Suppose you have a tall cylindrical pail, and you fill it up with water until the water level reaches height H. The pail is spun around (centered in the center) and the water leaves the center and gathers to the sides of the pail due centrifugal force. Eventually, a parabolic cone 'hole' is formed in the water, with the vertex of the parabola just touching the bottom of the pail.
What is the height of the water at the sides? (in terms of H)
2006-06-27 22:52:33 · 8 answers · asked by Pinsir003 3 in Science & Mathematics ➔ Physics
Assume that the pail is tall enough
2006-06-27 23:10:12 · update #1
depends on the size of the pail, the height of H, and the speed at which you spin it
2006-06-27 22:56:50 · answer #1 · answered by black_widow_by_trade 1 · 2⤊ 0⤋
H(i mean what else?)
but if u mean in terms of distance from the axis ,it can be found by finding the equation of the parabola u take an element of liquid of mass m at the surface of the hole at a general distance x and calculate the forces acting on it i.e.gravitational force m.g and centrifugal force and then find the relation between the height (remember 2 take the vortex as origin and axis of the cylinder as y-axis) find the relation between x,H integrate it .2 get the parabola's equation .place the desired x 2 get the desired y(height) from the plane containing the vortex &perpendicular 2 the axis.I dint work this out bcoz it would NOT prove useful in this case as you mentioned a liquid-WATER in whose case we have to consider the viscosity,surface tension,and other factors since water is not an ideal liquid.It would become extremely difficult(as far as i know)
Anyway any process would require the angular velocity with which ur spinning as it may vary from H to infinity if u spun it infinitely fast The radus of the cylinder is also needed
2006-06-28 06:14:40 · answer #2 · answered by Anonymous · 0⤊ 0⤋
Are you sure it's parabolic? It's a rather complex system. But it would not depend just on H, but also on the diameter of the cylinder. For a given cylinder, the larger H, the faster you'd need to spin.
2006-06-28 12:04:22 · answer #3 · answered by Frank N 7 · 0⤊ 0⤋
2H?
i supposed the volume displaced by the vortex is equal to the volume of water added to increase H.
2006-06-28 05:59:18 · answer #4 · answered by Anonymous · 0⤊ 0⤋
H +(vol of cone/pi x width of container squared)
2006-06-28 06:02:39 · answer #5 · answered by Vermin 5 · 0⤊ 0⤋
H
2006-06-28 05:57:20 · answer #6 · answered by Dark Angel 5 · 0⤊ 0⤋
2h?
2006-06-28 05:59:28 · answer #7 · answered by presidentofallantarctica 5 · 0⤊ 0⤋
1.5H
2006-06-28 06:14:23 · answer #8 · answered by Anonymous · 0⤊ 0⤋