Source: https://jmrplens.github.io/phonometry/reference/api/materials/airflow-resistance/ Airflow resistance of porous materials: ISO 9053-1 and ISO 9053-2. Two standardised measurement methods share the same three quantities and units (ISO 9053-1:2018, Clause 3; ISO 9053-2:2020, Clause 3): - **Airflow resistance** `R = dp / q_v` in Pa\*s/m3, with `dp` the air pressure difference across the specimen (Pa) and `q_v` the volumetric airflow rate through it (m3/s) (ISO 9053-1:2018, 3.1). - **Specific airflow resistance** `R_s = R * A` in **Pa\*s/m** (not Pa\*s/m2), with `A` the cross-sectional area of the specimen perpendicular to the flow (m2) (ISO 9053-1:2018, 3.2). Equivalently `R_s = dp / u` with `u` the linear airflow velocity, since `u = q_v / A`. - **Airflow resistivity** `sigma = R_s / d` in Pa\*s/m2, with `d` the specimen thickness in the flow direction (m), for homogeneous materials (ISO 9053-1:2018, 3.3). Equivalently `sigma = R * A / d`. The linear airflow velocity is `u = q_v / A` (ISO 9053-1:2018, 3.4). **Static (DC) method, ISO 9053-1:2018.** A steady unidirectional flow in the laminar regime is used. The recommended reference linear airflow velocity is `u = 0.5e-3 m/s` (0.5 mm/s, clause 7.5); if measured stepwise the highest velocity shall not exceed `15e-3 m/s` (15 mm/s), beyond which the flow may be non-linear. When measured stepwise the pressure difference is plotted against `u` and fitted with a regression of at least second order constrained through the origin, `dp = a*u + b*u**2`; `dp` and `R_s` are then evaluated at `u = 0.5e-3 m/s` (clause 7.5). Because `R_s = dp / u = a + b*u`, the linear coefficient `a` is the zero-velocity specific airflow resistance. **Alternating (AC) method, ISO 9053-2:2020.** A sinusoidally moving piston (frequency 1 Hz to 4 Hz, typically 2 Hz; clause 6.2) drives an alternating volume flow into an air cavity terminated either by the specimen or by an airtight termination. The airflow resistance follows from the sound-pressure-level difference between the two terminations (ISO 9053-2:2020, Formula (2), 8.7): ```text R = kappa' * P_S / (2*pi*f*V) * (h_t/h_s) * 10**((L_ps - L_pt)/20) ``` with `kappa'` the effective ratio of specific heats for air (Annex A), `P_S` the static (atmospheric) pressure (Pa), `f` the piston frequency (Hz), `V` the cavity volume with the airtight termination (m3), `h_t`/`h_s` the piston stroke amplitudes with the airtight termination / specimen cell, and `L_ps`/`L_pt` the cavity sound pressure levels with the specimen / airtight termination (dB). Only the level *difference* enters, so the sound level device needs no absolute calibration (clause 8.7). The RMS piston volume flow is `q_v = 2*pi*f*h*A_P` (ISO 9053-2:2020, 6.2), with `h` the stroke amplitude and `A_P` the piston cross-sectional area. The **effective** ratio of specific heats `kappa'` accounts for heat conduction between the oscillating air and the cavity walls, which makes the compression not fully adiabatic. ISO 9053-2:2020 Annex A (normative) gives its evaluation from the cavity geometry and air properties ([`effective_kappa`](/phonometry/reference/api/materials/airflow-resistance/#effective_kappa), Formula (A.7)); the Annex A.3 worked example yields `kappa' = 1.370` (about 2 % below the adiabatic `kappa = 1.4008`). When no cavity/air data are supplied, [`alternating_airflow_resistance`](/phonometry/reference/api/materials/airflow-resistance/#alternating_airflow_resistance) falls back to the **uncorrected adiabatic** value `kappa = 1.4` (Formula (A.1)); for a conforming result compute `kappa'` per Annex A and pass it explicitly. Neither part defines a temperature/atmospheric normalisation of the result. > Auto-generated from the source docstrings by `scripts/generate_api_docs.py` (`make api-docs`). Do not edit by hand. ## airflow_resistance ```python airflow_resistance(pressure_drop: float, volume_flow_rate: float) -> float ``` Airflow resistance `R = dp / q_v` (ISO 9053-1:2018, 3.1). `pressure_drop` is the pressure difference `dp` across the specimen (Pa) and `volume_flow_rate` is the volumetric airflow rate `q_v` (m3/s). Returns `R` in Pa\*s/m3. ## airflow_resistivity ```python airflow_resistivity(specific_resistance: float, thickness: float) -> float ``` Airflow resistivity `sigma = R_s / d` in Pa\*s/m2 (ISO 9053-1:2018, 3.3). `specific_resistance` is `R_s` (Pa\*s/m) and `thickness` is `d` (m), the specimen thickness in the flow direction. Returns `sigma` in Pa\*s/m2. ## AirflowResistanceWarning Advisory for out-of-range or non-conforming ISO 9053 airflow inputs. ## alternating_airflow_resistance ```python alternating_airflow_resistance( level_specimen: float, level_termination: float, *, piston_stroke_specimen: float, piston_stroke_termination: float, frequency: float, cavity_volume: float, static_pressure: float = 101325.0, kappa_prime: float = 1.4, background_level: float | None = None, ) -> float ``` Alternating-method airflow resistance (ISO 9053-2:2020, Formula (2), 8.7). Implements: ```text R = kappa' * P_S / (2*pi*f*V) * (h_t/h_s) * 10**((L_ps - L_pt)/20) ``` `level_specimen` (`L_ps`) and `level_termination` (`L_pt`) are the cavity sound pressure levels (dB) with the specimen cell and the airtight termination; `piston_stroke_specimen` (`h_s`) and `piston_stroke_termination` (`h_t`) the corresponding stroke amplitudes (m); `frequency` the piston frequency `f` (Hz, 1-4 Hz); `cavity_volume` the airtight-termination cavity volume `V` (m3); `static_pressure` the atmospheric pressure `P_S` (Pa, default 101325); `kappa_prime` the effective ratio of specific heats `kappa'`; `background_level` the optional cavity background level `L_pb` (dB) for the Formula (4) check. Returns `R` in Pa\*s/m3. `kappa_prime` defaults to the **uncorrected adiabatic** `kappa = 1.4` (Formula (A.1)). For a result conforming to the normative Annex A, compute the heat-conduction-corrected `kappa'` with [`effective_kappa`](/phonometry/reference/api/materials/airflow-resistance/#effective_kappa) from the cavity geometry and pass it here (the Annex A.3 example gives `kappa' = 1.370`). Emits [`AirflowResistanceWarning`](/phonometry/reference/api/materials/airflow-resistance/#airflowresistancewarning) when the piston frequency is outside 1-4 Hz or when the Formula (3)/(4) validity criteria are not met. ## effective_kappa ```python effective_kappa( cavity_surface: float, cavity_volume: float, frequency: float, *, speed_of_sound: float = 345.9, air_density: float = 1.186, specific_heat_ratio: float = 1.4008, specific_heat_cp: float = 938.7, thermal_conductivity: float = 0.02355, ) -> float ``` Effective ratio of specific heats `kappa'` (ISO 9053-2:2020, Annex A, Formula (A.7)). Heat conduction between the oscillating air and the cavity walls makes the compression not fully adiabatic, lowering `kappa` to: ```text kappa' = kappa / sqrt(1 + (kappa-1)*(S/V)*b + 0.5*((kappa-1)*(S/V)*b)**2) (A.7) ``` with `b` the thermal boundary-layer thickness (Formulae (A.4)/(A.5), [`thermal_boundary_layer_thickness`](/phonometry/reference/api/materials/airflow-resistance/#thermal_boundary_layer_thickness)), `S` the total internal surface area of the air cavity (m2) and `V` its volume (m3). `cavity_surface` is `S` (m2), `cavity_volume` `V` (m3) and `frequency` the piston frequency `f` (Hz); `specific_heat_ratio` `kappa` (adiabatic) and the remaining air properties default to the ISO 9053-2:2020 Annex A.3 values. Returns the dimensionless `kappa'` for use in [`alternating_airflow_resistance`](/phonometry/reference/api/materials/airflow-resistance/#alternating_airflow_resistance); the Annex A.3 worked example (`S = 0.0471 m2`, `V = 7.854e-4 m3`, `f = 2 Hz`) yields `kappa' = 1.370`. ## linear_airflow_velocity ```python linear_airflow_velocity(volume_flow_rate: float, area: float) -> float ``` Linear airflow velocity `u = q_v / A` (ISO 9053-1:2018, 3.4). `volume_flow_rate` is `q_v` (m3/s) and `area` is `A` (m2); returns `u` in m/s. ## piston_volume_flow_rate ```python piston_volume_flow_rate( frequency: float, stroke_amplitude: float, piston_area: float, ) -> float ``` RMS piston volume flow `q_v = 2*pi*f*h*A_P` (ISO 9053-2:2020, 6.2). `frequency` is the piston frequency `f` (Hz), `stroke_amplitude` the stroke amplitude `h` (m) and `piston_area` the piston cross-section `A_P` (m2). Returns `q_v` in m3/s. ## specific_airflow_resistance ```python specific_airflow_resistance( resistance: float | None = None, area: float | None = None, *, pressure_drop: float | None = None, velocity: float | None = None, ) -> float ``` Specific airflow resistance `R_s` in Pa\*s/m (ISO 9053-1:2018, 3.2). Two equivalent routes are accepted; supply exactly one: - `resistance` (`R`, Pa\*s/m3) and `area` (`A`, m2): `R_s = R * A`. - `pressure_drop` (`dp`, Pa) and `velocity` (`u`, m/s): `R_s = dp/u` (from `R_s = R*A` with `u = q_v/A`). The unit is pascal second per metre (Pa\*s/m), not Pa\*s/m2. ## static_airflow_resistance ```python static_airflow_resistance( velocities: ArrayLike, pressure_drops: ArrayLike, area: float, thickness: float | None = None, *, evaluation_velocity: float = 0.0005, ) -> StaticAirflowResult ``` Stepwise static-method airflow resistance (ISO 9053-1:2018, clause 7.5). Fits the measured pressure difference against the linear airflow velocity with a second-order regression constrained through the origin, `dp = a*u + b*u**2`, and evaluates the resistances at `evaluation_velocity` (the clause 7.5 reference `0.5e-3 m/s` by default). `velocities` are the linear airflow velocities `u` (m/s) and `pressure_drops` the matching pressure differences `dp` (Pa) of at least two measurement steps; `area` is the cross-section `A` (m2) and `thickness` the specimen thickness `d` (m, optional, enabling `sigma`). Because `R_s = dp/u = a + b*u`, the returned `linear_coefficient` `a` is the zero-velocity specific airflow resistance. A velocity above the clause 7.5 upper limit (15 mm/s) raises [`AirflowResistanceWarning`](/phonometry/reference/api/materials/airflow-resistance/#airflowresistancewarning). ## StaticAirflowResult ```python StaticAirflowResult( resistance: float, specific_resistance: float, resistivity: float | None, evaluation_velocity: float, pressure_drop: float, linear_coefficient: float, quadratic_coefficient: float, ) ``` Result of an ISO 9053-1:2018 stepwise (static-method) determination. `resistance` (`R`, Pa\*s/m3), `specific_resistance` (`R_s`, Pa\*s/m) and `resistivity` (`sigma`, Pa\*s/m2; `None` when no thickness is supplied) are evaluated at `evaluation_velocity` (m/s, the ISO 9053-1 clause 7.5 reference 0.5 mm/s by default). `linear_coefficient` (`a`) and `quadratic_coefficient` (`b`) are the through-origin fit `dp = a*u + b*u**2` (clause 7.5); `a` is the zero-velocity specific airflow resistance (Pa\*s/m). `pressure_drop` is the fitted `dp` at `evaluation_velocity` (Pa). ### StaticAirflowResult.plot() ```python StaticAirflowResult.plot( ax: Axes | None = None, *, language: str = 'en', **kwargs: Any, ) -> Axes ``` Plot the fitted `dp(u)` curve with the evaluation point. Requires matplotlib (`pip install phonometry[plot]`); returns the `Axes`. ### StaticAirflowResult.report() ```python StaticAirflowResult.report( path: str, *, metadata: ReportMetadata | None = None, engine: str = 'reportlab', verbose: bool = False, language: str = 'en', ) -> str ``` Render an ISO 9053-1 static airflow-resistance test-report fiche to a PDF. Writes a one-page accredited airflow-resistance report (ISO 9053-1:2018, static/direct airflow method): the standard-basis line, an optional metadata header block (client, manufacturer, specimen, the specimen thickness `d`, test facility, date, climate ...), a two-panel body with a compact metrics table (the evaluation velocity, the fitted pressure difference `dp`, the airflow resistance `R`, the specific airflow resistance `R_s`, the airflow resistivity `sigma` when a thickness is available, and the through-origin fit coefficients `a` and `b`) beside the fitted `dp(u)` curve, a boxed specific airflow resistance `R_s` with the airflow resistance `R` and the resistivity `sigma` alongside, and a footer with the fixed disclaimer. ISO 9053-1 is a material characterisation, so there is no pass/fail verdict. The clause 7.5 stepwise procedure fits `dp = a*u + b*u**2` through the origin and evaluates the resistances at the reference velocity `u = 0.5 mm/s`; the linear coefficient `a` is the zero-velocity specific airflow resistance. Resistance quantities are printed to the nearest whole Pa\*s unit and the evaluation velocity to one decimal place (mm/s). **Parameters** | Name | Description | | :--- | :--- | | `path` | Destination path of the PDF file. | | `metadata` | Optional [`ReportMetadata`](/phonometry/reference/api/building/insulation/#reportmetadata); `None` produces a body-and-disclaimer fiche. The applicable descriptive fields are `client`, `manufacturer`, `specimen`, `thickness` (the specimen thickness `d`, in metres, shown in millimetres), `test_room`, `test_date`, `temperature`, `relative_humidity`, `measurement_standard`, `laboratory`, `operator`, `report_id` and `notes`. The `requirement` field is ignored (ISO 9053-1 has no verdict). | | `engine` | Rendering back end; only `"reportlab"` is supported. | | `verbose` | Accepted for a uniform `.report()` signature; the airflow-resistance fiche has a single body layout, so it has no effect. | | `language` | Fiche language: `"en"` (default, English, decimal point) or `"es"` (Spanish, decimal comma). | **Returns:** The written `path` as a `str`. **Raises** | Exception | When | | :--- | :--- | | ValueError | If `engine` is not `"reportlab"`. | | ImportError | If reportlab or matplotlib is not installed. The fiche always embeds the fitted `dp(u)` curve, so both are required (`pip install "phonometry[report,plot]"`). | ## thermal_boundary_layer_thickness ```python thermal_boundary_layer_thickness( frequency: float, *, speed_of_sound: float = 345.9, air_density: float = 1.186, specific_heat_cp: float = 938.7, thermal_conductivity: float = 0.02355, ) -> float ``` Thermal boundary-layer thickness `b` (ISO 9053-2:2020, Formulae (A.4)/(A.5)). ```text l_h = k_a / (rho0 * c0 * C_P) (A.5) b = sqrt(2 * c0 * l_h / omega) (A.4), omega = 2*pi*f ``` `frequency` is the piston frequency `f` (Hz); `speed_of_sound` `c0` (m/s), `air_density` `rho0` (kg/m3), `specific_heat_cp` `C_P` (J/(kg\*K)) and `thermal_conductivity` `k_a` (J/(s\*m\*K)) are air properties, defaulting to the IEC 61094-2:2009 values used in ISO 9053-2:2020 Annex A.3. Returns `b` in metres; with the Annex A.3 example (`f = 2 Hz`) this is `1.83e-3 m`.