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?
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?