Calculations

Calculations

• Coordinate rounding

  A coordinate or label value rounded for the drawing.

  f(v) = +v.toFixed(3); 0 when v is not finite

  Process diagram entities process/draw.js

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• Stream label

  The text under a stream arrow: its name, temperature in degrees Celsius and pressure in bar.

  T (°C) = T − 273.15; P (bar) = P ÷ 1e5; both to 3 decimals

  Process diagram entities process/draw.js

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• Point inside a node boundary

  Whether a tag or line label lies inside a hazard study node's region.

  count the sides whose ends straddle the point's height and cross to its right; inside when the count is odd

  Process diagram entities process/draw.js

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• Controller faceplate numbers

  The set point, measurement, output and error a controller faceplate shows from a simulation.

  error = set point − last measurement

  Process diagram entities process/draw.js

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• Bar-screen head loss

  The head lost through a bar screen.

  h = β × (w ÷ b)^(4/3) × v² ÷ 2g × sin θ

  Water treatment unit processes and sludge sizing process/env/water.js

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• Ideal settling basin

  The overflow rate and the fraction of particles removed.

  v₀ = Q ÷ A; removal = min(1, vs ÷ v₀)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Granular filter head loss

  The head lost through a clean filter bed in laminar flow.

  h = 180 × L × ν × (1 − ε)² × v ÷ (g × ε³ × d²)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Disinfection survival

  The fraction of organisms surviving a contact time, and the log removal.

  s = exp(−k × Cⁿ × t); log removal = −log₁₀(s)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Contact time for a log removal

  The contact time needed to reach a wanted log removal.

  t = log₁₀ removal × ln 10 ÷ (k × Cⁿ)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Sludge retention time

  The mass of sludge in the system divided by the mass leaving per day.

  SRT = V × X ÷ (Qw × Xw + Qe × Xe)

  Water treatment unit processes and sludge sizing process/env/water.js

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• Tank footprints for the site plan

  The plan area and the side of a square footprint for each tank.

  area = V ÷ depth; side = √area

  Water treatment unit processes and sludge sizing process/env/water.js

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• Complete-mix tank sizing

  Sludge production, tank volume, retention time, food-to-mass ratio and oxygen demand.

  Px = Y × Q × (S₀ − S) ÷ (1 + kd × θc); V = θc × Px ÷ X; O₂ = Q × (S₀ − S) − 1.42 × Px

  Water treatment unit processes and sludge sizing process/env/design.js

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• Return sludge ratio

  The return flow as a fraction of the plant flow.

  Qr ÷ Q = (X − Xe) ÷ (Xr − X)

  Water treatment unit processes and sludge sizing process/env/design.js

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• Clarifier loadings

  Surface overflow rate and solids loading of a clarifier.

  overflow = Q ÷ A; solids = (Q + Qr) × X ÷ 1000 ÷ A ÷ 24

  Water treatment unit processes and sludge sizing process/env/design.js

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• Reading to SI units

  Converts a temperature, pressure, flow or length reading to SI, including gauge pressures.

  K = °C + 273.15; K = (°F − 32) × 5 ÷ 9 + 273.15; Pa = gauge × factor + atmosphere; else value × factor

  Plant readings: units, comparison and trends process/env/historian.js

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• Marker text

  The value shown next to a tag on the diagram and the 3D model.

  Plant readings: units, comparison and trends process/env/historian.js

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• Plant against model

  How far each plant reading is from the value the model gives.

  deviation = (plant − model) ÷ |model| (÷ 1 when the model value is 0)

  Plant readings: units, comparison and trends process/env/historian.js

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• Trend thinning

  Reduces a long series to at most a given number of points for plotting, keeping its shape.

  per bucket: keep the sample with the largest triangle area against the previous kept point and the next bucket's mean

  Plant readings: units, comparison and trends process/env/historian.js

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• Series summary

  Count, minimum, maximum, mean and standard deviation of a series.

  mean = Σ v ÷ n; sd = √(Σ (v − mean)² ÷ n)

  Plant readings: units, comparison and trends process/env/historian.js

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• Cylindrical shell thickness

  The required thickness of a cylindrical shell under internal pressure.

  t_circ = P·R ÷ (S·E − 0.6P); t_long = P·R ÷ (2S·E + 0.4P); t = larger of the two

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Formed head thickness

  The required thickness of an ellipsoidal, torispherical or hemispherical head.

  ellipsoidal: t = P·D·K ÷ (2S·E − 0.2P), K = (2 + (D ÷ 2h)²) ÷ 6; torispherical: t = P·L·M ÷ (2S·E − 0.2P), M = (3 + √(L ÷ r)) ÷ 4

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Conical section thickness

  The required thickness of a cone.

  t = P·D ÷ (2·cos α × (S·E − 0.6P))

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Maximum allowable working pressure

  The pressure a shell of given thickness may carry.

  P_c = S·E·t ÷ (R + 0.6t); P_l = 2S·E·t ÷ (R − 0.4t); P = smaller of the two

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Hydrostatic test pressure

  The test pressure from the allowable working pressure.

