Water poured from an open bucket by tilting it? My question comes from pouring water from a say 2 gal. round bucket.
Does the top water pour out first or as you tilt the water the top water weight travels back and the bottom of the bucket pours out first or some where in like half way down the bucket the water mixes to pour out? 
Any answer?
 A: It is easy to test by putting some food coloring in the water and observing it while pouring the water out. Which is what I did to check my assumptions.
While the exact details may depend on such factors as material of the bucket, shape of its edge, quality of the water, the rate of pouring, etc., the overall picture is that the water from the surface flows out first.
This makes sense, considering, simplistically, that the surface layer of molecules loses lateral support as the bucket is tilted and the surface rises above the edge. The water from the layer below, would have to rise in addition to moving sideways, but there does not seem to be any forces for that, since this layer still should have lateral support from the wall and all forces acting on it are balanced.
There are many subtleties and uncertainties in this process due to the surface tension, viscosity, etc. For instance, due to the surface tension, the water has to rise a little above the edge of the bucket before it starts flowing, so it takes more than just "one layer of molecules" to create a sufficient lateral force disbalance, but, based on the test results, this does not seem to have much effect on the overall sequence.
A: V.F.'s answer is correct and here's another argument why it should be so. The surface layer flows faster than any lower layer due to two conditions: 1) No slip at the bucket walls, and 2) Stress free condition at the free surface (which is the top layer). If you took a vertical section of the flow, then the velocity profile would look qualitatively the same as that of a layer of fluid flowing over a flat surface (because it too is subject to the same boundary conditions):

Image source: chegg.com
tpg2114's concern that soap bubbles on the surface tend not to flow out faster is answered by the fact that they experience a vertically upward buoyancy force, which has a component in the upstream direction.
A: Water is always mixing itself (see Brownian Motion) to some extent.  Tilting the bucket will just encourage more mixing.
Thermal differences will also show differences.  Try this experiment with dyes to see what happens when you pour water with hot and cold layers:
https://www.youtube.com/watch?v=bN7E6FCuMbY
You'll find that fluid dynamics is very complicated and difficult to predict using human intuition.
Here's another set of examples of various fluid properties:  https://www.youtube.com/watch?v=CCxbI1qRsWY
