Area of Ellipsoidal Heads
Area of Ellipsoidal Heads
(OP)
Does anyone have a simple formula for determining the surface area of 2:1 ellipsoidal heads? Metric or imperial.
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RE: Area of Ellipsoidal Heads
V= Volume in gallons
D= Diameter in feet
L/D= Length of Cylinder section to diameter ratio
a = constant= 1.164 for ASME flanged and dished heads
1.909 for 2 to 1 Elliptical heads
3.92 for hemispherical heads
Here is formula for a cyclinderical vessel with 2 heads. It's an approximation but fairly accurate. You can work from this. I'll try to find my calculations for each head type.
RE: Area of Ellipsoidal Heads
Not sure what you are calculating there..??
Surface area for 2:1 in metric units = 1.084 x D62 where D = vessel diameter
Volume of 2:1 = 0.131 x D^3
RE: Area of Ellipsoidal Heads
Not sure what you are calculating there..??
Surface area for 2:1 in metric units = 1.084 x D^2 where D = vessel diameter
Volume of 2:1 = 0.131 x D^3
RE: Area of Ellipsoidal Heads
This is a formula we used early on for the total volume of a vessel(in gallons) with different type heads base on the L/D of the cylinder.
Its origin was from a United States Steel handbook "Low Temperature and Cryogenic Steels"
Sorry
RE: Area of Ellipsoidal Heads
Thanks for the information but in your formula, what are the units for diameter (D), mm or m?
RE: Area of Ellipsoidal Heads
Length and Diameter of cylinder are both in feet.
This formula came from the early 60's so there wasn't much use at the time of metric units except by chemists.
Where one uses a spreadsheet today we made tables of values and in the handbook I mentioned there are tables of different Diameters vs Gallons using different L/D curves.
I have some more information and will try to find it.
RE: Area of Ellipsoidal Heads
Your formula is good but I need a formula for surface area of semi-elipsoidal 2:1 heads. I'm in a remote area and am trying to complete some API calculations for safety valve relieving capacity requirements. I'm too far away from my own resource material in my office.
RE: Area of Ellipsoidal Heads
In my formula 'D' is in metres for both surface area and volume.
Excuse my ignorance but why is the surface area of a dished end required to safety valve relieving capacity requirements? - I would have thought volume would be reuired.......??
RE: Area of Ellipsoidal Heads
API 521, Paragraph 3.15.2.1.2, Equation (8). This is for supercritical fluids, gases or vapors when the pressure is generated by exposure to open fires. A' is the exposed surface area of the vessel in square feet.
RE: Area of Ellipsoidal Heads
Give the outside diameter of your vessel and the type of head and its' thickness and I can give you something to work with.
RE: Area of Ellipsoidal Heads
See Appendix F "Steel Plate Engineering Data" Volume 2.
RE: Area of Ellipsoidal Heads
The vessel is 153" OD, the heads are 2:1 semi-elliptical with a nominal thickness of 1.875".
RE: Area of Ellipsoidal Heads
For a 1.875" thick head
The head blank prior to forming for a 144" OD head is 188".
The head blank prior to forming for a 72" OD head is 99"
It works out that your head blank should have been between 198" and 200" Dia.
What I would do is pull a tape on your head and use that number or check and see if it approaches these numbers or use these numbers and be on the conservative side.
The loss on forming usually isn’t very much though will vary by manufacturer.
These number are from a series of tables that were used for cost estimation of a vessel in the old days.
Part of a class I had in 1967.
I'm still looking for the other information on heads that I had.
RE: Area of Ellipsoidal Heads
http://www.pveng.com/Soft/Heads/Heads.htm
Click on the 4 Head Spreadsheets link.
But the surface area of a formed head may be 10% more than that of the blank diameter before formation (because of thinning).
Regards,
Believe it or not : Had we trusted Archimedes and assigned him the work of lifting the earth(or any mass equivalent to that of earth on earth),with a lever of suitable length, it would have taken him 23 million million years to lift the earth by one centimeter, if he worked at the rate of 1 HP.
RE: Area of Ellipsoidal Heads
1.084 x Dia. squared.
This is from "Pressure Vessel Design Manual" by Moss.
GJ
RE: Area of Ellipsoidal Heads
A = [(1/4) * pi + (1/24) * sqrt(3) * ln(sqrt(3) + 2) ] * d^2
-Christine
RE: Area of Ellipsoidal Heads
the calculation of the length of an ellipse and of the area of an ellipsoid are known as being 'elliptic' (as the word says) problems: this means that closed form solutions do not exist for them, only approximate values.
You should revise your calculus exercise.
prex
http://www.xcalcs.com
Online tools for structural design
See http://www.xcalcs.com/docs/symbolinfo.htm if you want to use symbols on these fora
RE: Area of Ellipsoidal Heads
x ^ 2 / (d / 4) ^ 2 + y ^ 2 /(d / 2) ^ 2 = 1
or
y = sqrt (d ^ 2 / 4 - 4 * x ^ 2)
if you rotate the ellipse about the x-axis, and the surface can be found by integrating from 0 to d/4:
2 * pi * y * sqrt (1 + y' ^ 2)
where y' is the derivative of y.
-Christine
RE: Area of Ellipsoidal Heads
A = [(1/4) * pi + (1/24) * pi * sqrt(3) * ln(sqrt(3) + 2) ] * d^2
which works out to A = 1.084d^2
-Christine
RE: Area of Ellipsoidal Heads
As this is a spheroid (a special case of ellipsoid) it can be integrated: I was mistaken by the erroneous result of your first formula.
BTW that formula and others are available at http://mathworld.wolfram.com/SurfaceofRevolution.html
prex
http://www.xcalcs.com
Online tools for structural design
See http://www.xcalcs.com/docs/symbolinfo.htm if you want to use symbols on these fora