Investor demonstration · read-only

Read-only demonstration. Four sanitised or hypothetical engineering projects. Each states its own validation status; nothing shown is engineer approved.

ENGINEERING WORKSPACE

Methods

London Office Mechanical Design · exact revisions and backend authority

Development workspace · no professional sign-off. Native execution remains unverified until licensed Windows evidence is recorded.

AHU outdoor-air cooling: heat recovery, dehumidifying coil, fan heat and reheat

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key
hx.ahu.outdoor_air_cooling@1
slot
ahu.outdoor_air_cooling
title
AHU outdoor-air cooling: heat recovery, dehumidifying coil, fan heat and reheat
basis
first_principles
equations
  • ṁ_da = q_oa·ρ/(1 + W_o)
  • t_1 = t_o − ε_hr·(t_o − t_ex) when t_o > t_ex, else t_1 = t_o (recovery bypassed)
  • Dehumidifying (W_o > W_max): W_c = W_max; p_w = p·W_c/(ε + W_c); t_c from p_ws(t_c) = p_w/φ_c
  • Sensible only (W_o ≤ W_max): W_c = W_o; t_c = t_s − Q_fan/(ṁ_da·(c_p,a + W_c·c_p,v))
  • Q_cool = ṁ_da·(h_1 − h_c); Q_cool,s = ṁ_da·(c_p,a + W_o·c_p,v)·(t_1 − t_c); Q_cool,l = Q_cool − Q_cool,s; ṁ_w = ṁ_da·(W_o − W_c)
  • t_f = t_c + Q_fan/(ṁ_da·(c_p,a + W_c·c_p,v)); Q_reheat = max(0, ṁ_da·(c_p,a + W_c·c_p,v)·(t_s − t_f))
  • Energy balance: ṁ_da·(h_o − h_supply) = Q_hr + Q_cool − Q_fan − Q_reheat
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Draw-through supply fan: its heat is added after the coil.
  • Heat recovery is sensible only; moisture transfer is not modelled.
  • The coil leaving state is a stated design condition, not a coil performance model.
limitations
  • Humidification is not modelled.

AHU outdoor-air heating: heat recovery, fan heat and heating coil

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key
hx.ahu.outdoor_air_heating@1
slot
ahu.outdoor_air_heating
title
AHU outdoor-air heating: heat recovery, fan heat and heating coil
basis
first_principles
equations
  • ṁ_da = q_oa·ρ/(1 + W_o)
  • t_1 = t_o + ε_hr·(t_ex − t_o) when t_ex > t_o, else t_1 = t_o
  • Q_heat = max(0, ṁ_da·(c_p,a + W_o·c_p,v)·(t_s − t_1) − Q_fan)
  • Energy balance: ṁ_da·(h_supply − h_o) = Q_hr + Q_heat + Q_fan
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Fan heat is credited against the heating coil as stated (0 = no credit).
  • Heat recovery is sensible only; frost protection is not modelled.
limitations
  • Humidification is not modelled: the supply keeps the outdoor moisture.

Supply airflow to meet a sensible cooling or heating load

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key
hx.airflow.supply_air_for_sensible_load@2
slot
airflow.supply_for_sensible_load
title
Supply airflow to meet a sensible cooling or heating load
basis
first_principles
equations
  • cooling: ΔT = t_room − t_supply ; heating: ΔT = t_supply − t_room ; ΔT > 0
  • ṁ = Q_s / (c_p · ΔT)
  • q = ṁ / ρ
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Sensible heat only; the supply ΔT is a design decision, not derived.
limitations
  • Uses the stated air density and specific heat; dry-air values understate moist-air heat capacity by about 1–2 %.

Coincident peak and derived diversity from aligned load profiles

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key
hx.diversity.coincident_peak@2
slot
diversity.coincident_peak
title
Coincident peak and derived diversity from aligned load profiles
basis
aggregation
equations
  • Q_sum,peaks = Σ_i max_t Q_i(t)
  • Q_coincident = max_t Σ_i Q_i(t)
  • f_d = Q_coincident / Q_sum,peaks
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Profiles are aligned in time with equal steps.
limitations
  • The result is only as representative as the supplied profiles.

Diversified load from a stated diversity factor

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key
hx.diversity.stated_factor@2
slot
diversity.factor
title
Diversified load from a stated diversity factor
basis
aggregation
equations
  • Q_sum = Σ Q_i ; Q_div = f_d · Q_sum
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • The factor must be cited (rule, client standard or assumption).

Electrical input of plant from its duty and a stated performance ratio

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key
hx.duties.electrical_input_from_performance@1
slot
duties.electrical_input
title
Electrical input of plant from its duty and a stated performance ratio
basis
definition
equations
  • P_elec = Q / (EER or COP)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Uses one design-point ratio; seasonal performance is a separate method.

Fan design duty from the index-run pressure loss

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key
hx.duties.fan_duty@1
slot
duties.fan
title
Fan design duty from the index-run pressure loss
basis
first_principles
equations
  • Δp_fan = (Δp_index + Δp_plant) · (1 + m)
  • P_air = q · Δp_fan ; P_input = P_air / η ; SFP = P_input / q
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • The index run carries the full design flow at the fan.
limitations
  • Preliminary duty; fan selection needs manufacturer performance data.

Operating point of a fan or pump curve on the square-law system curve

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key
hx.duties.operating_point@1
slot
duties.operating_point
title
Operating point of a fan or pump curve on the square-law system curve
basis
first_principles
equations
  • R = Δp_d / q_d² (system through the duty point)
  • curve: piecewise linear through the supplied points, inside their range only
  • operating point: p_curve(q) = R·q²
  • excess at design flow: Δp_excess = p_curve(q_d) − Δp_d
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.manufacturer.catalogue
    title
    Manufacturer catalogue or data sheet (identify the document, version and locator on each product record)
    publisher
    Manufacturer
    licence
    manufacturer_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
assumptions
  • The system passes through the origin (closed circuit, no static lift or controlled minimum pressure).
  • Between supplied points the curve is taken as straight; supply enough points.
limitations
  • No extrapolation: a duty outside the supplied curve range is refused.
  • Parallel/series sets, variable-speed affinity scaling and efficiency/power selection are separate steps.

Preliminary plant duty: diversified zone load plus system loads and margin

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key
hx.duties.preliminary_equipment_duty@2
slot
duties.equipment
title
Preliminary plant duty: diversified zone load plus system loads and margin
basis
aggregation
equations
  • Q_plant = (Q_zones,diversified + Σ Q_system) · (1 + m)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Preliminary duty for option appraisal; not a procurement selection. Part-load, redundancy and manufacturer ratings are separate decisions.

Pump design duty from the index-circuit pressure loss

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key
hx.duties.pump_duty@1
slot
duties.pump
title
Pump design duty from the index-circuit pressure loss
basis
first_principles
equations
  • Δp_pump = (Δp_index + Δp_plant) · (1 + m)
  • H = Δp_pump / (ρ g) ; P_hyd = q · Δp_pump ; P_input = P_hyd / η
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bipm.si_brochure
    title
    The International System of Units (SI Brochure)
    publisher
    Bureau International des Poids et Mesures (BIPM)
    licence
    open_access
    edition
    9th edition, 2019
    locator
    Not supplied
assumptions
  • Closed circuit: static head is not included.
limitations
  • Preliminary duty; pump selection needs manufacturer curves.

Duty with a flow allowance on a fixed system (square law)

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key
hx.duties.square_law_flow_margin@1
slot
duties.flow_margin
title
Duty with a flow allowance on a fixed system (square law)
basis
first_principles
equations
  • q' = q · (1 + m)
  • Δp' = Δp · (1 + m)² (fixed system: Δp = R·q²)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
assumptions
  • Fully turbulent flow in a fixed system, so pressure loss ∝ flow².
limitations
None recorded

Recovered energy from a sensible heat-recovery duty over stated hours

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key
hx.energy.heat_recovery@1
slot
energy.heat_recovery
title
Recovered energy from a sensible heat-recovery duty over stated hours
basis
definition
equations
  • E_rec = Q_rec · t
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • The recovered duty is constant over the stated hours.
limitations
  • Sensible heating recovery only; latent/total recovery is not modelled.

Operational carbon from delivered energy and a sourced emission factor

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key
hx.energy.operational_carbon@1
slot
energy.carbon
title
Operational carbon from delivered energy and a sourced emission factor
basis
definition
equations
  • C = E · EF
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    uk.gov.ghg_conversion_factors
    title
    Greenhouse gas reporting: conversion factors (year to be recorded per factor)
    publisher
    UK Government (DESNZ)
    licence
    government_publication_licence_to_verify
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • No emission factor is built in: the factor is a sourced record with its version, date and licence. Operational carbon only (embodied carbon is a hook).

Energy from a stated power and stated operating hours

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key
hx.energy.power_hours@1
slot
energy.power_hours
title
Energy from a stated power and stated operating hours
basis
definition
equations
  • E = P · t
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Power and hours are stated inputs; no operating pattern is assumed.

Energy from a rated power and a stated operating profile

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key
hx.energy.profile@1
slot
energy.profile
title
Energy from a rated power and a stated operating profile
basis
aggregation
equations
  • E = Σ P · f_i · Δt
  • t_eq = Σ f_i · Δt
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • The profile is stated data with its source; none is built in.

Retrofit carbon saving of an option against a baseline

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key
hx.energy.retrofit_carbon_saving@1
slot
energy.retrofit_carbon_saving
title
Retrofit carbon saving of an option against a baseline
basis
definition
equations
  • S = X_baseline − X_option
  • s = S / X_baseline
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Both results must share one declared basis (period, scope, factor versions); that comparability check is made before this method runs.

Retrofit energy saving of an option against a baseline

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key
hx.energy.retrofit_energy_saving@1
slot
energy.retrofit_energy_saving
title
Retrofit energy saving of an option against a baseline
basis
definition
equations
  • S = X_baseline − X_option
  • s = S / X_baseline
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Both results must share one declared basis (period, scope, factor versions); that comparability check is made before this method runs.

Steady-state interstitial condensation check (Glaser vapour-diffusion method)

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key
hx.fabric.interstitial_condensation_glaser@1
slot
fabric.interstitial_condensation
title
Steady-state interstitial condensation check (Glaser vapour-diffusion method)
basis
first_principles
equations
  • R_j = d_j/λ_j ; Z_j = d_j·r_v,j (or stated) ; R_T = R_si + ΣR_j + R_se ; Z_T = ΣZ_j
  • t_n = t_i − (t_i − t_e)·ΣR(si…n)/R_T
  • p_v,n = p_v,i − (p_v,i − p_v,e)·ΣZ(si…n)/Z_T (no condensation)
  • p_s,n = p_ws(t_n) (Hyland & Wexler; over ice below 0.01 °C)
  • p_v(Z) = greatest convex function with p_v ≤ p_s at every interface (taut string)
  • g_c,k = (p_v,k−1 − p_v,k)/(Z_k − Z_k−1) − (p_v,k − p_v,k+1)/(Z_k+1 − Z_k)
  • planes with g_c ≤ 1e-12 kg/m²·s (a tangency) are not reported
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
  • publication id
    bs_en_iso_13788
    title
    Hygrothermal performance of building components and building elements — Internal surface temperature to avoid critical surface humidity and interstitial condensation — Calculation methods
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • One-dimensional steady heat conduction and vapour diffusion at one design condition.
  • Layers are listed from the inside surface outwards; surfaces have no vapour resistance.
  • Material properties are constant; moisture storage, capillary transport, air leakage and latent heat release are neglected.
limitations
  • Checks interfaces only; a thick layer may need sub-dividing to find a plane inside it.
  • A single steady condition is a screening check: it does not assess seasonal accumulation and evaporation, which a monthly assessment would.
  • Responsibility for the construction's hygrothermal design normally rests with the architect or envelope designer.

U-value of a construction of homogeneous plane layers

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key
hx.fabric.layered_u_value@1
slot
fabric.u_value
title
U-value of a construction of homogeneous plane layers
basis
first_principles
equations
  • R_j = d_j / λ_j (or a stated R_j)
  • R_T = R_si + Σ R_j + R_se
  • U = 1 / R_T
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
  • publication id
    bs_en_iso_6946
    title
    Building components and building elements — Thermal resistance and thermal transmittance — Calculation methods
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • One-dimensional steady heat flow through plane, homogeneous layers.
  • Layers are listed from the inside surface outwards.
limitations
  • Bridged layers, repeating thermal bridges, fixings and corrections for air voids are not included; linear bridges are entered separately as ψ-values in heat loss.
  • Ground floors (ground thermal resistance, perimeter/area effects) are not covered.

Circular equivalent of a rectangular duct for equal friction and flow (Huebscher)

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key
hx.fluid.equivalent_diameter_huebscher@1
slot
fluid.rectangular_equivalent_diameter
title
Circular equivalent of a rectangular duct for equal friction and flow (Huebscher)
basis
published_correlation
equations
  • D_e = 1.30 · (a·b)^0.625 / (a + b)^0.25
references
  • publication id
    huebscher_1948
    title
    Huebscher, R.G. (1948) Friction equivalents for round, square and rectangular ducts
    publisher
    ASHVE Transactions 54
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • For comparison and selection; section friction uses the hydraulic diameter.

Duct or pipe section: velocity, friction and total pressure loss

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key
hx.fluid.section_pressure_drop@2
slot
fluid.section_pressure_drop
title
Duct or pipe section: velocity, friction and total pressure loss
basis
first_principles
equations
  • A = πD²/4 (circular) or a·b (rectangular); D_h = D or 2ab/(a + b)
  • v = q / A ; Re = ρ v D_h / μ
  • f = 64/Re (Re < 2300) ; 1/√f = −2 log₁₀(ε/(3.7 D_h) + 2.51/(Re √f)) otherwise
  • R = f · ρv²/(2 D_h) ; Δp_straight = R · L
  • Δp_fittings = Σζ · ρv²/2 ; Δp_components = Σ explicit component losses
  • Δp_total = Δp_straight + Δp_fittings + Δp_components
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    colebrook_1939
    title
    Colebrook, C.F. (1939) Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws
    publisher
    Journal of the Institution of Civil Engineers 11
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Incompressible, fully developed, isothermal flow in the section.
  • Fitting ζ values are referenced to the section's mean velocity.
limitations
  • Transitional flow (2300 ≤ Re < 4000) is flagged; its friction factor is uncertain.
  • Loss coefficients and component losses must be explicit data; none are built in.
  • Pressure recovery (negative ζ) is not modelled.

Supply temperature and recovered heat from a stated sensible effectiveness

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key
hx.heat_recovery.sensible_effectiveness@1
slot
heat_recovery.sensible
title
Supply temperature and recovered heat from a stated sensible effectiveness
basis
definition
equations
  • t_s = t_o + ε · (t_e − t_o)
  • Q_rec = ṁ_s · c_p · (t_s − t_o)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Effectiveness is defined on the supply side at these flows (balanced, or the supply side has the minimum capacity rate).
limitations
  • Sensible only; frost protection and latent transfer are not modelled.

Residual (balancing) pressure of each circuit relative to the index circuit

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key
hx.hydronics.balancing_residual_pressures@1
slot
hydronics.balancing_residuals
title
Residual (balancing) pressure of each circuit relative to the index circuit
basis
network_analysis
equations
  • Δp_index = max_c Δp_c
  • Δp_residual,c = Δp_index − Δp_c (to be absorbed by circuit c's regulating device)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
assumptions
  • All circuits are fed from a common point (the riser or header) at design flow.
  • Each circuit's loss already includes its regulating device fully open.
limitations
  • Does not select the valve size or set position: that needs the manufacturer's characteristic, and the supplier should be told the residual pressure.
  • Variable-flow systems need the residuals re-checked at part load.

Infiltration flow from a stated infiltration air change rate

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key
hx.infiltration.from_air_change_rate@1
slot
infiltration.air_change_rate
title
Infiltration flow from a stated infiltration air change rate
basis
definition
equations
  • q_inf = n_inf · V
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • The infiltration rate itself must come from a source, test or assumption.

Infiltration flow from tested air permeability and an explicit divisor

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key
hx.infiltration.from_air_permeability@1
slot
infiltration.air_permeability
title
Infiltration flow from tested air permeability and an explicit divisor
basis
definition
equations
  • q_inf = q_50 · A_env / N
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • The divisor N converts test-pressure leakage to average natural infiltration.
limitations
  • N is empirical and exposure-dependent; it must come from a cited rule or an engineer's assumption. No default is provided.

Straight (undiversified) sum of space or zone loads

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key
hx.loads.aggregate_sum@1
slot
loads.aggregate
title
Straight (undiversified) sum of space or zone loads
basis
aggregation
equations
  • Q_total = Σ Q_i
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • All loads coincide (no diversity); use a diversity method otherwise.
limitations
None recorded

Steady-state cooling load foundation from stated components

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key
hx.loads.cooling_components@1
slot
loads.cooling_components
title
Steady-state cooling load foundation from stated components
basis
first_principles
equations
  • Q_people,s = n · q_s,person ; Q_people,l = n · q_l,person
  • Q_lighting = A_floor · q_lighting or stated P_lighting
  • Q_equipment = A_floor · q_equipment or stated P_equipment
  • Q_conduction = Σ U_i · A_i · (t_out − t_in)
  • Q_solar = Σ A_k · G_k · g_k (+ stated gains)
  • Q_air,s = ρ · c_p · q · (t_out − t_in) ; Q_air,l = ρ · q · (W_out − W_in) · h_fg
  • Q_s = Σ sensible components ; Q_l = Σ latent components ; Q = Q_s + Q_l
  • SHR = Q_s / Q
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    cibse.guide_a
    title
    CIBSE Guide A: Environmental design
    publisher
    CIBSE
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady state at the design condition: no thermal mass, time lag or sol-air effects.
  • All included components coincide at the design hour.
  • Air latent load uses h_fg = h_g,0 (2501 kJ/kg), the psychrometric-convention vapour enthalpy at 0 °C, as a traceable physical constant.
limitations
  • Solar gain is only taken from stated inputs; it is never calculated here.
  • Dynamic, admittance, time-of-day peak and thermal-mass methods are unsupported.
  • Components not included in the assembly are absent, not zero.

Space heat gain foundation (steady state)

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key
hx.loads.heat_gain_steady_state@2
slot
loads.heat_gain
title
Space heat gain foundation (steady state)
basis
first_principles
equations
  • Q_people,s = n · q_s,person ; Q_people,l = n · q_l,person
  • Q_lighting = A_floor · q_lighting
  • Q_equipment = A_floor · q_equipment + Q_equipment,other
  • Q_conduction = Σ U_i · A_i · (t_out − t_in)
  • Q_s = Q_people,s + Q_lighting + Q_equipment + Q_conduction + Q_solar
  • Q_l = Q_people,l + Q_latent,other ; Q_total = Q_s + Q_l
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    cibse.guide_a
    title
    CIBSE Guide A: Environmental design
    publisher
    CIBSE
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady state at the design condition: no thermal mass, time lag or sol-air effects.
  • All gains are coincident at the design hour unless diversity is applied separately.
limitations
  • Gains must be ≥ 0: a negative gain has no defined meaning in this method.
  • Solar gain is not calculated; supply it from simulation or a stated source.
  • Outdoor-air (ventilation) load is a system/coil load, not included here.
  • Per-person, lighting and equipment gains must come from sources, rules or assumptions; no defaults are built in.

Design heat loss foundation (steady-state transmission + ventilation)

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key
hx.loads.heat_loss_steady_state@1
slot
loads.heat_loss
title
Design heat loss foundation (steady-state transmission + ventilation)
basis
first_principles
equations
  • ΔT = t_in − t_out
  • Φ_fabric = Σ U_i · A_i · ΔT ; Φ_bridging = Σ ψ_j · L_j · ΔT
  • Φ_ventilation = ρ · c_p · q_v · (1 − η_hr) · ΔT ; Φ_infiltration = ρ · c_p · q_inf · ΔT
  • Φ_total = Φ_fabric + Φ_bridging + Φ_ventilation + Φ_infiltration
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bs_en_12831_1
    title
    Energy performance of buildings — Method for calculation of the design heat load — Part 1: Space heating load
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady state at the design outdoor temperature; no internal or solar gains.
limitations
  • No intermittent-heating surcharge, ground-floor or adjacent-space methods; supply such adjustments explicitly. Not a BS EN 12831-1 calculation.

Sensible load from a total cooling load and a stated sensible heat ratio

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key
hx.loads.sensible_from_total@1
slot
loads.sensible_from_total
title
Sensible load from a total cooling load and a stated sensible heat ratio
basis
definition
equations
  • Q_s = SHR · Q_total
  • Q_l = Q_total − Q_s
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • The ratio must be stated by a source or engineer; none is assumed.

Space heating load assembly (steady state, component-traced)

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key
hx.loads.space_heating_load@1
slot
loads.space_heating
title
Space heating load assembly (steady state, component-traced)
basis
first_principles
equations
  • ΔT = t_in − t_out
  • Φ[i] = U_i · A_i · ΔT ; Φ_fabric = Σ Φ[i]
  • Φ[j] = ψ_j · L_j · ΔT ; Φ_bridging = Σ Φ[j]
  • Φ_ventilation = ρ · c_p · q_v · (1 − η_hr) · ΔT
  • Φ_infiltration = ρ · c_p · q_inf · ΔT
  • Φ_allowances = Σ Φ[k] (stated allowances)
  • Φ_total = Φ_fabric + Φ_bridging + Φ_ventilation + Φ_infiltration + Φ_allowances
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bs_en_12831_1
    title
    Energy performance of buildings — Method for calculation of the design heat load — Part 1: Space heating load
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    cibse.guide_a
    title
    CIBSE Guide A: Environmental design
    publisher
    CIBSE
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady state at the stated design temperatures; no internal or solar gains.
limitations
  • No margin, intermittency factor or design temperature is built in: allowances are stated inputs. Not a BS EN 12831-1 or CIBSE Guide A method compliance claim.

Persisted network analysis: flows, section losses, paths, index run and duty

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key
hx.network.analyse@2
slot
networks.analyse
title
Persisted network analysis: flows, section losses, paths, index run and duty
basis
network_analysis
equations
  • q_section = Σ q_end (downstream terminals and sub-networks) = q_end(at the section) + Σ q_section(children)
  • Δp_section = Δp_straight + Σζ·ρv²/2 + Σ component losses (incl. the end loss)
  • Δp_path = Σ Δp_section along the path from the root
  • Δp_index = max over complete paths (all ties listed)
  • Δp_path_pressure = Δp_index + Δp_plant ; fan/pump duty from Δp_index, Δp_plant
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    colebrook_1939
    title
    Colebrook, C.F. (1939) Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws
    publisher
    Journal of the Institution of Civil Engineers 11
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady design flow at every end simultaneously (no diversity).
limitations
  • Trees only: looped networks and ring mains are refused (unsupported topology).
  • Balancing devices are not sized; the difference to the index run is reported only.
  • No fan or pump curve selection: duty is a preliminary design point.
  • Unknown values are never taken as zero: the analysis is then incomplete, with no index run, path pressure or duty.

Section design flow as the sum of downstream terminal flows

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key
hx.networks.flow_aggregation@1
slot
networks.flow_aggregation
title
Section design flow as the sum of downstream terminal flows
basis
first_principles
equations
  • q_section = Σ q_terminal (downstream terminals)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady flow; all terminals at design flow simultaneously (no diversity).
limitations
None recorded

Path totals and index run (greatest root-to-terminal pressure loss)

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key
hx.networks.index_run@1
slot
networks.index_run
title
Path totals and index run (greatest root-to-terminal pressure loss)
basis
network_analysis
equations
  • Δp_path = Σ Δp_section along the path
  • Δp_index = max over paths
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Balancing devices on non-index paths are not sized; the difference between each path and the index run is the pressure to be absorbed by balancing.

Pressure loss of plant components carrying the total flow

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key
hx.networks.plant_pressure_loss@2
slot
networks.plant_pressure_loss
title
Pressure loss of plant components carrying the total flow
basis
aggregation
equations
  • Δp_plant = Σ explicit component losses at q_total
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
None recorded

Dynamic viscosity of air (Sutherland's law)

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key
hx.properties.air_viscosity_sutherland@1
slot
properties.air_viscosity
title
Dynamic viscosity of air (Sutherland's law)
basis
published_correlation
equations
  • μ = μ₀ (T/T₀)^1.5 (T₀ + S)/(T + S), μ₀ = 1.716e−5 Pa·s, T₀ = 273.15 K, S = 110.4 K
references
  • publication id
    sutherland_1893
    title
    Sutherland, W. (1893) The viscosity of gases and molecular force
    publisher
    Philosophical Magazine 36
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Dry air; valid roughly −70 to 500 °C at near-atmospheric pressure.

Density of dry air from the ideal-gas law

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key
hx.properties.dry_air_density@1
slot
properties.air_density
title
Density of dry air from the ideal-gas law
basis
first_principles
equations
  • ρ = p / (R_da · T)
  • T = t + 273.15
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bipm.si_brochure
    title
    The International System of Units (SI Brochure)
    publisher
    Bureau International des Poids et Mesures (BIPM)
    licence
    open_access
    edition
    9th edition, 2019
    locator
    Not supplied
assumptions
  • Dry air behaves as an ideal gas at building-services conditions.
limitations
  • Moisture is neglected; use hx.psychrometrics.moist_air_state for moist air.

Arithmetic mean of two temperatures (e.g. flow and return)

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key
hx.properties.mean_temperature@1
slot
properties.mean_temperature
title
Arithmetic mean of two temperatures (e.g. flow and return)
basis
definition
equations
  • t_m = (t₁ + t₂) / 2
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
None recorded

Density of liquid water at atmospheric pressure (Kell 1975)

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key
hx.properties.water_density_kell@1
slot
properties.water_density
title
Density of liquid water at atmospheric pressure (Kell 1975)
basis
published_correlation
equations
  • ρ = (999.83952 + 16.945176 t − 7.9870401e−3 t² − 46.170461e−6 t³ + 105.56302e−9 t⁴ − 280.54253e−12 t⁵) / (1 + 16.879850e−3 t), t in °C
references
  • publication id
    kell_1975
    title
    Kell, G.S. (1975) Density, thermal expansivity, and compressibility of liquid water from 0° to 150°C
    publisher
    Journal of Chemical & Engineering Data 20(1)
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Pure, air-free water at about atmospheric pressure.
limitations
  • Valid 0–150 °C. Glycol mixtures and other fluids need their own property data.

Dynamic viscosity of liquid water (Vogel-type correlation)

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key
hx.properties.water_viscosity_vogel@1
slot
properties.water_viscosity
title
Dynamic viscosity of liquid water (Vogel-type correlation)
basis
published_correlation
equations
  • μ = A · 10^(B / (T − C)), A = 2.414e−5 Pa·s, B = 247.8 K, C = 140 K
references
  • publication id
    vogel_water_viscosity
    title
    Vogel-type correlation for the dynamic viscosity of liquid water (A = 2.414×10⁻⁵ Pa·s, B = 247.8 K, C = 140 K)
    publisher
    —
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Valid 0–370 °C with roughly ±2.5 % accuracy; pure water only.

Adiabatic mixing of two moist-air streams

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key
hx.psychrometrics.adiabatic_mixing@1
slot
psychrometrics.mixing
title
Adiabatic mixing of two moist-air streams
basis
first_principles
equations
  • W_m = (m₁W₁ + m₂W₂)/(m₁ + m₂)
  • h_m = (m₁h₁ + m₂h₂)/(m₁ + m₂)
  • t_m = (h_m − W_m·h_g,0)/(c_p,a + W_m·c_p,v)
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Adiabatic, steady mixing with no condensation.
limitations
None recorded

Cooling coil loads and condensate from entering and leaving air states

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key
hx.psychrometrics.coil_condensate@1
slot
psychrometrics.coil_condensate
title
Cooling coil loads and condensate from entering and leaving air states
basis
first_principles
equations
  • h = c_p,a·t + W·(h_g,0 + c_p,v·t)
  • Q_t = ṁ_da·(h_in − h_out)
  • Q_s = ṁ_da·(c_p,a + W_in·c_p,v)·(t_in − t_out)
  • Q_l = Q_t − Q_s
  • ṁ_w = ṁ_da·(W_in − W_out)
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Condensate enthalpy neglected (as in hx.psychrometrics.coil_load).
limitations
  • The leaving state is stated (e.g. from a selection); coil performance is not modelled here.

Coil total, sensible and latent load from entering and leaving air states

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key
hx.psychrometrics.coil_load@1
slot
psychrometrics.coil_load
title
Coil total, sensible and latent load from entering and leaving air states
basis
first_principles
equations
  • Q_t = m_da · (h_in − h_out)
  • Q_s = m_da · (c_p,a + W_in·c_p,v) · (t_in − t_out)
  • Q_l = Q_t − Q_s
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Condensate enthalpy neglected.
limitations
None recorded

Moist-air state from dry-bulb temperature, relative humidity and pressure

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key
hx.psychrometrics.moist_air_state@2
slot
psychrometrics.state_from_rh
title
Moist-air state from dry-bulb temperature, relative humidity and pressure
basis
first_principles
equations
  • p_w = φ · p_ws(t)
  • W = ε · p_w / (p − p_w), ε = M_w/M_da
  • h = c_p,a · t + W · (h_g,0 + c_p,v · t) [per kg dry air]
  • v = R_da · T · (1 + W/ε) / p [per kg dry air]
  • ρ = (1 + W) / v
  • t_dp (over water) or t_fp (over ice, when p_w < 611.657 Pa): p_ws(t) = p_w
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Ideal-gas mixture; enhancement factor taken as 1.
limitations
  • Dry bulb −100…200 °C; 0 < φ ≤ 100 %; not for supersaturated states.

