Common calculation formulas for pressure vessel design

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This post was last edited by B0SS on 2019-10-22 at 18:09.
1. Formula for calculating the mass of carbon steel plates:
Formula: 7.85 × length (m) × width (m) × thickness (mm)
Example: For a steel plate with dimensions 6m (length) × 2m (width) × 20mm (thickness):
Calculation: 7.85 × 6 × 2 × 20 = 1884 kg

2. Formula for calculating the mass of carbon steel pipes:
Formula: (outer diameter – wall thickness) × wall thickness (mm) × 0.02466 × length (m)
Example: For a pipe with outer diameter 114mm, wall thickness 4mm, and length 6m:
Calculation: (114 – 4) × 4 × 0.02466 × 6 = 65.102 kg

3. Formula for calculating the mass of carbon steel round bars:
Formula: diameter (mm) × diameter (mm) × 0.00617 × length (m)
Example: For a round bar with diameter Φ20mm and length 6m:
Calculation: 20 × 20 × 0.00617 × 6 = 14.808 kg

4. Formula for calculating the mass of carbon steel square bars:
Formula: side length (mm) × side length (mm) × length (m) × 0.00785
Example: For a square bar with side length 50mm and length 6m:
Calculation: 50 × 50 × 6 × 0.00785 = 117.75 kg

5. Formula for calculating the mass of carbon steel flat bars:
Formula: side width (mm) × thickness (mm) × length (m) × 0.00785
Example: For a flat bar with side width 50mm, thickness 5.0mm, and length 6m:
Calculation: 50 × 5 × 6 × 0.00785 = 11.775 kg

6. Formula for calculating the mass of carbon steel hexagonal bars:
Formula: distance between opposite sides × distance between opposite sides × length (m) × 0.00068
Example: For a hexagonal bar with distance between opposite sides 50mm and length 6m:
Calculation: 50 × 50 × 6 × 0.0068 = 102 kg

7. Formula for calculating the mass of carbon steel deformed steel bars:
Formula: diameter (mm) × diameter (mm) × 0.00617 × length (m)
Example: For a deformed steel bar with diameter Φ20mm and length 12m:
Calculation: 20 × 20 × 0.00617 × 12 = 29.616 kg

8. Formula for calculating the mass of carbon steel rectangular hollow sections:
Formula: (side length + side width) × 2 × thickness × 0.00785 × length (m)
Example: For a rectangular hollow section with dimensions 100mm × 50mm, thickness 5mm, and length 6m:
Calculation: (100 + 50) × 2 × 5 × 0.00785 × 6 = 70.65 kg

9. Formula for calculating the mass of carbon steel square hollow sections:
Formula: side width (mm) × 4 × thickness × 0.00785 × length (m)
Example: For a square hollow section with side width 50mm, thickness 5mm, and length 6m:
Calculation: 50 × 4 × 5 × 0.00785 × 6 = 47.1 kg

10. Formula for calculating the mass of carbon steel equal-leg angle bars:
Formula: leg width (mm) × thickness × 0.015 × length (m) (approximate calculation)
Example: For an angle bar with leg width 50mm, thickness 5mm, and length 6m:
Calculation: 50 × 5 × 0.015 × 6 = 22.5 kg (table value: 22.62 kg)

11. Formula for calculating the mass of carbon steel unequal-leg angle bars:
Formula: (leg width + leg width) × thickness × 0.0076 × length (m) (approximate calculation)
Example: For an angle bar with dimensions 100mm × 80mm, thickness 8mm, and length 6m:
Calculation: (100 + 80) × 8 × 0.0076 × 6 = 65.67 kg (table value: 65.676 kg)

Other non-ferrous metals:
12. Formula for calculating the mass of brass pipes:
Formula: (outer diameter – wall thickness) × thickness × 0.0267 × length (m)
Example: For a brass pipe with outer diameter 20mm, thickness 1.5mm, and length 6m:
Calculation: (20 – 1.5) × 1.5 × 0.0267 × 6 = 4.446 kg

13. Formula for calculating the mass of copper pipes:
Formula: (outer diameter – wall thickness) × thickness × 0.02796 × length (m)
Example: For a copper pipe with outer diameter 20mm, thickness 1.5mm, and length 6m:
Calculation: (20 – 1.5) × 1.5 × 0.02796 × 6 = 4.655 kg

14. Formula for calculating the mass of aluminum checker plates:
Formula: length (m) × width (m) × thickness (mm) × 2.96
Example: For an aluminum checker plate with width 1m, length 3m, and thickness 2.5mm:
Calculation: 1 × 3 × 2.5 × 2.96 = 22.2 kg

Brass sheet: specific gravity 8.5
Copper sheet: specific gravity 8.9
Zinc sheet: specific gravity 7.2
Lead sheet: specific gravity 11.37
Calculation method: specific gravity × thickness = mass per unit area

