How to Calculate the Volume of a Partially Filled Semi Ellipsoid
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I am trying to figure out how to calculate the volume of a partially filled horizontal cylindrical tank which has semi elliptical heads. The tank is filled to some height 'h'.
The minor axis of the semi ellipsoid is half the radius of the tank. I could calculate the volume of the partially filled cylindrical portion of the tank but I have a feeling this requires a triple integral and I do not know what to do. Any help would be appreciated.
integration volume
asked Nov 17 at 22:54
Jack
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I am trying to figure out how to calculate the volume of a partially filled horizontal cylindrical tank which has semi elliptical heads. The tank is filled to some height 'h'.
The minor axis of the semi ellipsoid is half the radius of the tank. I could calculate the volume of the partially filled cylindrical portion of the tank but I have a feeling this requires a triple integral and I do not know what to do. Any help would be appreciated.
integration volume
asked Nov 17 at 22:54
Jack
6710
1
The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I am trying to figure out how to calculate the volume of a partially filled horizontal cylindrical tank which has semi elliptical heads. The tank is filled to some height 'h'.
The minor axis of the semi ellipsoid is half the radius of the tank. I could calculate the volume of the partially filled cylindrical portion of the tank but I have a feeling this requires a triple integral and I do not know what to do. Any help would be appreciated.
integration volume
asked Nov 17 at 22:54
Jack
6710
I am trying to figure out how to calculate the volume of a partially filled horizontal cylindrical tank which has semi elliptical heads. The tank is filled to some height 'h'.
The minor axis of the semi ellipsoid is half the radius of the tank. I could calculate the volume of the partially filled cylindrical portion of the tank but I have a feeling this requires a triple integral and I do not know what to do. Any help would be appreciated.
integration volume
integration volume
asked Nov 17 at 22:54
Jack
6710
asked Nov 17 at 22:54
Jack
6710
asked Nov 17 at 22:54
Jack
6710
asked Nov 17 at 22:54
Jack
6710
asked Nov 17 at 22:54
Jack
6710
6710
1
The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09
add a comment |
1
The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09
1
1
The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09
The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09
add a comment |
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The quickiest way would be to decree the (semi) ellipsiod is actually (half) a sphere rescaled differently along each dimension, thus the partially filled volume is (half) the spherical cap (en.wikipedia.org/wiki/Spherical_cap) rescaled in the same fashion. But are you actually required to use a triple integral? Is your question about how to determine the integration limits?
– Rócherz
Nov 17 at 23:09