62 555
Assignments Done
Successfully Done
In June 2018

Answer to Question #14968 in Differential Equations for Julia

Question #14968
Find the form of the surface of fluid inside separating centrifuge while working and angular velocity of the fluid to reach the given height H.
Expert's answer
Let's look at the problem in Cartesian coordinates.
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
the surface:

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.

Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!


No comments. Be first!

Leave a comment

Ask Your question

Privacy policy Terms and Conditions