Outdoor-air fraction of a supply airflow

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key
hx.psychrometrics.outdoor_air_fraction@1
slot
psychrometrics.outdoor_air_fraction
title
Outdoor-air fraction of a supply airflow
basis
definition
equations
  • x_oa = q_oa / q_supply
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Both flows at the same (stated) conditions.
limitations
None recorded

Saturation vapour pressure of water (Hyland & Wexler 1983)

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key
hx.psychrometrics.saturation_pressure@1
slot
psychrometrics.saturation_pressure
title
Saturation vapour pressure of water (Hyland & Wexler 1983)
basis
published_correlation
equations
  • ln p_ws = C1/T + C2 + C3·T + C4·T² + C5·T³ + C6·T⁴ + C7·ln T (ice, T < 273.15 K)
  • ln p_ws = C8/T + C9 + C10·T + C11·T² + C12·T³ + C13·ln T (water, T ≥ 273.15 K)
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Valid −100 °C to 200 °C.

Moist-air state from dry-bulb and thermodynamic wet-bulb temperatures

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key
hx.psychrometrics.state_from_wet_bulb@1
slot
psychrometrics.state_from_wet_bulb
title
Moist-air state from dry-bulb and thermodynamic wet-bulb temperatures
basis
first_principles
equations
  • Adiabatic saturation energy balance: h(t, W) + (W*_s − W)·c_w·t* = h(t*, W*_s)
  • W = ((h_g,0 + (c_p,v − c_w)·t*)·W*_s − c_p,a·(t − t*)) / (h_g,0 + c_p,v·t − c_w·t*)
  • W*_s = ε·p_ws(t*)/(p − p_ws(t*))
  • p_w = p·W/(ε + W); φ = p_w/p_ws(t); h = c_p,a·t + W·(h_g,0 + c_p,v·t)
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • The wet bulb is the thermodynamic (adiabatic-saturation) wet bulb; a screen or psychrometer wet bulb differs slightly.
limitations
  • Wet bulb at or above 0 °C only (no ice-bulb relation).

Supply air state and flow for a room's sensible and latent cooling loads

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key
hx.psychrometrics.supply_state@1
slot
psychrometrics.supply_state
title
Supply air state and flow for a room's sensible and latent cooling loads
basis
first_principles
equations
  • ṁ_da = Q_s / ((c_p,a + W_r·c_p,v)·(t_r − t_s))
  • h = c_p,a·t + W·(h_g,0 + c_p,v·t)
  • h_s = h_r − (Q_s + Q_l)/ṁ_da
  • W_s = (h_s − c_p,a·t_s)/(h_g,0 + c_p,v·t_s)
  • SHR = Q_s/(Q_s + Q_l)
  • t_dp (or t_fp below 611.657 Pa): p_ws(t) = p·W_s/(ε + W_s)
references
  • publication id
    hyland_wexler_1983
    title
    Hyland, R.W. and Wexler, A. (1983) Formulations for the thermodynamic properties of the saturated phases of H2O from 173.15 K to 473.15 K
    publisher
    ASHRAE (ASHRAE Transactions 89(2A))
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.moist_air_property_values
    title
    Moist-air property values used by hx.psychrometrics: c_p,a = 1.006 kJ/kg·K, c_p,v = 1.86 kJ/kg·K, c_w = 4.186 kJ/kg·K, h_g,0 = 2501 kJ/kg, M_da = 28.966 g/mol, M_w = 18.015268 g/mol
    publisher
    —
    licence
    physical_property_data
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Steady state; ideal-gas mixture; enhancement factor taken as 1.
limitations
  • The supply dry bulb is a stated design decision; none is assumed.
  • Duct and fan heat gains are not included; state them as loads if relevant.

Duct sizing: smallest catalogue size within velocity and friction limits

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key
hx.sizing.duct_catalogue_selection@1
slot
sizing.duct
title
Duct sizing: smallest catalogue size within velocity and friction limits
basis
catalogue_selection
equations
  • for each size in ascending area: v = q/A, R = f·ρv²/(2D_h) (Colebrook–White)
  • select the first size with v ≤ v_max and R ≤ R_max
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    colebrook_1939
    title
    Colebrook, C.F. (1939) Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws
    publisher
    Journal of the Institution of Civil Engineers 11
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Selection only among supplied sizes; noise, space and cost are not assessed.

Pipe sizing: smallest catalogue size within velocity and friction limits

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key
hx.sizing.pipe_catalogue_selection@1
slot
sizing.pipe
title
Pipe sizing: smallest catalogue size within velocity and friction limits
basis
catalogue_selection
equations
  • for each size in ascending area: v = q/A, R = f·ρv²/(2D_h) (Colebrook–White)
  • select the first size with v ≤ v_max and R ≤ R_max
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    colebrook_1939
    title
    Colebrook, C.F. (1939) Turbulent flow in pipes, with particular reference to the transition region between the smooth and rough pipe laws
    publisher
    Journal of the Institution of Civil Engineers 11
    licence
    scientific_literature
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Selection only among supplied sizes; noise, space and cost are not assessed.

