# HELP: contact area of Cylinder inside a larger Cylinder?

#### mhl

Laydies and Gents

can anyone help me here? suppose there are well known formulas for this.

That is, contact area of a known size cylinder lying inside a larger know size cylinder....

hope problem is clear

thank you

best regards

martin

#### danong

Contact area? is it involving volume or just area? or sth other than pure value of area?
my guess is that, let CyLarge and CySmall,
so if u re finding volume, calculate the CyLarge volume subtract CySmall volume.
if it's area, CyLarge Area - CySmall Area.

sorry if i misreading ur question. =)

#### mhl

Hmm. To clearify:

I am tryoing to find the contact area of a given cylinder that is lying inside another cylinder. That mean the outside area of the smallest cylinder touching the inner wall of a known larger cylinder.

Ex: a 1 meter long cylinder with 5" diameter lyes inside a 1 meter long cylinder with 7" diameter. What is the contact area between the two cylinders....?

hope this was better.

#### HallsofIvy

No, it isn't. If the two cylinders have their axes vertical, under gravity, then the "contact" area is just the area of the two bases of the smaller cylinder:$49 \pi m^2$. If the two cylinders have there axes horizontal, then there would be a very slight contact between the curved areas. Although, I suspect that in ideal cylinders, that would just be a single line of contacet, having 0 area: so we are back to $49\pi m^2$.

#### mhl

mmm, yes hallsofivy, that was my though as well (the axis are horizontal, they are lying down i guess).

Still, does that mean that a given cylinder, for example OD of 1m, lying on a straight plane has the same contact area to it's underlayer (tha plane) as the same cylinder lying inside a cylinder with ID of 1.001m??? (all things ideally and so on and so fourth)....

thoughs...?

#### neg_ion13

Would it be a limit? like lim as deltaX approaches 0 of (Xo * Height)?

#### AlephZero

Homework Helper
Still, does that mean that a given cylinder, for example OD of 1m, lying on a straight plane has the same contact area to it's underlayer (tha plane) as the same cylinder lying inside a cylinder with ID of 1.001m???
Yes, if you assume both cylinders are perfectly rigid.

For real cylinders the answer is no, because they are flexible. Google for "Hertz contact" for more about that.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving