Partial Volumes of frustums 1

[Elise]

Does anybody know how the calculate the partial volumes of HORIZONTAL frustums.
a) for true conical frustum
b) eccentric frustum - see previous post.

 

[prex]

What do you mean by partial volume?
See also the other post.

prex

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[rb1957]

maybe this helps ...

http://mathworld.wolfram.com/ConicalFrustum.html

 

[reidh]

Am I missing something? Why would the volume of a horizontal frustum be different from that of a vertical frustum?

Reidh

 

[rb1957]

reidh,

i guess it doesn't if you're talking about the axis of the cone (being horizontal or vertical), but i thin it would if you're talking about the cutting planes (being perpendicular or parallel to the axis of the cone). I've interpreted the question as tho' the axis of the cone is vertical and the cutting planes are horizontal; elise ?

 

[Elise]

The frustum is used in a hotrizontal shell and tube heat exchanger kettle. so the bottom of the frustum is parallel with the floor...

 

[Elise]

By partial volume.
Image a layer of liquid that does not totally fill the frustum..
There are formulas for calculating partila volumes of horizontal pipes for the frustum its totally different ?

 

[prex]

Now I understand what you mean.
A quick trip onto

http://www.integrals.com

gives
2L/(R₁-R₀) [•] [arccos(1-h/r) [•] r³/3-[√]((2-h/r)h/r) [•] (10h²+31rh+6r²)r/45]
where h is the independent variable (filled height with h<2R₀) and the expression in square brackets is to be evaluated first for r=R₁, then for r=R₀ and the difference of the two values inserted in the brackets; the other symbols should be simple to figure out.
Hope you'll understand that I cannot guarantee in any way the exactness of that formula...

prex

http://www.xcalcs.com

: Online tools for structural design

http://www.megamag.it

: Magnetic brakes for fun rides

http://www.levitans.com

: Air bearing pads

 

[SnTMan]

Elise, FYI, more commonly known as "eccentric cones" in the biz.

Regards,

Mike