Weight Calculation of Dishends

Is it possible that PV Elite has determined your overall weight based on thickness determined by your MAWP input?

Dear, RDGRNR

Thank you for your reply.

Let me explain my problem, I have a 2:1 ellipsoidal d'end having 4000mm ID, straight face 50mm, thickness provided is 20mm, pressure is 10 kg/cm² at 100°C. The Surface area that I am getting form PVElite output as well as Manual calculation (A=1.084*OD² + pi*OD*S.F) is 18.326976m². The weight calculated by PVElite is 3129.1 Kg (density 7833.4Kg/m³) and manually I am getting 2870.5 Kg. Also I have not taken any miscellaneous weight (0%) in the PVElite input. Then why there is the difference.

I agree with RDGRNR that PVElite may have calculated a required thickness > 20 mm, and then calculated the weight accordingly.

Dear Tornado,

Thank you for reply, but even the required thickness is 14.23mm which is less than 20mm which I have entered in the input, even then there is a difference.

I'm not familiar with PV Elite, but I would think the most likely reason is that it takes 20mm as the minimum thickness, so calculates on something thicker to allow for thinning when the dished end is formed. Maybe it uses values for thickness and dia of the original flat plate the dished is formed from. The flat plate dia isn't exactly the length of an arc over the finished dished end, due to the effect of thinning. If the supplier will give you these figures, you can check.

I've not come across Moss's formula, so I don't know whether it is just for 2:1 ellipsoidal ends or the more general case for any depth. But I have my own formula

Area = pi^_*r^2_*(1 + (h/r)^1.4)

Putting in h = r/2 for a 2:1 end, it gives area = 1.083^_*OD² in close agreement with your #2. Formula of course is for the elliptical surface, doesn't include the straight flange.

As you can easily see, above formula is correct when h = 0, giving A = pi.r² (flat end), and when h = r, giving A = 2.pi.r² (hemispherical end). The maximum error is about 1% and then only for unusual values of h/r. For h/r = 0.5 (2:1 end) error is < 0.1%. Errors checked by finding (hopefully) "correct" area by numerical integration.

Cheers......Codey

Hello Guest

Ref my #5 - can you post Moss's formula if it's a general formula for any head height? Or if it's only for 2:1 S/E heads, tell us that.

I'm curious!

Cheers..........Codey

Moss has given separate formulas for hemi., torispherical, and 2:1 S/E dishends.

1.084*OD² is for the surface area of 2:1 ellipsoidal dishend.

Thanks Guest

We don't really need Moss's help for the hemishere , it's 2*pi*(D/2)² = 1.571*(D/2)².

Would it be too much to ask what he says for 2:1 torispherical?

Cheers.........Codey

Hello Codemaster,

For 100%-6% (where 100% means the crown radius is 100% of the head dia. and 6% means the knuckle radius is 6% of the head diameter) flanged and dished (Torispherical) head the formula for Surface area is 0.9286*OD².

For other combinations of crown and knuckle

R = Radius of the head.

h = Depth of the Dishend.

Surface area of the Flanged and Dished head.

A= pi*R²*(1+(h²/R² )*(2-h/R))

By the way, codemaster could you please let me know if you have any idea of how to design a multilayered vessel???? I am Searching for it for quite some time now but haven't got any success. Do reply.

Hello Guest

Thanks for that.

I looked at your post re multilayered vessel but sorry, I can't add anything to what others have said. Somebody suggested keeping the 2 shells apart using spacers. That wouldn't be too easy to build, and the spacers give a potential heat flow path.

The outer shell sees a vacuum condition, so the "fill" material has to be firm enough to support it against collapse, or the outer shell itself has to be designed to suit.

Cheers...........Codey