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15 December 2003, 07:05 PM
#1
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if the following drawings are sections through two tubes
I need a formula to work out the value of Y if we know the value of
X. to make the second tube the same mass as the first
hope it makes sense
Stu
I need a formula to work out the value of Y if we know the value of
X. to make the second tube the same mass as the first
hope it makes sense
Stu
15 December 2003, 07:39 PM
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Is the overall length the same between the two?
If the wall thickness is also the same in both then the mass can never be the same for a fixed length because there is more material in the second tube.
If the wall thickness is also the same in both then the mass can never be the same for a fixed length because there is more material in the second tube.
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15 December 2003, 08:11 PM
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I've had a quick go at this, and it's not a simple problem. I end up with an awfully long quadratic equation that doesn't look as though it's going to simplify much. Here it is:
L(R^2-(R-z)^2)=Y((R-x)^2-(R-z-x)^2)+2z(R^2-(R-z-x)^2)+(L-Y-2z)(R^2-(R-z)^2)
where L is the overall length of the tube and z is the wall thickness.
Expanding this out gives: LR^2-L(R^2-2zr+z^2)=Y(R^2-2xR+x^2-(R^2wib-ble-barF^Ine-eee-ed.a+beeR^4....
Where's this problem come from, anyway?
L(R^2-(R-z)^2)=Y((R-x)^2-(R-z-x)^2)+2z(R^2-(R-z-x)^2)+(L-Y-2z)(R^2-(R-z)^2)
where L is the overall length of the tube and z is the wall thickness.
Expanding this out gives: LR^2-L(R^2-2zr+z^2)=Y(R^2-2xR+x^2-(R^2wib-ble-barF^Ine-eee-ed.a+beeR^4....
Where's this problem come from, anyway?
15 December 2003, 08:22 PM
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ha ha!
I have an expression (after a page of algebra) that:-
a) I can't be arsed to simplify
b) Is probably grotesquely wrong anyway!
L(t²-2rt)=(L-Y-2t)(t²-2rt)+2t(r²-(r-t-x)²)+Y((r-x)²-(r-x-t)²)
where t is the tude thickness
had too much wine to think about this any further! If it is really important to you it can probably be solved iteratively with a program (sorry maths geeks!
)
[Edited by ajm - 12/15/2003 8:24:23 PM]
I have an expression (after a page of algebra) that:-
a) I can't be arsed to simplify
b) Is probably grotesquely wrong anyway!
L(t²-2rt)=(L-Y-2t)(t²-2rt)+2t(r²-(r-t-x)²)+Y((r-x)²-(r-x-t)²)
where t is the tude thickness
had too much wine to think about this any further! If it is really important to you it can probably be solved iteratively with a program (sorry maths geeks!
)[Edited by ajm - 12/15/2003 8:24:23 PM]
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