Calculations

Calculations

• Scale of the takeoff sheet

  Feet per PDF point for the sheet the takeoff is measured on, and the mapping of drawing points to PDF points.

  K = 72 ÷ 25.4; feet per point = (feet per drawing unit) ÷ (m₀ × K)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/mep-core.js

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• Cleaning a run's data

  Checks a run's points, sizes, elevation, slope and valves before the run is stored.

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Move, rotate, scale or mirror a run

  The run's points, scale, elevation, symbol size and valve positions after a transform.

  s = √|m₀m₃ − m₁m₂|; k′ = k ÷ s; z′ = z × s

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Elevation along a run

  The centerline elevation a given plan distance along the run.

  z(s) = z₀ − slope × s

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Branches onto other runs

  Finds where a run's end sits on another run and works out the tee or wye, its angle and how far the branch is cut back.

  sin φ = |t_main × t_branch|; cut = (OD_main ÷ 2) ÷ sin φ; gap = OD_branch ÷ sin φ

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Elbows, reducers and trimmed pieces

  Places an elbow at each turn and a reducer at each size change, and trims the straight pieces to fit.

  T = R × tan(θ ÷ 2); reducer length = 1.5 × max(OD₁, OD₂)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Sections for the 3D pipe

  The cross-sections along the centerline that the 3D solid is built from.

  elbow steps = max(2, ceil(θ ÷ 15°)); z = z₀ − slope × s − OD ÷ 2

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Drawing units to feet or meters, and the slope factor

  Converts a plan length to feet or meters and corrects it for the run's slope.

  ft = du × k ÷ 12; m = du × k × 25.4 ÷ 1000; factor = √(1 + slope²)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Pipe length by size

  The length of pipe of each size in a run, in plan and along the slope.

  len = Σ lenOut(segment) × √(1 + slope²)

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Schedule totals

  Pipe length and steel weight by material and size, fitting counts, and the totals.

  weight = (weight per length) × length; total = Σ rows

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Slope label

  The slope written on the drawing and in the schedule: a fraction of an inch per foot, or a percentage.

  in/ft = slope × 12; % = slope × 100

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Plan of a run

  The lines and arcs drawn for a run: a single centerline, or two side lines with elbow arcs and reducers.

  side line = centerline ± n × OD ÷ 2; elbow arcs at R ± OD ÷ 2

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Size label

  The size written beside a pipe: NPS, DN, or a tube size with its outside diameter in millimeters.

  mm = OD (in) × 25.4

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/pipe.js

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• Typed pipe size

  Matches what a person types (2, 1-1/2, 1.5, DN50) to a size of the pipe table.

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

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• Typed slope

  Turns a typed slope into fall per unit of run.

  imperial: slope = (inches per foot) ÷ 12; metric: slope = percent ÷ 100

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

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• Point pulled onto a centerline

  Moves a picked point that lies on a pipe onto that pipe's centerline.

  moved when distance ≤ max(OD ÷ 2, slack) + 1e-9

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

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• Schedule table on the drawing

  The rows of the pipe schedule placed in the drawing.

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

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• Schedule CSV export

  The pipe schedule written as a CSV file: pipe by size, fittings, and each run with its elevations.

  elevation = z × k (in) or z × k × 25.4 (mm)

  Pipe runs: layout, 3D solid and schedule addons/piping/main.js

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• Valve and fitting symbols placed on a run

  Rotates a symbol's entities to the run's direction and moves them to their place.

  x′ = pₓ + x cos θ − y sin θ; y′ = p_y + x sin θ + y cos θ

  Pipe runs: layout, 3D solid and schedule addons/piping/lib/symbols.js

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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

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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

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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

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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

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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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• Friction rate and velocity of a drawn section

  The friction rate and velocity of a duct section as drawn, in the units typed.

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

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