

From here

. . . all land in England was traditionally measured by the gyrd or rod, an old Saxon unit probably equal to 20 “natural feet.” The Norman kings had no interest in changing the length of the rod, since the accuracy of deeds and other land records depended on that unit. Accordingly, the length of the rod was fixed at 5.5 yards (16.5 feet). This was not very convenient, but 5.5 yards happened to be the length of the rod as measured by the 12-inch foot, so nothing could be done about it. In the Saxon land-measuring system, 40 rods make a furlong (fuhrlang), the length of the traditional furrow (fuhr) as plowed by ox teams on Saxon farms.

. . .

In all the English-speaking countries, land is traditionally measured by the acre, a very old Saxon unit that is either historic or archaic, depending on your point of view. There are references to the acre at least as early as the year 732. The word “acre” also meant “field”, and as a unit an acre was originally a field of a size that a farmer could plow in a single day. In practice, this meant a field that could be plowed in a morning, since the oxen had to be rested in the afternoon.

. . .

Most area units were eventually defined to be the area of a square having sides equal to some simple multiple of a distance unit, like the square yard. But the acre was never visualized as a square. An acre is the area of a long and narrow Anglo-Saxon farm field, one furlong (40 rods) in length but only 4 rods wide. This works out, very awkwardly indeed, to be exactly 43 560 square feet . If we line up 10 of these 4 x 40 standard acres side by side, we get 10 acres in a square furlong, and since the mile is 8 furlongs there are exactly 10 x 8 x 8 = 640 acres in a square mile.

Gotta love the old English units.

[SmackFu]

That link is wrong, it’s 160 square rods, not chains.

Anyway, the system is completely precise, it just uses old units.

1 Acre = 10 square chains
1 chain = 66 feet

(66 feet)[sup]2[/sup] * 10 * (12 inches)[sup]2[/sup] = 6,272,640 square inches/acre

And it was an actual chain used by surveyors.

[astro]

Also if we back into the one million gallons over an acre it equals 3.0689 feet of rainfall per acre

If we ask how many acres it would take for an inch of rainfall to yield one million gallons the answer is approximatley 36.82 acres.

[Achernar]

If you take the curvature of the Earth into account, you gain a little bit of water. To first order, it’s about 0.025 in[sup]3[/sup], or 0.0001 gallons. There’s no need to be sloppy.

[Bryan_Ekers]

Just thought I’d point out that a centimeter of rain falling on a hectare is exactly 100 metric tons, discounting curvature of the Earth.

[Una_Persson]

*Originally posted by Bryan Ekers *
**Just thought I’d point out that a centimeter of rain falling on a hectare is exactly 100 metric tons, discounting curvature of the Earth. **

It is impossible for it to be exactly 100 metric tons unless you specify the proper temperature (yes, water density does change as a function of temperature) and you specify the purity of the water (rainwater is not pure water).

[Bryan_Ekers]

Aaaagh, nitpicked to death…

[Collapses in the center of hectare field and drowns in centimeter-deep water]

[David_Simmons]

When are you guys going to stop hectareing each other?

[Una_Persson]

*Originally posted by Bryan Ekers *
Aaaagh, nitpicked to death…

Sorry, it seemed like people were just having some intellectual scientific fun…never mind me…

[mangeorge]

I’m sticking to my guns, hectareing or not.
27,154 inches per acre, times 40 acres = 1,086,160 inches.
So. If an inch of rain falls on my lower forty, I’m going to claim my million inches.
You folks can divvy up the extra 86,160 among yourselves. No fighting.
Peace,
mangeorge

[David_Simmons]

*Originally posted by Achernar *
**If you take the curvature of the Earth into account, you gain a little bit of water. To first order, it’s about 0.025 in[sup]3[/sup], or 0.0001 gallons. There’s no need to be sloppy. **

Yes and if the land is hilly a surveyed acre has a lot of surface area because the survey assumes the land is perfectly flat. In hilly country surveyers speak of having “lots of land to the acre.”