Cylindrical centrifuge filled with water.What happens first spills or bottom visible.

In summary: But thx anyway.In summary, the problem involves a cylindrical centrifuge filled with water to a depth of 1 meter. As the centrifuge accelerates, the water level rises along the wall and drops in the center, forming a parabola. The equation of the parabola can be found in terms of the depth of the water at its lowest point, h. As the centrifuge rotates faster, either water will be spilled out of the top or the bottom of the centrifuge will be exposed. It is hypothesized that the bottom will be exposed first. The solution to the problem involves using integrals to find the surface shape under the assumption of constant rotation.
  • #1
Doogan1
4
0
1. Homework Statement

A cylindrical centrifuge of raidus 1 m and height 2 m is filled with water to a depth of 1 meter. As the centrifuge accelerates, the water level rises along the wall and drops in the center; the crossection will be a parabola.

a) Find the equation of the parabola in the figure in terms of h, the depth of the water at its lowest point.

b) As the centrifuge rotates faster and faster, either water will be spilled out of the top, or the bottom of the centrifuge will be exposed. Which happens first?




2. Homework Equations

R=1
H=2m
depth of water= 1m

3. The Attempt at a Solution

I've been thinking this problem must have something to do with integrals, but i am lost in the fact that the parabola from the cross section is constantly growing. I just can't seem to find an equation for the parabola, but i have made a hypothesis that the bottom will be exposed first, based of course off of no mathmatical basis. Help desperately needed.
 
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  • #2
Welcome to PF!

Doogan1 said:
I've been thinking this problem must have something to do with integrals, but i am lost in the fact that the parabola from the cross section is constantly growing.

Hi Doogan1! Welcome to PF! :smile:

Don't panic … questions like this are carefully written so that you can ignore the change in rotation.

Just assume that the rotation is constant, and work out the surface shape on the assumption …
i] the surface just touches the top
ii] the surface just touches the bottom. :wink:
 
  • #3


Thx for replying and trying to help. I figured the problem out with my teacher today and basically it turned out to be just a big ol' integral.
 

1. What is a cylindrical centrifuge filled with water?

A cylindrical centrifuge is a laboratory instrument used for separating substances based on their density. It is filled with water to create a liquid medium in which the substances can be separated.

2. How does a cylindrical centrifuge work?

A cylindrical centrifuge works by spinning the sample at high speeds. This creates centrifugal force, which causes the denser substances to move towards the bottom of the tube, while the less dense substances remain towards the top.

3. What happens when a cylindrical centrifuge filled with water is spun?

When a cylindrical centrifuge filled with water is spun, the substances in the sample will separate based on their density. The denser substances will move towards the bottom, while the less dense substances will remain towards the top.

4. Will the bottom of the centrifuge be visible when it is filled with water?

Yes, the bottom of the centrifuge will be visible even when it is filled with water. This is because the centrifugal force will cause the denser substances to settle at the bottom, making it visible.

5. What happens first, spills or bottom visible?

The bottom will be visible first before any spills occur. This is because the centrifugal force will cause the denser substances to move towards the bottom, making it visible. Spills may occur if the centrifuge is not properly balanced or if the sample is too full, but this would happen after the bottom becomes visible.

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