Fire Dynamics Tools¶
General fire dynamics tools and calculations.
These tools are published by the U.S. Nuclear Regulatory Commission (U.S. NRC) and available at: https://www.nrc.gov/reading-rm/doc-collections/nuregs/staff/sr1805/s1/index
Chapter 2¶
Chapter 2 - Predicting Hot Gas Layer Temperature and Smoke Layer Height in a Room Fire with Natural and Forced Ventilation.
This module contains fundamental fire dynamics calculations including hot gas temperatures, smoke layer heights, heat transfer coefficients, and compartment geometry calculations.
These equations are essential for fire safety engineering analysis and compartment fire modeling.
Equation Modules¶
Equation 2.1 - Hot Gas Temperature Increase (MQH Method)¶
Natural ventilation calculations using the MQH correlation method.
- ofire.fire_dynamics_tools.chapter_2.equation_2_1.hot_gas_temperature_increase(q, a_v, h_v, a_t, h_k)¶
Calculate hot gas temperature increase for natural ventilation using the MQH method (Equation 2.1).
This function computes the temperature increase of hot gases in naturally ventilated enclosures based on the MQH (McCaffrey, Quintiere and, Harkleroad) correlation method.
\[\Delta T_g = 6.85 \cdot \left( \frac{Q^2}{\left(\sum_i A_v \cdot \sqrt{H_v}\right) \cdot (A_t \cdot h_k)} \right)^{1/3}\]where:
\(\Delta T_g\) is the hot gas temperature increase (K)
\(Q\) is the heat release rate (kW)
\(A_v\) is the ventilation opening area (m²)
\(H_v\) is the ventilation opening height (m)
\(A_t\) is the total interior surface area (m²)
\(h_k\) is the heat transfer coefficient (kW/m²K)
- Parameters:
- Returns:
Hot gas temperature increase (K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> q = 1000.0 >>> a_v = [2.5, 1.5] >>> h_v = [2.0, 1.0] >>> a_t = 75.0 >>> h_k = 0.035 >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_1.hot_gas_temperature_increase(q, a_v, h_v, a_t, h_k)
Equation 2.2 - Compartment Interior Surface Area¶
Calculate total interior surface area for compartments.
- ofire.fire_dynamics_tools.chapter_2.equation_2_2.compartment_interior_surface_area(w_c, l_c, h_c, a_v)¶
Calculate compartment interior surface area (Equation 2.2).
This function computes the total interior surface area of a compartment by calculating the areas of all walls, floor, and ceiling, then subtracting the ventilation opening area.
\[A_t = 2 \cdot (W_c \cdot L_c) + 2 \cdot (H_c \cdot W_c) + 2 \cdot (H_c \cdot L_c) - A_v\]where:
\(A_t\) is the total interior surface area (m²)
\(W_c\) is the compartment width (m)
\(L_c\) is the compartment length (m)
\(H_c\) is the compartment height (m)
\(A_v\) is the ventilation opening area (m²)
- Parameters:
- Returns:
Total interior surface area (m²)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_2.compartment_interior_surface_area(7.5, 4.0, 2.75, 4.5)
Equation 2.3 - Heat Transfer Coefficient (Long Times/Thin Walls)¶
Calculate heat transfer coefficients for long times or thin walls.
- ofire.fire_dynamics_tools.chapter_2.equation_2_3.heat_transfer_coefficient_longtimes_or_thinwalls(k, delta)¶
Calculate heat transfer coefficient for long times or thin walls (Equation 2.3).
This function computes the heat transfer coefficient for materials during long exposure times or for thin-walled constructions where steady-state heat transfer conditions are reached.
\[h_k = \frac{k}{\delta}\]where:
\(h_k\) is the heat transfer coefficient (kW/m²K)
\(k\) is the thermal conductivity (kW/mK)
\(\delta\) is the material thickness (m)
- Parameters:
- Returns:
Heat transfer coefficient (kW/m²K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_3.heat_transfer_coefficient_longtimes_or_thinwalls(0.002, 0.25)
Equation 2.4 - Thermal Penetration Time¶
Calculate thermal penetration time for materials.
- ofire.fire_dynamics_tools.chapter_2.equation_2_4.thermal_penetration_time(rho, c_p, k, delta)¶
Calculate thermal penetration time (Equation 2.4).
This function computes the thermal penetration time, which is the time required for heat to significantly penetrate through a material thickness.
\[t_p = \frac{\rho \cdot c_p}{k} \cdot \left( \frac{\delta}{2} \right)^2\]where:
\(t_p\) is the thermal penetration time (s)
\(\rho\) is the density (kg/m³)
\(c_p\) is the specific heat capacity (kJ/kgK)
\(k\) is the thermal conductivity (kW/mK)
\(\delta\) is the material thickness (m)
- Parameters:
- Returns:
Thermal penetration time (s)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_4.thermal_penetration_time(2400.0, 1.17, 0.002, 0.25)
Equation 2.5 - Heat Transfer Coefficient (Short Times/Thick Walls)¶
Calculate heat transfer coefficients for short times or thick walls.
- ofire.fire_dynamics_tools.chapter_2.equation_2_5.heat_transfer_coefficient_shorttimes_or_thickwalls(k, rho, c, t)¶
Calculate heat transfer coefficient for short times or thick walls (Equation 2.5).
This function computes the heat transfer coefficient for materials during short exposure times or for thick-walled constructions where the material can be considered as a semi-infinite solid.
\[h_k = \left( \frac{k \cdot \rho \cdot c}{t} \right)^{1/2}\]where:
\(h_k\) is the heat transfer coefficient (kW/m²K)
\(k\) is the thermal conductivity (kW/mK)
\(\rho\) is the density (kg/m³)
\(c\) is the specific heat capacity (kJ/kgK)
\(t\) is the time (s)
- Parameters:
- Returns:
Heat transfer coefficient (kW/m²K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_5.heat_transfer_coefficient_shorttimes_or_thickwalls(0.002, 2400.0, 1.17, 1800.0)
Equation 2.6 - Hot Gas Temperature Increase (Beyler Closed Compartment)¶
Hot gas temperature increase for closed compartments using Beyler correlation.
- ofire.fire_dynamics_tools.chapter_2.equation_2_6.hot_gas_temperature_increase_beyler_closed_compartment(k, rho, c, t, m, c_p, q)¶
Calculate hot gas temperature increase using the Beyler correlation for closed compartments (Equation 2.6).
This function calculates the temperature increase of hot gases in a closed compartment using Beyler’s correlation, accounting for thermal properties of the enclosure and fire characteristics.
\[\Delta T_g = \frac{2 \cdot \frac{Q}{m \cdot c_p}}{\left(\frac{2 \cdot 0.4 \cdot \sqrt{k \cdot \rho \cdot c}}{m \cdot c_p}\right)^2} \cdot \left(\frac{2 \cdot 0.4 \cdot \sqrt{k \cdot \rho \cdot c}}{m \cdot c_p} \cdot \sqrt{t} - 1 + e^{-\frac{2 \cdot 0.4 \cdot \sqrt{k \cdot \rho \cdot c}}{m \cdot c_p} \cdot \sqrt{t}}\right)\]where:
\(\Delta T_g\) is the hot gas temperature increase (K)
\(Q\) is the heat release rate (kW)
\(m\) is the mass flow rate (kg/s)
\(c_p\) is the specific heat capacity of air (kJ/kgK)
\(k\) is the thermal conductivity (kW/mK)
\(\rho\) is the density (kg/m³)
\(c\) is the specific heat capacity of the internal lining (kJ/kgK)
\(t\) is the time (s)
- Parameters:
- Returns:
Hot gas temperature increase (K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_6.hot_gas_temperature_increase_beyler_closed_compartment(0.002, 2400.0, 1.17, 60.0, 100.0, 1.0, 500.0)
Equation 2.7 - Nondimensional Hot Gas Temperature Increase (FPA)¶
Nondimensional hot gas temperature increase for forced ventilation.
- ofire.fire_dynamics_tools.chapter_2.equation_2_7.nondimensional_hot_gas_temperature_increase(q, m, t_a, h_k, a_t, c_p)¶
Calculate nondimensional hot gas temperature increase for forced ventilation using FPA correlation (Equation 2.7).
This function computes the nondimensional temperature increase of hot gases in forced ventilation systems using the FPA (Foote, Pagni, and Alvares) correlation.
\[\frac{\Delta T_g}{T_a} = 0.63 \cdot \left( \frac{Q}{m \cdot c_p \cdot T_a} \right)^{0.72} \cdot \left( \frac{h_k \cdot A_t}{m \cdot c_p} \right)^{-0.36}\]where:
\(\Delta T_g / T_a\) is the nondimensional hot gas temperature increase (dimensionless)
\(Q\) is the heat release rate (kW)
\(m\) is the mass flow rate (kg/s)
\(c_p\) is the specific heat capacity (kJ/kgK)
\(T_a\) is the ambient temperature (K)
\(h_k\) is the heat transfer coefficient (kW/m²K)
\(A_t\) is the total interior surface area (m²)
- Parameters:
- Returns:
Nondimensional hot gas temperature increase (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_7.nondimensional_hot_gas_temperature_increase(300.0, 2.5, 293.0, 0.035, 100.0, 1.0)
Equation 2.8 - Hot Gas Temperature Increase (Deal and Beyler)¶
Hot gas temperature increase for forced ventilation using Deal and Beyler correlation.
