

Re: Geometry challenge
MJG Mar 10, 2017 10:48 AM (in response to dferry)You state that the two vanes are 90 deg from each other, but do not clarify orientation relative to the vertical offset of the circles. Please verify that the vanes are each 45 deg from vertical.
How accurate must the answer be? Assuming thickness t is small, is it sufficient to assume the area of a vane is equal to its length times thickness?

Re: Geometry challenge
dferry Mar 10, 2017 11:31 AM (in response to MJG)Sorry, the vanes are 45 from vertical (so we have symmetry). The answer needs to be quiet exact so I'm looking for a mathematically pure result. 1% error would be unacceptable. (It's a pump in case you're wondering.)


Re: Geometry challenge
FredKohlhepp Mar 10, 2017 11:25 AM (in response to dferry)Need an exercise in polar coordinates.
Attached solves top half.
Bottom half is exercise for next.

top half.xps.zip 487.2 K

top half.mcdx.zip 50.3 K



Re: Geometry challenge
dferry Mar 10, 2017 12:38 PM (in response to dferry)Thanks Werner. I knew I just wasn't looking at it simply enough. Bottom half solution is solved by simply entering a negative eccentricity (e). Matches my CAD answers exactly so I'm calling it solved.
I'll have to absorb everyone else's solutions also. Thanks everyone for the efforts.

Re: Geometry challenge
vlehner Mar 11, 2017 4:00 AM (in response to dferry)Hi dferry,
although the problem is still solved, i calculated it with Prime 4.0.
A very good challenge and exercise for creating multiple Integrals.
And yes to calculate the smaller Area there must be changed only "ey" to a negative sign.
I added an analytical solution for both Areas at the end of the Worksheet.
best regards, Volker

Kreisflaechen.pdf 4.8 MB

Kreisflaechen.mcdx.zip 125.3 K
