Torispherical heads partial volumes

The equations for a liquid occupying partial volumes of torispherical heads follow. 

For the torispherical head in the vertical position shown in Figure 2,21(c), the knuckle-cylinder partial volume is... 

FIGURE 2.21 Partial volume of torispherical heads (a) vertical position, (b) horizontal position, (c) knuckle region in vertical position, (d) knuckle region in horizontal position. 

FIGURE 2.22 Partial volume of torispherical head in vertical position showing the dish and knuckle volumes. 

FIGURE 2.23 Sketch for the example of the partial volume in a torispherical head in the horizontal position. 

A 102 inch OD F D (flanged and dished, or torispherical) head made to ASME specifications (KR > 0.60/ and KR > Sijj, where = head thickness) is spun from a 1-inch plate. The head is in the horizontal position. The liquid level is 35 inches inside the head. Determine the volume of the liquid that occupies the partial volume of the head. 

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