formula to calculate the volume and surface area of spheroid 2

[LSThill]

Team Members:

formula to calculate the volume and surface area of spheroid steel tank:
Given:
30M BBL Horzon Sphereord
h = 57'0" ; dia = 77'-0"

 

[vpl]

Isthill

I have the CRC Math Tables which give definitions for two different types of spheroids: oblate and prolate. The first is defined as rotating an elipse about its minor axis, while the second is rotating an elipse about its major axis.

Having said that, I have run across "spheroid" tanks - i.e., a conical tank with a spherical top and or bottom (or sides, if horizontal).

All three have different formulas, could you be more specific about the application?

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[LSThill]

vpl (Nuclear)


API 620 PAGE 5-14, FOR 30,000BBL HORTONSPHEROID 30 WP STEEL TANKS

 

[vpl]

Isthill

I don't have access to the API spec, but from reading the summary of the document on IHS, it appears you have a vertical cylindrical tank with a spherical top and, probably, a flat bottom.

The easiest way is to "separate" the cylindrical tank from the spherical top and calcuate the surface area and volume for each.

Definitions:
H = height of cylinder (excluding spherical section)
h = height of spherical section only
R = radius
[π] = pi
S = surface area = Sc + Ss
Sc = cylindrical surface area
Ss = spherical surface area
V = volume = Vc + Vs
Vc = cylindrical volume
Vs = spherical volume

Sc = 2[π]RH
Ss = 2[π]Rh
or S = 2[π]R(H+h)

Vc = 2[π]R²H
Vs = 1/3[π]h²(3R - h

Hope this helps!

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[LSThill]

Team Member & vpl (Nuclear)

You need to go back to 1940 to 1947

1947 - Chicago Bridge & Iron Company The Storage of Volatile Liquids, Technical Bulletin No. 20

Contents:
Evaporation Loss Prevention
Horton Floating Roofs
Horton Lifter Roof
Hortondome Roof, Vaporsphere & Vaportank
Hortonspheroid & Hemispheroid
The Hortonsphere
Oil Storage tanks
Tables & Formulae
Horton Pickling Process

The above Technical Information may help other Engineer in the Mechanical Integrity Solutions: Suitability for Service (SFS)



L S THILL

 

[JStephen]

These are fairly basic calculus problems- dust off the ol' textbook.

Generally, you can just integrate volume along the vertical axis, and the integrals will be in the CRC Math Handbook or other similar references. Break the shape into cylindrical, spherical, torospherical segments as required.

For surface area, divide the area into circular strips of width (Rda), where R is the radius normal to the surface, and da is the angle.

 

[vpl]

Isthill

I apologize for trying to answer your question. Obviously you have a specific application which you apparently need someone qualified on a specific standard and type of tank. You appear to be unwilling to share information rather specifying that I go to a technical bulletin issued nearly 60 years ago.

As I have no need for that technical bulletin in my work, I will refrain from trying to hunt up a copy in order to answer your question.

Patricia Lougheed

Please see FAQ731-376 for tips on how to make the best use of the Eng-Tips Forums.

 

[JoeTank]

Isthill,
Are you referring to the noded spheroid on page 5-14?

Joe Tank

 

[deanc]

http://www.mathforum.org/dr.math/faq/formulas/faq.sphere.html

 

[deanc]

http://mathworld.wolfram.com/topics/Spheres.html

In case the first one is short.

 

[LSThill]

deanc (Specifier/Regul)

DO YOU HAVE:

1947 - Chicago Bridge & Iron Company The Storage of Volatile Liquids, Technical Bulletin No. 20

 

[deanc]

Think I can get it.....but may take a few days.

http://grapevine.abe.msstate.edu/~fto/tools/vol/index.html

Check this one for fun....from

http://www.martindalecenter.com/

Very nice site!