Partial Volume of Dished Head

[chbake]

We are looking for a formula to determine the volume of a dished head as a function of height; or the height measured from the flange connection of the head vertically to the head's top. For example, what volume is contained in a dished head measured vertically 1" from the flange connection. This problem is integral calculus at it's best. Is there a simple solution, formula or function that nails this concept down?

 

[Estassoc]

For a dished head of inside diameter (D), inside crown radius (rc) and inside knuckle radius (rk), you'll be able to calculate the inside height (h) using plain mathematical formulas.

h = rc - {[(rc - rk)^2 - (0.5xD - rk)^2]^0.5}

The inside volume of a dished head consist of two parts:
a) The volume of a spherical sector whose radius is equal
to rc less the volume of a right circular cone of radius
(0.5xD - rk) and a height of (rc - h).

b) The volume derived by revolving a circular sector whose
radius is equal to rk about the longitudinal axis of
the dished head. The radius of revolution is equal to
the horizontal distance from the centroid of the
circular sector to the longitudinal axis.

If you agree with the above analysis, then there might not
be a straight forward formula to get the volume of a
dished head particularly on cases where the inside depth
where you want the volume taken is less than the calculated inside height of the dished head (as per formula shown above).

 

[Shmulik]

Please see at the following:
thread794-39958
thread770-12414

 

[Jeffro]

hi chbake here are some basic formuli

2:1 S.E Head Volume, 3.1416xDiameter cubed Divided by 24

Hemi Head, 3.1416xDiameter cubed Divided by 12

These volumes are to the tangent point between the curved face and the straight flange.
hope this is helpful

 

[deanc]

Go to the "Lightnin" web site. They have a nice slip chart.