Volume of a barrel.
03-21-2016, 08:00 PM
Post: #9
 Dieter Senior Member Posts: 2,397 Joined: Dec 2013
RE: Volume of a barrel.
(03-21-2016 07:46 AM)ggauny@live.fr Wrote:  It is said that this formula is STRICTELY EXACT.

The formula in section 552 of the old book indeed is exact... IF (and only if) the shape of the barrel is an ellipse. ;-) This formula translates to Pi*h/12*(2D²+d²) if d and D are the two diameters (at the end and in the middle) of the barrel. This is exactly the formula that is mentioned on the website posted by Tugdual – for barrels that are shaped like an ellipse. ;-)

NO, this formula is NOT exact for ANY barrel. That's not possible. All this is very easy to understand: take a look at the graphics of the barrel in any of these papers. If you only have the end diameters and the one in the middle, you can construct an infinite number of different barrels that are, say, 50 cm at the end and 60 cm in the center. On one of them the shape is similar to an ellipse, on others it's more like a parabola, and you can also draw a barrel that has another shape that cannot be defined by any standard geometric figure. And of course they all have different volumes, even if the diameters at the end and in the middle are the same. They are only the same at these three points.

Gérard, please take a look at the wikipedia website Tugdual posted. This site says it all. Or try that one. Take a look at the diagram. The lines AFB resp. DEC can slightly differ even if the diameters d and D are the same. So the volumes are slightly different as well. Which is exactly the point here.

Yes, there is a general and exact solution. That's the one with the integral. Here you need the function that defines the line AFB or DEC. Please read the chapter "Calcul".

Dieter
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 Messages In This Thread Volume of a barrel. - ggauny@live.fr - 03-20-2016, 08:25 AM RE: Volume of a barrel. - jch - 03-20-2016, 03:11 PM RE: Volume of a barrel. - Dieter - 03-20-2016, 03:35 PM RE: Volume of a barrel. - Tugdual - 03-20-2016, 10:51 PM RE: Volume of a barrel. - ggauny@live.fr - 03-21-2016, 07:44 AM RE: Volume of a barrel. - Tugdual - 03-21-2016, 12:04 PM RE: Volume of a barrel. - ggauny@live.fr - 03-21-2016, 07:46 AM RE: Volume of a barrel. - Dieter - 03-21-2016 08:00 PM RE: Volume of a barrel. - ggauny@live.fr - 03-21-2016, 08:04 AM RE: Volume of a barrel. - Tugdual - 03-22-2016, 06:38 AM RE: Volume of a barrel. - Dieter - 03-22-2016, 06:42 AM RE: Volume of a barrel. - ggauny@live.fr - 03-22-2016, 07:56 AM RE: Volume of a barrel. - Dieter - 03-22-2016, 07:39 PM RE: Volume of a barrel. - Tugdual - 03-22-2016, 07:43 PM

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