Topics: Volume, Sphere, Ellipsoid Pages: 11 (2058 words) Published: November 20, 2012
Calculating Tank Volume
Saving time, increasing accuracy
By Dan Jones, Ph.D., P.E.

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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.

Variables and Definitions (See Figs. 1-5) a is the distance a horizontal tank's heads extend beyond (a > 0) or into (a < 0) its cylindrical section or the depth the bottom extends below the cylindrical section of a vertical tank. For a horizontal tank with flat heads or a vertical tank with a flat bottom a = 0. Af is the cross-sectional area of the fluid in a horizontal tank's cylindrical section. D is the diameter of the cylindrical section of a horizontal or vertical tank. DH, DW are the height and width, respectively, of the ellipse defining the cross section of the body of a horizontal elliptical tank. DA, DB are the major and minor axes, respectively, of the ellipse defining the cross section of the body of a vertical elliptical tank. f is the dish-radius parameter for tanks with torispherical heads or bottoms; fD is the dish radius. h is the height of fluid in a...