CONTENTS OF CYLINDRICAL TANKS Machinery's Handbook, 31st Edition
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(1) (2) (3) (4) (5) where: C = liquid volume conversion factor; the exact value depends on the length and liquid volume units used during measurement: 0.00433 US gal/in 3 ; 7.48 US gal/ft 3 ; 0.00360 UK gal/in 3 ; 6.23 UK gal/ft 3 ; 0.001 liter/cm 3 ; or 1000 liters/m 3 V T = total volume of liquid tank can hold V s = volume formed by segment of circle having depth x in the given tank (see diagram) V = volume of liquid at particular level in tank L = length of tank; r = radius of tank ( = 1 ⁄ 2 diameter) A = segment area of a corresponding unit circle taken from the table starting on page 84. y = actual depth of contents in tank as shown on a gauge rod or stick x = depth of the segment of a circle to be considered in given tank. As can be seen in the diagram, both x and y are the actual depth of contents when the tank is less than half full, but x is the depth of the void ( d - y ) above the contents when the tank is more than half full. In the discussion of the unit circle, page 84, r = 1, and so the height of a segment of a corresponding unit circle is x / r. Example: A tank is 20 feet long and 6 feet in diameter. Convert a long stick graduated in inches into a gauge graduated at two points, 1000 and 3000 US gallons. Solution: L 20 12 × 240 in. = = r 6 ⁄ 2 12 × 36 in. = = The 72-inch mark from the bottom on the inch-stick can be graduated for the rounded full volume of 4230 and the halfway point 36 in. for 4230 ⁄ 2 or 2115. It can be seen that the 1000-gal mark would be below the halfway mark. From Formulas (3) and (4): A 1000 = ------ = 0.7424 ; from the table starting on page 84, h can be interpolated as 0.5724; and x = y = 36 × 0.5724 = 20.61. If the desired level of accuracy permits, interpolation can be omitted by choosing h directly from the table on page 84 for the value of A nearest that calculated above. Therefore, the 1000-gal mark is graduated 20 5 ⁄ 8 in. from bottom of rod. It can be seen that the 3000 mark would be above the halfway mark. Therefore, the circu lar segment considered is the cross section of the void space at the top of the tank. From Formulas (3) and (5): A 3000 4230– 3000 1347 --------------- 0.9131 h 0.6648 x 36 0.6648 × 23.93 in. = = = = = , , Therefore, the 3000-gal mark is 72.00 - 23.93 = 48.07, or at the 48 1 ⁄ 16 -in. mark from the bottom. From Formula (1): K = 0.00433 × 36 2 × 240 = 1346.80 From Formula (2): V T = 3.1416 × 1347 = 4231.7 US gal. 1000 1347 K = Cr 2 L = tank constant (the same for any given tank) V T = p K , for a tank that is completely full V s = KA V = V s , for a tank that is less than half full V = V T - V s = V T - KA , for a tank that is more than half full
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