Fluid mechanics involving stability

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Discussion Overview

The discussion revolves around the stability of a hollow cylinder, specifically a 70 lb empty drum, when placed upright in water. Participants explore calculations related to the metacenter and center of gravity, addressing the differences from previous problems involving solid cylinders.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant is attempting to determine the stability of a hollow drum in water, noting the need for special considerations compared to a solid cylinder.
  • Another participant requests specific dimensions and conditions of the drum, including diameter, length, mass, and water density.
  • A participant shares their calculations for the metacenter, initially arriving at an incorrect value and expressing confusion over the parameters involved.
  • One participant points out an error in the displaced volume calculation and suggests checking the textbook for the correct formula.
  • A participant acknowledges the mistake in their moment of inertia calculation and corrects their metacenter value after revisiting their work.
  • Another participant notes additional inaccuracies in the calculations and emphasizes the importance of maintaining significant digits throughout the process.
  • A different participant raises a question about the criteria for stability, specifically whether it depends solely on the metacenter's position relative to the center of gravity.
  • One participant confirms that the metacenter must be above the center of gravity for stability in floating bodies.

Areas of Agreement / Disagreement

Participants express differing views on the calculations and approaches to determining stability, with some corrections and clarifications made, but no overall consensus on the final values or methods used.

Contextual Notes

Some calculations and assumptions remain unresolved, including the correct application of volume displacement and the significance of maintaining significant digits in calculations.

Jason03
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Im working on a problem involving a 70 lb empty drum. The diameter and length are given. I am trying to find if it will float stably if placed upright in water.

I did a similar problem to this involving a solid cylinder with no problem. But I am trying to figure what special considerations or differences I need to take into account to get the correct answer.

Im calculating the metacenter and the center of gravity as I did in the last problem but I am not coming up with the correct answer for this problem involving the hollow cylinder.

Just trying to see what parameter I need to take into account.
 
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What is the drum diameter and length in meters, and what is the empty drum mass in kg? Does the drum contain any water? If so, what is the depth of water inside the drum? What is the density of water inside and outside the drum, in kg/m^3?
 
The drum is sealed. and i is 2 in diameter by 4 feet long.

I have included my calculations below...My final calculation for the metacenter is coming out to be 13.85 inches...but the correct answer is 10.55 inches...also the metacenter in my second diagram should be higher (slightly below center of gravity)

page 1
http://img16.imageshack.us/img16/6374/page1mu5.jpg

page2
http://img16.imageshack.us/img16/262/page2ok9.jpg
 
Last edited by a moderator:
Jason03: Vd on page 2 is incorrect. Check your textbook to find out how to compute Vd, and try again.
 
I went back and looked and the displaced volume formula and you were correct. I was using the standard volume formula when I needed the displaced volume formula which is ((pi*d^2)/4)(x) where x is the distance the cylinder is submerged in the water. When I went back and did the calculations I still came up with the wrong answer. Than I realized my moment of inertia formula was correct but the answer I had written down was just plane wrong. I guess i just typed it incorrectly into my calculator...Now I have the correct answer of a meta center at 10.2 inches from the base.

So thank you!
 
I saw that moment of inertia mistake earlier today, but when I finally made my post, I was only thinking about Vd, and forgot about the moment of inertia mistake. Also, cg on page 2 is wrong.

Your answer is fairly inaccurate. Generally always maintain four significant digits throughout all your intermediate calculations, then round only the final answer to three significant digits, unless the final answer begins with 1, in which case round the final answer to four significant digits. Try it again and you should get 10.55, if you are doing it right.
 
i have a quick question about stability..sorry if I am hijacking the thread..

If you are determining wether something will be stable or not, is it only dependent on wether the metacenter is above the center of gravity?
 
uradnky: Yes, that is correct, if it is a floating body.
 

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