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Tanks and Hoppers by the Numbers
Capacity, levels, mass, sheet and patterns for fabricated tanks and hoppers: cylinders, cones, frustums, prismoids, calibration tables and developments
Calculate tanks and hoppers with numbers: capacity and freeboard, frustums and the prismoidal formula, level tables, mass and loads, sheet area, and cone and hopper patterns.
Start readingAbout this book
Tanks, bins and hoppers are among the most common things a fabrication shop makes, and almost every question about them is a calculation. How much does it hold, and how much when it is filled to the working level? How high must it be to hold 1,500 litres? What does the dipstick read at 1,000 litres? What does it weigh full, and what does each leg carry? How much sheet does it take, and what shape is the flat pattern of its cone? Each answer is geometry that has been known for centuries, and each is easy to get wrong by a unit, a radius used as a diameter, or a formula applied to a shape it does not fit.
This book works through those calculations in the order a tank is designed, drawn and made. It starts with capacity and what “full” means, then covers prisms and cylinders, cones and frustums, the prismoidal formula, partly filled tanks and calibration tables, mass and support loads, sheet area, and the patterns for cones, frustums and pyramid hoppers. It ends with the checks a tank should pass before it is cut.
It suits designers, drafters, fabricators and process engineers. It assumes school geometry and a calculator or spreadsheet. The Library’s collection chapter on areas, volumes and masses for the workshop gives a broad introduction; this book goes deep on one family of products.
The running case
Every chapter follows one fictional job. This is an illustration. A fabricator builds equipment for a small food processor: a stainless steel holding tank, TK-1, with an internal diameter of 1,200 mm, a straight shell 1,500 mm high and a conical bottom 400 mm deep draining to a 100 mm outlet; and a square powder hopper, HP-400, 1,000 × 1,000 mm at the top, tapering over 900 mm to a 250 × 250 mm outlet, with a 300 mm straight upstand above.
The business, the processor and the equipment are invented; none describes KEVOS® work or a real product. Prices are illustrations in Australian dollars, excluding GST.
Source limits and professional responsibility
The geometry in this book is exact, and every calculation was checked by running it. The structural design of a tank or bin, its wall thickness, its supports, its behaviour under pressure, vacuum, wind or the flow of a bulk solid, is a separate engineering task. Tanks for flammable and combustible liquids, pressure vessels and large bins are governed by Australian Standards such as AS 1692 for steel tanks for flammable and combustible liquids and AS 1210 for pressure vessels, and by the regulator in each state. This book is educational. Real tanks and hoppers must be designed and approved by a competent engineer to the standards that apply.
Who this book is for
Mechanical designers, drafters, fabricators and process engineers who size, draw, quote or build fabricated tanks, bins and hoppers in sheet and plate.
What you will learn
- Calculate the gross and working capacity of tanks made from prisms, cylinders, cones and frustums.
- Use the prismoidal formula for transitions and check when a simpler formula is exact.
- Build a level-to-volume table for vertical and horizontal tanks and check it against a fill.
- Estimate the mass of a tank and its contents and the loads on its legs or supports.
- Develop cone, frustum and pyramid hopper patterns and the sheet needed to cut them.
Inside this book
Chapters
- 01Capacity, and what full meansDefine a tank's gross, working and usable capacity, keep litres, cubic metres and millimetres straight, and catch a tank sized 109 litres short because gross was mistaken for working.
- 02Prisms and cylindersCalculate rectangular, cylindrical and elliptical tanks, find the height for a given capacity, allow for a sloping floor, compare sheet used per litre, and catch a cylinder four times too big.
- 03Cones, pyramids and frustumsCalculate cone and pyramid bottoms and the frustums that hoppers are made of, find wall and hip slopes, and catch an average-of-the-ends estimate that overstated a hopper by 21%.
- 04The prismoidal formulaUse one formula for prisms, frustums, wedges, spheres and transitions, know why it is exact for them, apply it to a square-to-round transition and a dissimilar hopper, and check it.
- 05Partly filled tanks and level tablesTurn a level into a volume for cone-bottomed and horizontal tanks, build a calibration table, mark a dipstick, and catch a level transmitter scaled linearly that overstated the contents by 220 litres.
- 06Mass, loads and supportsEstimate a tank's empty and full mass, list every load case including the hydrostatic test and an overfill, share loads between legs and load cells, and catch a floor checked 14% light.
- 07Surface area and sheetCalculate the sheet a tank needs: shell blanks at the mean diameter, cone and lid areas, nesting on stock sheets, yield, weld length and material cost, and catch a shell blank cut 9 mm short.
- 08Cone and frustum patternsDevelop a cone or frustum into a flat annular sector by calculation: slant height, pattern radii, sector angle and chord, at the right diameter for the joint, and catch a cone 19 mm too big round.
- 09Hopper walls and transitions by triangulationFind true lengths from plan and height, develop pyramid hopper walls, an offset hopper and a square-to-round transition by triangulation, and catch walls cut with the vertical height for the slant.
- 10Checks before the tank is cutCheck a tank's calculations before cutting: the calculation sheet, independent checks, tolerance effects on capacity, the water fill and head, and catch a hopper's patterns mirrored front to back.
Apply This in Practice
Use these KEVOS® tools to try the method from this reading with your own numbers.
Applies this method
Spherical Sections: Areas and Volumes (Hollow Sphere, Sector, Segment, Zone, Ring)
Works out the volume, area and sphere radius of the spherical caps and whole spheres this chapter uses for dished tank bottoms, with the other spherical sections beside them.
Used in Cones, pyramids and frustums
References and source notes
The manuscript and worked examples are original KEVOS® writing. References inform particular concepts; their authors do not endorse this book. Web references were consulted on 26 October 2026.
- William Neubecker, David Williams Company, New York. Mensuration for Sheet Metal Workers (1907). Supplied source, read as a subject map of the areas, surfaces and capacities a sheet metal shop calculates, including tanks, hoppers, flaring vessels and the prismoidal formula. Its imperial examples are not reproduced; this book's examples, figures and exercises are its own, in SI units.
- Standards Australia. AS 1692-2006 (R2016) Steel tanks for flammable and combustible liquids (2006). Named by number and scope only, as the Australian Standard for steel tanks for the bulk storage of flammable and combustible liquids. No values are quoted from it.