Rising of a liquid during rotataion in a cylinder

You have correctly used the equations for calculating the rotational speed and gauge pressure in the given scenario. Your answer to the second part of the question seems to be correct as well. The gauge pressure at the centre of the bottom of the tank would be equal to the pressure generated by the weight of the liquid column above it, which in this case is equal to the density of the liquid multiplied by the height of the liquid column and the acceleration due to gravity. Great job summarizing the content!
  • #1
NimzCr7
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Homework Statement


[/B]
A 25-cm-diameter, 100-cm-high cylindrical container, (as shown), is partially filled with 75-cm-high liquid (density = 900 kg/m3). Determine the rotational speed at which the liquid will start spilling. Calculate the gauge pressure at the centre of the bottom of the tank when the liquid starts spilling.
http://uupload.ir/files/7ipj_capture.png

Homework Equations



zs = h0 - ω2 / 4g ( R2 - 2r2)
p = ρgh

The Attempt at a Solution



http://uupload.ir/files/md0_29883624_1664433426984266_1728994950_o.jpg [/B]

If someone could please verify me answers, that would be great. In particular, I'm a bit concerned about my answer to the second part of the question.
Thanks
 
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  • #2
Looks correct to me.
 

What causes a liquid to rise during rotation in a cylinder?

The centrifugal force created by the rotation of the cylinder causes the liquid to move towards the outer edge, resulting in its rise.

Does the speed of rotation affect the height of the liquid rise?

Yes, the faster the rotation, the higher the liquid will rise due to the greater centrifugal force.

Is the rise of the liquid affected by the viscosity of the liquid?

Yes, the higher the viscosity of the liquid, the slower it will rise due to the resistance to flow caused by the centrifugal force.

What happens to the liquid when the cylinder stops rotating?

When the cylinder stops rotating, the centrifugal force disappears and the liquid will return to its original level.

Can the rise of the liquid be used to measure the rotational speed of the cylinder?

Yes, the height of the liquid rise can be used to calculate the rotational speed of the cylinder using the equation v = ωr, where v is the speed of the liquid, ω is the angular velocity of the cylinder, and r is the radius of the cylinder.

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