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Determine the volume of a dished head.
T Head thickness, after forming Sp Spherical radius, internal Kr Knuckle radius, internal D Outside Head diameter Sf Straight flange
Internal diameter, id = D - ( 2 x T )
Head depth (less straight flange), Hd = Sp - Sqrt( [ ( Sp - Kr ) 2 - ( ( id /2 ) - Kr ) 2 ]
Knuckle, included angle = ArcSin( ( Sp - Hd ) / ( Sp - Kr ) )
Depth of Knuckle Section, H1 = Kr x Sin( Knuckle included angle )
Depth of Spherical Section, H2 = Hd - H1
Temporary variable, A = ( id / 2 ) - Kr
Temporary variable, B = Sqrt( Kr2 - H12 )
Diameter where spherical radius intersects the knuckle radius, D2 = id - ( 2 x Kr ) + ( 2 x B )
Volume1 = Pi x A x H1 x [ A + Sqrt( Kr2 - H12 ) ] + [ Pi x ( Kr2 ) x [ H1 + [ A x ArcSin( H1 /Kr ) ]] - [ ( Pi /3 ) x H13 ]]
Volume2 = H22 x Pi [ Sp - ( H2 /3 ) ]
Volume3 = [ ( id2 x Pi ) /4 ] x Sf ...volume contained in straight flange
Hv, head volume ( not including straight flange portion )
Hv = ( Volume1 + Volume2 ) /1000000
Total Head volume, mm² = ( Volume1 + Volume2 + Volume3 ) /1000000
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