Calculations

Calculations

• Checks against typed targets

  Compares the average, minimum, uniformity and power density with the targets the person typed.

  avg ≥ target; min ≥ target; min ÷ avg ≥ target; LPD ≤ limit

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

  • CadCraft
  • BimCraft
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• Grid CSV

  Writes each grid point and its illuminance.

  x, y, z = round(mm); lux = value.toFixed(1)

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

  • CadCraft
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• Lighting report CSV

  Writes one row per area with its totals and statistics, then every grid point.

  area and lux 1 decimal; lumens and watts 0; W/m² and min ÷ avg 2

  Luminaire files and point-by-point illuminance addons/lighting/lib/mep/photometry.js

  • CadCraft
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• Inputs of an illuminance run

  The mounting height, working height, grid spacing and light loss factor asked for a run.

  mount ≥ 100 mm; work ≥ 0; spacing ≥ 50 mm; 0.05 ≤ LLF ≤ 1

  Luminaire files and point-by-point illuminance addons/lighting/main.js

  • CadCraft
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• Result printed in the command line

  The summary line of an illuminance run.

  min, avg, max: whole lux; uniformity 2 decimals; area and W/m² 1 decimal

  Luminaire files and point-by-point illuminance addons/lighting/main.js

  • CadCraft
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• Drawing units to millimeters on export

  Converts every exported symbol position, line vertex and symbol size to millimeters.

  mm = round(v × mmPerUnit, 3 decimals)

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

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• Drawing extent on export

  The width and height stated for the exported drawing.

  w = ceil(mm(max x) + 50); h = ceil(mm(max y) + 50)

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

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• Symbol position and size on import

  Places an imported plant item in the drawing at the file's position and size.

  x = x_file × perMm; l = SymbolSize × perMm

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

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• Line ends moved onto connections on import

  Moves an imported line end onto the nearest symbol connection when it is close enough.

  moved when distance ≤ 0.6 × symbol size

  DEXPI and PCF plant exchange files addons/pid/lib/dexpi-pid.js

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• Numbers read from DEXPI attributes

  Turns an attribute's text into a number.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

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• Position and rotation of a plant item

  The location of an item and its rotation in the plane, read from its Position element.

  rotation = atan2(Reference.Y, Reference.X)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

  • CadCraft
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• Position and direction written to DEXPI

  Writes an item's location and its direction vector.

  Reference = (round(cos θ, 9 decimals), round(sin θ, 9 decimals), 0)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/dexpi.js

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• Numbers written to PCF

  How a coordinate or a bore is written in a PCF file.

  text = round(n, 4 decimals)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• End point lines read from PCF

  Reads a component's end point: three coordinates, a bore and an end type.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• PCF units to millimeters

  Converts coordinates and bores from the units named in the file header to millimeters.

  x_mm = x × factor; factors: inch 25.4, foot 304.8, meter 1000, cm 10

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• Bend angle read from PCF

  Reads a component's angle in degrees.

  angle = value ÷ 100

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• Geometry checks on a PCF file

  Flags pipes with no length, elbows whose center is not equally far from both ends, and straight parts that change bore.

  |r₀ − r₁| > 0.01 × max(r₀, r₁, 1)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• Length of a PCF component

  The straight distance between a component's two end points, in millimeters.

  length = √(Δx² + Δy² + Δz²)

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• Which PCF components meet

  Finds end points and branch points that coincide, and the ends left open.

  joined when √(Δx² + Δy² + Δz²) ≤ tol

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

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• Point lines written to PCF

  Writes an end point, branch point or center point line.

  DEXPI and PCF plant exchange files addons/pid/lib/interop/pcf.js

  • CadCraft
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• Pipe runs converted for the network

  Turns drawn pipe runs into polylines in millimeters with an elevation at every corner and an inside diameter per size.

  mm = drawing units × k × 25.4; z = z₀ − slope × (plan distance) × k × 25.4

  Water supply and duct network sizing addons/piping/lib/pipenet.js

  • CadCraft
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• Source matched to a run end

  Finds the run end nearest the point picked as the supply source.

  accepted when plan distance ≤ tol (60 mm by default)

  Water supply and duct network sizing addons/piping/lib/pipenet.js

  • CadCraft
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• Result rows in display units

  Converts each segment's flow to liters per second and its loss to kilopascals.

  L/s = m³/s × 1000; kPa = Pa ÷ 1000

  Water supply and duct network sizing addons/piping/lib/pipenet.js

  • CadCraft
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• Network CSV export

  The per-run results written as CSV.

  Water supply and duct network sizing addons/piping/lib/pipenet.js

  • CadCraft
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• Physical constants for water

  Gravity, water properties and unit factors used by the supply calculation.

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Hazen–Williams friction loss

  Pressure lost to friction per meter of water pipe.

