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Is the surface of water ever "perfectly" flat?
« Reply #30 on: February 09, 2015, 07:15:23 pm »
Excellent discussion of precision flatness in water and molten tin too!

Full thread is at this link:

Is the surface of water ever "perfectly" flat?

Before anybody goes off on a bent about "perfectly," let me explain; No, I'm not an Indian graduate student. When I say "perfectly" I mean by a machinist's standards; does it pass the test of a surface plate's flatness spec (like accurate to .0001").

 I know there's either a concave or convex meniscus at the edge, and I know that the surface of the water will follow the curvature of the surface of the earth. But what I don't know, is if I were able to "freeze" (not as in freeze by cold temperature turning it into ice, which would change the size & shape, but "freeze" as in magically make it turn instantly solid without morphing) a bathtub full of water, would I have a "perfectly" flat surface in the middle, say 1" in from the edges? Or would it still have some radius (a tigher radius than the earth's radius) to it, like it's just the surface of one giant water droplet that just happens to be in a bathtub?

Glenn Holland
Except for surface tension at the edges and with no motion, the surface should be almost flat.

 Other liquids such as molten tin exhibit near flatness and the surface can be used as a reference and also a mold for casting other flat shapes. s an example, plate glass is made by applying molten glass over the surface of molten tin.

In your bathtub example, in theory, the inside surface area would have a curvature to it. It would be slight. The curvature would have a radius R, to the center of gravity of the earth.

 You can get damn close with a machined surface to true flatness.

 Probably the closest we can get to flatness is.........a stretched sheet of graphene.

Dont forget about the Moon's gravitational attraction.

Absolutely. The first bathtub curve will be modulation by a second and inverse curve with radius r.....to the center of gravity of the moon.

I once had a conversation with a structural engineer about using a water level vs a laser level on a large building. Something like 1000 feet and you're out of spec for, "flat" with the water level.

 He never answered me. Probably because his daddy was an engineer and "forced" him to get a 4 year degree. It worked. He's financially secure and can't figure out how structures were built before lasers were available.

 Anyway, I did the math to get the 1000 foot number, and you can too...if you care enough.
 X^2 Y^2 Radius = 4000 miles etc.
Do the math and find out how flat bath tub water is!

Alright I'll take a stab at it, but first, ...
 If you're looking for level, I say, a hose full of water is the only thing that's going to give you a true level.
 If you use a bubble level or laser, you're shooting two tangent lines out from your position on the face of the earth, into space. if you were run your level or laser in either direction along that line, as soon as you leave dead center (where you took the measurement), you're going to be off by more and more ****hairs the further you go out.

So, having said that, I'll use the Distance to the Horizon formula in order to determine the difference between FLAT and LEVEL, at 1000ft.
 distance to horizon formula:
 d = 1.22h
 d = distance in miles
 h = height in ft

 Rearrange to solve for h:
 h=0.1894mi/1.22 = 0.15525ft = 1.863"

 Now confirm with Pythagorean theorem:

 436,957,148,390,400ft2 + 1,000,000ft2 = c^2

 C-A = 0.02391941642909571014096ft = 0.287033"

Big difference there. I suspect the Pythagorean theorem is the closer one to correct. What was your number?

 Anyway, same Pythagorean method substituting in my 4ft instead of your 1000ft, yields .00000459253" over 4ft. Good enough for me ;)

Agelbert NOTE: Me too! Water is REALLY FLAT!  :o  8) The question is, HOW could the ancient Egyptians, who probably were quite good at math before Pythagoras (thanks to ET  ;D previous knowledge from maybe the Sumerians), make use of this BETTER THAN .001" water flatness precision?

Water WILL follow rock surface contours to a degree. So, on a planed marble surface, it will not be as flat as in a still pool of water. But there is a limit to high much it will climb before it starts stretching and thinning out.

I'll get back to you. 

Man, those ETs ancient Egyptians were smart "copper" using cookies, weren't they
Ashvin?  ;D 

« Last Edit: February 09, 2015, 08:37:05 pm by AGelbert »
Wait on the Lord: be of good courage, and he shall strengthen thine heart:
wait, I say, on the Lord. -- Psalm 27:14


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