Two-port control valve: fully-open pressure drop, authority and largest Kv

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key
hx.valves.two_port_authority@1
slot
valves.control_valve_authority
title
Two-port control valve: fully-open pressure drop, authority and largest Kv
basis
definition
equations
  • Δp_v = (q_h / Kv)² · 1 bar (q_h in m³/h)
  • β = Δp_v / Δp_avail
  • Kv_max = q_h / √(β_min · Δp_avail / 1 bar) (largest Kv with β ≥ β_min)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bsria.bg30_2007
    title
    A Guide to HVAC Building Services Calculations
    publisher
    BSRIA
    licence
    licensed_not_held
    edition
    2nd edition, 2007
    locator
    Not supplied
assumptions
  • Authority is expressed against the stated available differential pressure; other conventions (e.g. against the valve plus the controlled branch only) give different numbers and must not be mixed with this criterion.
  • Water-like fluid: Kv is defined for water; a glycol mixture needs a density correction not applied here.
limitations
  • Selects no valve: it checks a catalogue Kv or bounds the choice. Characteristic, rangeability, close-off rating and actuator force come from the manufacturer.
  • Four-port valves matched to a terminal by its manufacturer are not covered.

Air change rate from a volume flow

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key
hx.ventilation.air_change_rate_from_flow@1
slot
ventilation.air_change_rate_from_flow
title
Air change rate from a volume flow
basis
definition
equations
  • n_ac = q / V
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
None recorded

Supply/extract balance of a stated ventilation mode

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key
hx.ventilation.balance@1
slot
ventilation.balance
title
Supply/extract balance of a stated ventilation mode
basis
definition
equations
  • Δq = q_supply − q_extract
  • r = Δq / max(q_supply, q_extract)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • The mode (mechanical, natural, mixed) is a stated input, recorded only.

Outdoor-air rate combining per-person and per-area components as stated

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key
hx.ventilation.combined_outdoor_air@1
slot
ventilation.combined
title
Outdoor-air rate combining per-person and per-area components as stated
basis
definition
equations
  • q_p = n · q_person ; q_A = A · q_area
  • q_v = q_p + q_A (combination 'sum')
  • q_v = max(q_p, q_A) (combination 'greater_of')
  • check: q_v ≥ q_min (reported, never enforced by raising q_v)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    uk.bregs.approved_document_f
    title
    The Building Regulations — Approved Document F: Ventilation
    publisher
    HM Government
    licence
    government_publication_licence_to_verify
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bs_en_16798_1
    title
    Energy performance of buildings — Ventilation for buildings — Part 1: Indoor environmental input parameters for design and assessment of energy performance of buildings
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
  • Rates, the combination rule and any minimum come from a rule, requirement or assumption with its citation; none is built in. An unheld statutory rate is 'requires input', never a value.

Volume flow from an air change rate

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key
hx.ventilation.flow_from_air_change_rate@1
slot
ventilation.flow_from_air_change_rate
title
Volume flow from an air change rate
basis
definition
equations
  • q = n_ac · V
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
None recorded
limitations
None recorded

Outdoor-air rate from occupancy and floor-area components

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key
hx.ventilation.outdoor_air_rate@1
slot
ventilation.outdoor_air_rate
title
Outdoor-air rate from occupancy and floor-area components
basis
definition
equations
  • q_v = n · q_p + A · q_A
  • n_ac = q_v / V (when V is given)
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    uk.bregs.approved_document_f
    title
    The Building Regulations — Approved Document F: Ventilation
    publisher
    HM Government
    licence
    government_publication_licence_to_verify
    edition
    Not supplied
    locator
    Not supplied
  • publication id
    bs_en_16798_1
    title
    Energy performance of buildings — Ventilation for buildings — Part 1: Indoor environmental input parameters for design and assessment of energy performance of buildings
    publisher
    BSI
    licence
    licensed_not_held
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Occupancy and area components are additive.
limitations
  • The rates are not built in: they must be resolved from a rule pack, client requirement or assumption with its citation. Zone air-distribution effectiveness is not applied.

Water flow to carry a cooling or heating load

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key
hx.waterflow.flow_for_load@2
slot
waterflow.flow_for_load
title
Water flow to carry a cooling or heating load
basis
first_principles
equations
  • cooling: ΔT = t_return − t_flow ; heating: ΔT = t_flow − t_return ; ΔT > 0
  • ṁ = Q / (c_p · ΔT)
  • q = ṁ / ρ
references
  • publication id
    hx.physics.first_principles
    title
    First-principles physical relations (conservation of energy and mass, ideal-gas law)
    publisher
    —
    licence
    public_domain_physics
    edition
    Not supplied
    locator
    Not supplied
assumptions
  • Specific heat and density are taken constant over the ΔT.
limitations
None recorded