Torispherical Head Tank Volume
Calculating Tank Volume
Saving time, increasing accuracy
By Dan Jones, Ph.D., P.E.
C
alculating fluid volume in a horizontal or vertical cylindrical or elliptical tank can be complicated, depending on fluid height and the shape of the heads (ends) of a horizontal tank or the bottom of a vertical tank. Exact equations now are available for several commonly encountered tank shapes. These equations can be used to make rapid and accurate fluid-volume calculations. All equations are rigorous, but computational difficulties will arise in certain limiting configurations.
All volume equations give fluid volumes in cubic units from tank dimensions in consistent linear units. All variables defining tank shapes required for tank volume calculations are defined in the “Variables and Definitions” sidebar. Graphically, Figs. 1 and 2 show horizontal tank variables and Figs. 3 and 4 show vertical tank variables. Exact fluid volumes in elliptical horizontal or vertical tanks can be found by first calculating the fluid volumes of appropriate cylindrical horizontal or vertical tanks using the equations described above, and then by adjusting those results using appropriate correction formulas. Horizontal Cylindrical Tanks Fluid volume as a function of fluid height can be calculated for a horizontal cylindrical tank with either conical, ellipsoidal, guppy, spherical, or torispherical heads where the fluid height, h, is measured from the tank bottom to the fluid surface, see Figs. 1 and 2. A guppy head is a conical head where the apex of the conical head is level with the top of the cylindrical section of the tank as shown in Fig. 1. A torispherical head is an ASME-type head defined by a knuckle-radius parameter, k, and a dish-radius parameter, f, as shown in Fig. 2. An ellipsoidal head must be exactly half of an ellipsoid of revolution; only a hemiellipsoid is valid – no “segment” of an ellipsoid will work as is true in the case of a spherical head where the head may be a
Saving time, increasing accuracy
By Dan Jones, Ph.D., P.E.
C
alculating fluid volume in a horizontal or vertical cylindrical or elliptical tank can be complicated, depending on fluid height and the shape of the heads (ends) of a horizontal tank or the bottom of a vertical tank. Exact equations now are available for several commonly encountered tank shapes. These equations can be used to make rapid and accurate fluid-volume calculations. All equations are rigorous, but computational difficulties will arise in certain limiting configurations.
All volume equations give fluid volumes in cubic units from tank dimensions in consistent linear units. All variables defining tank shapes required for tank volume calculations are defined in the “Variables and Definitions” sidebar. Graphically, Figs. 1 and 2 show horizontal tank variables and Figs. 3 and 4 show vertical tank variables. Exact fluid volumes in elliptical horizontal or vertical tanks can be found by first calculating the fluid volumes of appropriate cylindrical horizontal or vertical tanks using the equations described above, and then by adjusting those results using appropriate correction formulas. Horizontal Cylindrical Tanks Fluid volume as a function of fluid height can be calculated for a horizontal cylindrical tank with either conical, ellipsoidal, guppy, spherical, or torispherical heads where the fluid height, h, is measured from the tank bottom to the fluid surface, see Figs. 1 and 2. A guppy head is a conical head where the apex of the conical head is level with the top of the cylindrical section of the tank as shown in Fig. 1. A torispherical head is an ASME-type head defined by a knuckle-radius parameter, k, and a dish-radius parameter, f, as shown in Fig. 2. An ellipsoidal head must be exactly half of an ellipsoid of revolution; only a hemiellipsoid is valid – no “segment” of an ellipsoid will work as is true in the case of a spherical head where the head may be a