# Liquid in a centrifuge

#### Seatl

Hey,

As part of an investigation, I constructed a basic centrifuge consisting of a fast rotating beaker filled with liquid.

I have observed that an increased angular velocity forces the liquid out of the centre and further up the sides of the centrifuge, as expected. However, I am having difficultly explaining exactly why this happens in terms of the forces acting of the liquid. Could any one help?

In addition, could anyone suggest what other factors other than speed of rotation might affect the height obtained by the liquid?

Thanks

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#### NateTG

Homework Helper
Can you list all of the forces that are acting on the liquid? A common issue is that people forget a force. Also, are you using a rotating frame of reference or not?

#### Danger

Gold Member
Seatl said:
In addition, could anyone suggest what other factors other than speed of rotation might affect the height obtained by the liquid?

Thanks
The first two that come to mind are the viscosity of the liquid and the gravitaional/atmospheric environment in which the experiment is conducted.

#### mathman

The simplest part of the explanation is inertia. The liquid is trying to move in a straight line. Since it is being forced to move in a circle, there is a component of its direction vector moving it outward in the centrifuge.

#### Clausius2

Gold Member
Seatl said:
Hey,

As part of an investigation, I constructed a basic centrifuge consisting of a fast rotating beaker filled with liquid.

I have observed that an increased angular velocity forces the liquid out of the centre and further up the sides of the centrifuge, as expected. However, I am having difficultly explaining exactly why this happens in terms of the forces acting of the liquid. Could any one help?

In addition, could anyone suggest what other factors other than speed of rotation might affect the height obtained by the liquid?

Thanks
The whole amount of fluid is rotating as a rigid solid at an angular speed $$\omega$$. The free surfaces is characteristically curved like a parabola.

Danger, viscous forces are ultimately the responsible of communicating the movement of the beaker to fluid. Once the steady regimen is reached, such forces don't play any role.

The centrifugal force pushes fluid outwards the centre of rotation. Such pushing is balanced with an increasing of liquid height, because static pressure on the free surface must remain being the atmospheric one. As it is not an hydrostatic system, the pressure is not given by liquid height, but by an appropriate arrangement of both hydrostatic and centrifugal terms. External zones are zones of great pressure, and so they will need a greater liquid column in order to reach the same atmospheric pressure on the free surface.

#### Evilinside

Gosh, If I got that question on a test I would have gave response along the lines of

Say the viscous fluid was in a test tube and the test tube is being rotated. Then the entire solid will attempt remain inact or rigid. For example if the bottom half of the test tube has force exerted on it at an angle, then it will exert a pulling force it's upper half so then it moves with the lower half, it is a rigid structure. When rotating, the force is always exerted at an angle which could be put in to the vectors of tangential acceleration and revolutional accelerational. In this case there isn't opposite force to pull the viscous fluid back downward, as with the test tube due to its rigidity, although the test tube still exerts a force on the fluid at an angle with its x and y components. Therefore the viscous fluid will continue being being pushed upward by the y component of the force.

or something like. I think this is what mathman was saying, hope a response with that basic idea wouldn't have been wrong.

Last edited:

#### stallion

mathman said:
The simplest part of the explanation is inertia. The liquid is trying to move in a straight line. Since it is being forced to move in a circle, there is a component of its direction vector moving it outward in the centrifuge.

What he said

#### Seatl

End

Thanks all, that's perfect

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