Note: In these formulas, the unit of length is meters; the unit of area is square meters; all other units are millimeters.
Perimeter of a rectangle = (length + width) × 2
Perimeter of a square = side length × 4
Area of a rectangle = length × width
Area of a square = side length × side length
Area of a triangle = base × height ÷ 2
Area of a parallelogram = base × height
Area of a trapezoid = (upper base + lower base) × height ÷ 2
Diameter = radius × 2
Radius = diameter ÷ 2
Circumference of a circle = pi × diameter = pi × radius × 2
Area of a circle = pi × radius × radius
Surface area of a cuboid = (length × width + length × height + width × height) × 2
Volume of a cuboid = length × width × height
Surface area of a cube = edge length × edge length × 6
Volume of a cube = edge length × edge length × edge length
Lateral surface area of a cylinder = circumference of base circle × height
Surface area of a cylinder = areas of upper and lower bases + lateral surface area
Volume of a cylinder = base area × height
Volume of a cone = base area × height ÷ 3
Volume of a cuboid (cube or cylinder) = base area × height
For planar figures: C denotes perimeter; S denotes area. For a square with side length a: C = 4a ； S = a² for a rectangle: a, b – side lengths; C = 2(a + b) ； Triangle: S = ab; a, b, c – side lengths; H – height on side a; s – half of the perimeter; A, B, C – interior angles. Where s = (a + b + c)/2. S = ah/2 = ab/2·sinC = 1/2 = a²sinBsinC/(2sinA).
Quadrilateral: d, D – lengths of diagonals; α – angle between diagonals. S = dD/2·sinα.
Parallelogram: a, b – side lengths; h – height on side a; α – angle between sides. S = ah = absinα.
Rhombus: a – side length; α – angle between sides; D – length of longer diagonal; d – length of shorter diagonal. S = Dd/2 = a²sinα.
Trapezoid: a and b – lengths of upper and lower bases; h – height; m – length of midline. S = (a + b)h/2 = mh.
Circle: r – radius; d – diameter. C = πd = 2πr. S = πr² = πd²/4.
Sector: r – radius of sector; a – central angle in degrees. C = 2r + 2πr×(a/360). S = πr²×(a/360).
Arc: l – length of arc; b – length of chord; h – perpendicular distance from center to chord; r – radius; α – central angle in degrees. S = r²/2·(πα/180 – sinα) = r²arccos(–(r – h))/(2rh – h²)¹/² = παr²/360 – b/2·1/2 = r(l – b)/2 + bh/2 ≈ 2bh/3.
Ring: R – radius of outer circle; r – radius of inner circle; D – diameter of outer circle; d – diameter of inner circle. S = π(R² – r²) = π(D² – d²)/4.
Ellipse: D – major axis length; d – minor axis length. S = πDd/4.
Solid figures: Area S and volume V.
Cube: a – side length. S = 6a². V = a³.
Rectangular prism: a – length; b – width; c – height. S = 2(ab + ac + bc). V = abc.
Prism: S – area of base; h – height. V = Sh.
Pyramid: S – area of base; h – height. V = Sh/3.
Frustum of a pyramid: S1 and S2 – areas of upper and lower bases; h – height. V = h/3(S1 + S2 + 4S0).
Hypocylinder: S1 – area of upper base; S2 – area of lower base; S0 – area of middle cross-section; h – height. V = h(S1 + S2 + 4S0)/6.
Cylinder: r – radius of base; h – height; C – perimeter of base; S_base – area of base; S_side – lateral surface area; S_total – total surface area. C = 2πr. S_base = πr². S_side = Ch. S_total = Ch + 2S_base. V = S_baseh = πr²h.
Hollow cylinder: R – radius of outer circle; r – radius of inner circle; h – height. V = πh(R² – r²).
Right circular cone: r – radius of base; h – height. V = πr²h/3.
Frustum of a cone: r – radius of upper base; R – radius of lower base; h – height. V = πh(R² + Rr + r²)/3.
Sphere: r – radius; d – diameter. V = 4/3πr³ = πd²/6.
Spherical cap: h – height of spherical cap; r – radius of sphere; a – radius of base of spherical cap. V = πh(3a² + h²)/6 = πh²(3r – h)/3a² = h(2r – h).
Frustum of a sphere: r1 and r2 – radii of upper and lower bases of frustum; h – height. V = πh/6.
Torus: R – radius of torus; D – diameter of torus; r – radius of cross-section of torus; d – diameter of cross-section of torus. V = 2π²Rr² = π²Dd²/4.
Bucket-shaped solid: D – diameter of bucket wall; d – diameter of bucket bottom; h – height of bucket. V = πh(2D² + d²)/12 (when the generators are circular with center at the center of the bucket). V = πh(2D² + Dd + 3d²/4)/15 (when the generators are parabolic)