  P_test = 1.3 × MAWP × stress ratio

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• External pressure, elastic formulas

  The critical and allowable external pressure of a plain cylinder.

  long: P = 2E·(t ÷ D)³ ÷ (1 − ν²); short: P = 2.42E·(t ÷ D)^2.5 ÷ ((1 − ν²)^0.75 × (L ÷ D − 0.45·√(t ÷ D))); P_a = P_cr ÷ 4

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Limits of reinforcement

  How far along and normal to the wall material counts as reinforcement of an opening.

  along wall = max(d, Rn + tn + t); normal = min(2.5t, 2.5tn + te)

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Opening reinforcement areas

  The area an opening removes and the areas available to replace it.

  A = d·tr + 2tn·tr·(1 − fr₁); available = A₁ + A₂ + A₄₁ + A₅; margin = available ÷ A − 1

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Saddle bending stresses

  Longitudinal bending moments and stresses of a horizontal vessel on two saddles.

  M₁ = Q·a·(1 − (1 − a ÷ L + (R² − H²) ÷ 2aL) ÷ (1 + 4H ÷ 3L)); σ = M ÷ (π·R²·t)

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Wind velocity pressure

  The wind pressure on a vessel from the wind speed.

  q = 0.613 × Kz × Kzt × Kd × V² × I

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Wind force and overturning moment

  The wind force on a vertical vessel and its moment at the base.

  F = q × 10⁻⁶ × Cf × D × H; M = F × H ÷ 2

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Seismic base shear and moment

  A first estimate of the seismic shear and overturning moment.

  V = Cs × W; M = Cs × W × 2H ÷ 3

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Skirt stresses

  Compressive and tensile stress at the base of a skirt from weight and overturning.

  A = π·D·t; Z = π·D²·t ÷ 4; σ = M ÷ Z ± W ÷ A

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Flat head thickness

  The required thickness of a circular flat head or cover.

  t = d × √(C·P ÷ (S·E))

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Minimum design metal temperature

  The stress ratio and the temperature reduction read from points a person types.

  ratio = tr·E ÷ (tn − c); MDMT = base − ΔT(ratio)

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Data sheet values

  The rows and text of the vessel data sheet.

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• Equipment parameters for the plant model

  The diameter, length and support height handed to the plant equipment.

  Pressure vessel thickness and support formulas process/equip/vessel.js

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• External pressure from chart factors

  The allowable external pressure of a cylinder from the chart factor A and the material curve a person types.

  chart: P_a = 4B ÷ (3·D_o ÷ t); elastic: P_a = 2A·E ÷ (3·D_o ÷ t)

  Pressure vessel thickness and support formulas process/equip/vessel2.js

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• Stiffening ring inertia

  The moment of inertia a stiffening ring must have.

  I_s = D_o² × L_s × (t + A_s ÷ L_s) × A ÷ 14

  Pressure vessel thickness and support formulas process/equip/vessel2.js

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• Table values in millimeters

  Converts each published row to millimeters, mm² and kg/m.

  mm = in × 25.4; mm² = in² × 25.4 × 25.4; kg/m = lb/ft × 1.48816394; r = (k_des − t_f) × 25.4

  Steel section dimensions, areas and outlines shapes/sections.js

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• Exact section area

  The cross-section area worked out from the dimensions, with fillets and rounded corners included.

  I: 2·b_f·t_f + (d − 2t_f)·t_w + (4 − π)·r²; RHS: 2t(h + b − 2t) − (4 − π)(r_o² − r_i²); CHS: π(D − t)·t

  Steel section dimensions, areas and outlines shapes/sections.js

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• Section outline

  The outline of a section as loops of points, centered on its bounding box.

  arc point = (cx + r·cos a, cy + r·sin a), a = a₀ + (a₁ − a₀)·i ÷ n

  Steel section dimensions, areas and outlines shapes/sections.js

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• Rounded rectangle loop

  The outer or inner loop of a rectangular hollow section with rounded corners.

  Steel section dimensions, areas and outlines shapes/sections.js

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• Loop area

  The signed area of an outline loop.

  A = ½ × Σ (xᵢ·yᵢ₊₁ − xᵢ₊₁·yᵢ)

  Steel section dimensions, areas and outlines shapes/sections.js

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• Loop perimeter

  The length around an outline loop.

  L = Σ √(Δx² + Δy²)

  Steel section dimensions, areas and outlines shapes/sections.js

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• Part sizes in millimeters

  The table dimensions of each size of a part family, with inch sizes converted.

  mm = in × 25.4; pitch = 25.4 ÷ threads per inch

  Standard parts and library items shapes/parts.js

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• Hexagon area

  The area of a hexagon from its width across flats.

  A = (√3 ÷ 2) × s²

  Standard parts and library items shapes/parts.js

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• Mass from volume

  The mass of a part in kilograms from its volume in mm³.

  kg = mm³ × 10⁻⁹ × 7850, rounded to 4 decimals

  Standard parts and library items shapes/parts.js

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• Inch length as a fraction

  Writes an inch length as a whole number and a fraction for the part's designation.

  n = round(v × 64); reduce n ÷ 64

  Standard parts and library items shapes/parts.js

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• Part dimensions and mass

  The full set of dimensions, the bounding box and the mass of one part.

  e = 2s ÷ √3; bolt mass = (hex area × k + π ÷ 4 × d² × l) × ρ; gear: d = m·z, d_a = m(z + 2), d_f = m(z − 2.5), d_b = d·cos 20°

  Standard parts and library items shapes/parts.js

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• Coordinate rounding in library items

  Rounds every coordinate written into a library item's drawing.

  round(v × 1000) ÷ 1000

  Standard parts and library items shapes/items.js

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