  Δp/L = 10.67 × Q^1.852 ÷ (C^1.852 × D^4.871) × ρ g

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Darcy–Weisbach friction loss for water

  Pressure lost to friction per meter of water pipe from the friction factor.

  V = Q ÷ (πD² ÷ 4); Re = V D ÷ ν; Δp/L = (f ÷ D) × ρ V² ÷ 2

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Velocity in a pipe

  The mean velocity of a flow in a round pipe.

  V = Q ÷ (π D² ÷ 4)

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Demand from fixture units

  The design flow for a number of fixture units, read from a demand curve.

  s = ln(y₁ ÷ y₀) ÷ ln(x₁ ÷ x₀); q = y₀ × (fu ÷ x₀)^s

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Loss in fittings

  Pressure lost in a segment's bends, valves and the junction it leaves.

  Δp = (Σ K) × ρ V² ÷ 2; bend K = K₉₀ × min(1.5, angle ÷ 90)

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Flow, size and loss of one pipe segment

  Velocity, friction rate, the smallest size that passes, and the total pressure loss of a segment.

  Δp = rate × L + fittings + ρ g Δz

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Pressure lost to each outlet

  The pressure drop from the source to an outlet and what is left of the supply pressure.

  Δp = Σ segments on the path; left = available − Δp ÷ 1000

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Flow, size and loss of one duct segment

  Velocity, friction rate, equivalent diameter, needed diameter and pressure loss of a duct segment.

  by velocity: D = √(4Q ÷ (π v_max)); Δp = rate × L + fittings

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Critical path, damper pressures and fan pressure

  The duct path with the largest loss, the pressure each other terminal's damper must take up, and the fan's required pressure.

  damper = Δp_critical − Δp_terminal; fan = Δp_critical + equipment loss

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Duct diameter for a friction rate

  The round diameter that gives a target friction rate at a flow.

  Water supply and duct network sizing addons/piping/lib/mep/flow.js

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• Foot of a point on a run

  The nearest point of a 3D polyline to a point, as a distance along the run and a distance away.

  u = clamp((p − a)·v ÷ |v|², 0, 1); s = Σ earlier lengths + |v| u

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Point at a distance along a run

  The 3D point a given distance along a polyline.

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Bend angle at a corner

  The angle a run turns through at a corner, in degrees.

  angle = acos(u·v ÷ (|u| |v|)) × 180 ÷ π

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Cut points and nodes

  Cuts runs where another run ends on them or a fixture connects, and merges nearby cut points into nodes.

  cut when distance ≤ tol; merged when distance ≤ tol

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Segment length, rise and bends

  The length in meters, the rise and the bend angles of each segment between two nodes.

  length = Σ |vᵢ₊₁ − vᵢ| ÷ 1000; Δz = (z_b − z_a) ÷ 1000

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Loads summed toward the source

  The total load (fixture units or flow) carried by each segment.

  sum(segment) = load at its far node + Σ sums of its children

  Water supply and duct network sizing addons/piping/lib/mep/network.js

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• Air properties and unit factors

  Standard-air properties, duct roughness values and the factors for cfm, L/s, inches of water, feet per minute, inches and millimeters.

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Colebrook friction factor

  The Darcy friction factor for a Reynolds number and relative roughness.

  1 ÷ √f = −2 log₁₀(ε ÷ (3.7 D) + 2.51 ÷ (Re √f))

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Altshul–Tsal friction factor

  An explicit friction factor kept as a cross-check of the iterated one.

  f′ = 0.11 (ε ÷ D + 68 ÷ Re)^0.25; f = f′ if f′ ≥ 0.018, else 0.85 f′ + 0.0028

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Friction loss of a round duct

  Friction rate, velocity, Reynolds number and friction factor for an airflow in a round duct.

  V = Q ÷ (πD² ÷ 4); Re = V D ÷ ν; rate = (f ÷ D) × ρ V² ÷ 2

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Round diameter for a friction rate

  The round duct diameter that gives a target friction rate at an airflow.

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Round equivalent of a rectangular duct

  The round diameter with the same friction and flow as a rectangle a × b.

  De = 1.30 (a b)^0.625 ÷ (a + b)^0.25

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Flat-oval area, perimeter and round equivalent

  The area and perimeter of a flat-oval duct and its equivalent round diameter.

  A = πb² ÷ 4 + b(a − b); P = πb + 2(a − b); De = 1.55 A^0.625 ÷ P^0.25

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Area and perimeter of a section

  The cross-section area, perimeter and equivalent diameter of a rectangular, round or oval size.

  rect: A = w h, P = 2(w + h); round: A = πw² ÷ 4, P = πw

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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• Duct size by equal friction

  The stocked duct size for an airflow and a target friction rate, with its velocity and actual rate.

  Q = q × (cfm or L/s factor); size = first stocked size ≥ exact diameter

  Water supply and duct network sizing addons/piping/lib/mep/sizing.js

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