Answer to Question #14968 in Differential Equations for Julia
Let (0, 0) be the
coordinate of the center of centrifuge, w be the angular velocity
Any section (that crosses the origin and is perpendicular to XoY
plane) of the surface
has a form of parabola:
Z - Z0 = w^2 * x^2 /
When we substitute x -> sqrt(x^2 + y^2) we get the equation of
Z - Z0 = w^2 * (x^2 + y^2) / (2g).
H = Z0
+ r^2 * w^2 / (2g),
where r is the radius of centrifuge.
As h = 1/2 *
(Z0 + H), so
w = 2/r * sqrt(g*(H - h)) - angular velocity.
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