volume of a circular segment
volume of a circular segment
(OP)
Can someone tell me how to calculate the volume of a circular segment? I have found the formulae to calculate the area, and length of arc, etc, pretty much everything except the volume.
Any help would be appreciated
Thanks
Any help would be appreciated
Thanks





RE: volume of a circular segment
RE: volume of a circular segment
thanks for your reply, but I do not mean a spherical sector, I mean a circular segment, with depth/thickness, such as a rocker for a rockinghorse, etc.
Paul
RE: volume of a circular segment
RE: volume of a circular segment
I wondered about that also, at first I thought that was the way to do it. Maybe it is, it certainly makes sense. I just thought I'd put the question out to see if anyone has had to tackle that sort of problem before. - you know how sometimes if you look at a problem long enough you start to question the solution, or wonder if you've left something out. Just being careful.
Thanks
Paul
RE: volume of a circular segment
'Burington', P.14, Art. 48.
RE: volume of a circular segment
and get the volume of the ring.
If you know the sector angle, the volume of
the sector would be the sector angle/360
and then time the volume of the ring.
RE: volume of a circular segment
RE: volume of a circular segment
Given the equation of a circle as (x-x0)^2 + (y-y0)^2 = R^2 and setting the center of the circle to the origin, (x0,y0) = (0,0), the equation is simply:
A = INT (A/B) [sqrt(R^2 - x^2)], A & B = limits.
A = R^2[B - sinB cosB]
Clearly if you have a circular sector, R = outer radius, r = inner radius, then the difference between the two slices is the area required in between.
A = (R^2 - r^2) [B - sinB cosB]
This is very easily verified, for if the sector was a complete circle, B = pi by symmetry, then we get A = pi (R^2 - r^2), which is the area of the donut.
So if the circular sector is of thickness, t:
V = (r^2 - r^2) [B - sinB cosB] t
You may wish to convert to polar coordinates and retry, personally I find Cartesian to be a bit more challanging.
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada
RE: volume of a circular segment
L*w*t
where
w= width of segment
t= thickness
RE: volume of a circular segment
Function reinforcement(wHeight, wwidth)
If wwidth = 0 Then wwidth = 1
reinforcement = (wHeight / (6 * wwidth)) * ((3 * wHeight ^ 2) + (4 * wwidth ^ 2))
End Function
Using it always came within 3 decimal points of what some textbooks had for weight of weld reinforcement but I never had anyone check it out. Anyone with a formula more accurate that I may use that only requires the width of the segment and height from the chord? It literally took me weeks for the one above
Thanks
Any
Gerald Austin
Iuka, Mississippi
http://www.weldinginspectionsvcs.com
RE: volume of a circular segment
Kenneth J Hueston, PEng
Principal
Sturni-Hueston Engineering Inc
Edmonton, Alberta Canada