Ellipsoid caps' volume for vert vessel 1

I'm not sure if I completely understand your question, but if you want to calculate the volume of a semi-elliptical head, the GPSA handbook has a method that works quite well.


Regards,

Bob

Can you expound on what GPSA stands for please?

Go to this link:



Regards,

Bob

The Pressure Vessel Handbook is also an excellent source of information, data, graphs and equations. Spreadsheets can be developed and one does not have to reinvent the wheel.

Checkout thread794-27356

There's formula's for both
Semi-ellipsoidal heads and torispherical heads.
(response 23. july)

Regards
Mogens

Hi Mogens,

I may be wrong, but I believe the equations posted in that thread were for the metal volume (to arrive at the weight of the head). The vessel volume is quite a long expression with a lot of arc tans, etc...


Regards,

Bob

Hi Bob

You're right, it was for the metal volume, but in order to find the metal volume you have to find the head (inside) volume so the formula is there. Anyway here's a short recap:


Semi-Ellipsoidal Head:
Volume = 2/3*pi*(D/2)^2*(D/4) = 1/24*pi*D^3


Torispherical head (Any type):
Vol=PI()/3*D^3*(2*K^3*(1-SIN(angle))-(K-L)*(1/2-L)^2
*SIN(angle)+L^2*((1/2-L)*3*angle+2*L*SIN(angle)))

Where:

D equals (inside) Diameter of Cylinder
R equals (inside) Radius of spherical part (dome)
r equals (inside) (secondary) radius of torus (knuckle radius)

and where

K=R/D (for ASME F/D head K=1.00)
L=r/D (for ASME F/D head L=0.06)
angle=ACOS((1/2-L)/(K-L)) (angle in radians)

angle is angle of torus part i.e. the angle where Knuckle radius = r) For ASME F/D head this angle is 1.084 radians (=62.09 degrees)


Heads specified as Semi-Ellipsoidal will in reality be torispherical, with K=0.8 L=0.155(DIN 28013 Korbogen), however normally it is accurate enough to use the simpler semi-ellipsoid formula.

regards
Mogens

To all engineers who might be interested:

I went through a lot of grief as a young engineer, putting together data for the calculation of process vessel volumes. As an old Dino-sour now, I've had the time to put the information into an Excel Workbook. You can calculate the total or partial volume in any vertical or horizontal vessel at various heights of fill. This applies to vessels with 2:1 Ellipsoidal, Torispherical (ASME F&D), Spherical, or "standard" dished heads.

If you would like to have a copy, drop me a line at:

artmontemayor37@hotsheet.com

and I'll try my best to email you a copy. I'm still working on it for improvements, so it will continue to grow. For example, I use it for specific identification of level instruments' locations in a tank. I also generate a "Strapping Table" for inventory calculations and other process decisions. I include full documentation and formulas to allow you to formally use it as project calculations and OSHA 1910 documentation. You need not wander through the Volume valley any longer.

Art Montemayor