Calculations

Calculations

• 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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• Loads at the joints

  Turns roof, snow and ceiling loads in kPa into forces in kN at the joints of the frame.

  top chord: w = (dead × L + snow × Δx) × spacing; bottom chord: w = ceiling × Δx × spacing; half to each end

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Wind and uplift forces at the joints

  Forces at the top-chord joints from wind pressure normal to the roof and from a net uplift on plan.

  F = p × spacing × L; n = (−Δz, Δx) ÷ L; joint force = −n F ÷ 2

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Load across each chord member

  The load per meter across each chord member, per load case, used for bending between panel points.

  c = |Δx| ÷ L; dead: w c; snow and uplift: w c²

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Linear solve

  Solves a square system of linear equations.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Member forces by the method of joints

  The axial force in every member and the support reactions for one set of joint loads.

  Σ member pulls + reactions = load at every joint; members + 3 = 2 × joints

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Member check

  The utilization of one member under an axial force and a bending moment.

  tension: T ÷ (Ft·CD·A); compression: fc ÷ (Fc·CD·Cp), Cp = q − √(q² − α ÷ c), q = (1 + α) ÷ 2c, α = FcE ÷ (Fc·CD), FcE = 0.822 Emin ÷ (le ÷ d)²

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Governing combination for a member

  The load combination that gives a member its highest utilization, with the largest and smallest force over all combinations.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Smallest sizes that pass

  The smallest timber size for the top chord, the bottom chord and the webs that keeps every member at or under a utilization of 1.

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Deflection estimate

  The largest vertical deflection at a bottom-chord joint and the span-to-deflection ratio.

  δ = Σ N n L × 1000 ÷ (E A)

  Truss member forces and timber checks addons/trusscraft/lib/analysis.js

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• Frame member stiffness

  The stiffness of each member of the attic frame, turned into the frame's axes and added to the whole.

  EA = E b d; EI = E b d³ ÷ 12; K = Tᵀ k T

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Uniform load on a level beam

  The joint forces and moments that stand in for a uniform load on the floor or ceiling tie.

  end force = w L ÷ 2; end moment = w L² ÷ 12

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Frame displacements, forces and moments

  Solves the frame and reads each member's axial force and each beam's largest moment.

  N = (EA ÷ L)(u_b − u_a); M = max(|Ma|, |Mb|, |w L² ÷ 8 − (|Ma| + |Mb|) ÷ 2|)

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Frame support reactions

  The reactions at the two supports of the attic frame.

  R = Σ K·D − F for the support's row

  Truss member forces and timber checks addons/trusscraft/lib/frame.js

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• Load combinations

  Member forces, chord moments and reactions for each combination of the load cases.

  force = Σ factor × case force; M = |w| L² ÷ momentDiv

  Truss member forces and timber checks addons/trusscraft/lib/design.js

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