# Fluid mechanics involving stability

• Jason03
In summary: I'm not sure if there are other considerations that need to be made when it comes to stability. In summary, the empty drum will not be stable if placed upright if it is less than 5 meters in diameter or less than 10 kilograms in mass.
Jason03
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.

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 dependant on wether the metacenter is above the center of gravity?

uradnky: Yes, that is correct, if it is a floating body.

## 1. What is the definition of stability in fluid mechanics?

Stability in fluid mechanics refers to the ability of a fluid system to resist changes in its state or motion. It is a measure of how likely a system is to return to its original state after being disturbed.

## 2. How is stability determined in fluid mechanics?

Stability in fluid mechanics is typically determined by analyzing the forces acting on a fluid system and examining the response of the system to disturbances. A system is considered stable if it returns to its original state after being disturbed, while an unstable system will continue to change or even collapse.

## 3. What are the different types of stability in fluid mechanics?

The three main types of stability in fluid mechanics are neutral, stable, and unstable. Neutral stability occurs when a system remains in its disturbed state without any increase or decrease in the disturbance. Stable stability refers to a system that returns to its original state after being disturbed, while unstable stability describes a system that continues to change and does not return to its original state.

## 4. How does fluid viscosity affect stability?

Fluid viscosity, or the resistance to flow, can have a significant impact on stability in fluid mechanics. Higher viscosity fluids tend to be more stable as they resist changes in motion and are less likely to form turbulent flows. However, excessively high viscosity can also lead to increased drag and hinder fluid motion, potentially causing instability.

## 5. What are some real-world applications of fluid mechanics involving stability?

Fluid mechanics involving stability has numerous real-world applications, including aircraft and spacecraft design, weather forecasting, and ocean and atmospheric dynamics. It is also crucial in the design of hydraulic systems, such as dams and water turbines, and in the study of blood flow in the human body.

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