- ofire.fire_dynamics_tools.chapter_2.equation_2_8.hot_gas_temperature_increase_forced_ventilation(q, m, c_p, h_k, a_t)¶
Calculate hot gas temperature increase for forced ventilation using Deal and Beyler correlation (Equation 2.8).
This function computes the temperature increase of hot gases in forced ventilation systems using the Deal and Beyler steady-state correlation.
\[\Delta T_g = \frac{Q}{m \cdot c_p + h_k \cdot A_t}\]where:
\(\Delta T_g\) is the hot gas temperature increase (K)
\(Q\) is the heat release rate (kW)
\(m\) is the mass flow rate (kg/s)
\(c_p\) is the specific heat capacity (kJ/kgK)
\(h_k\) is the heat transfer coefficient (kW/m²K)
\(A_t\) is the total interior surface area (m²)
- Parameters:
- Returns:
Hot gas temperature increase (K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_8.hot_gas_temperature_increase_forced_ventilation(300.0, 2.5, 1.0, 0.035, 100.0)
Equation 2.9 - Convective Heat Transfer Coefficient¶
Calculate convective heat transfer coefficients.
- ofire.fire_dynamics_tools.chapter_2.equation_2_9.convective_heat_transfer_coefficient(k, rho, c, t, delta)¶
Calculate convective heat transfer coefficient (Equation 2.9).
This function computes the convective heat transfer coefficient as the maximum of the coefficients for short/thick and long/thin wall conditions.
\[h_k = 0.4 \cdot \max \left( \left( \frac{k \cdot \rho \cdot c}{t} \right)^{1/2}, \frac{k}{\delta} \right)\]where:
\(h_k\) is the convective heat transfer coefficient (kW/m²K)
\(k\) is the thermal conductivity (kW/mK)
\(\rho\) is the density (kg/m³)
\(c\) is the specific heat capacity (kJ/kgK)
\(t\) is the time (s)
\(\delta\) is the material thickness (m)
- Parameters:
- Returns:
Convective heat transfer coefficient (kW/m²K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_9.convective_heat_transfer_coefficient(0.002, 2400.0, 1.17, 180.0, 0.2)
Equation 2.10 - Smoke Layer Interface Height (Yamana-Tanaka)¶
Natural ventilation calculations using the Yamana-Tanaka correlation.
- ofire.fire_dynamics_tools.chapter_2.equation_2_10.height_smoke_layer_interface_natural_ventilation(k, q, t, a_c, h_c)¶
Calculate height of smoke layer interface using Yamana-Tanaka correlation (Equation 2.10).
This function computes the height of the smoke layer interface in naturally ventilated compartments using the Yamana-Tanaka correlation for transient conditions.
\[Z = \left( \frac{2 \cdot k \cdot Q^{1/3} \cdot t}{3 \cdot A_c} + \frac{1}{H_c^{2/3}} \right)^{-3/2}\]where:
\(Z\) is the height of smoke layer interface (m)
\(k\) is the entrainment coefficient (dimensionless)
\(Q\) is the heat release rate (kW)
\(t\) is the time (s)
\(A_c\) is the compartment floor area (m²)
\(H_c\) is the compartment height (m)
- Parameters:
- Returns:
Height of smoke layer interface (m)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_10.height_smoke_layer_interface_natural_ventilation(0.12, 1000.0, 90.0, 250.0, 4.5)
Equation 2.11 - K Constant for Smoke Layer Height (Yamana-Tanaka)¶
Calculate entrainment coefficient for smoke layer height.
- ofire.fire_dynamics_tools.chapter_2.equation_2_11.k_constant_smoke_layer_height(rho_g, rho_a, g, c_p, t_a)¶
Calculate k constant for smoke layer height using Yamana-Tanaka correlation (Equation 2.11).
This function computes the entrainment coefficient k for the Yamana-Tanaka smoke layer height correlation based on hot gas density and ambient conditions.
\[k = \frac{0.21}{\rho_g} \cdot \left( \frac{\rho_a^2 \cdot g}{c_p \cdot T_a} \right)^{1/3}\]where:
\(k\) is the entrainment coefficient (dimensionless)
\(\rho_g\) is the hot gas density (kg/m³)
\(\rho_a\) is the ambient air density (kg/m³)
\(g\) is the gravitational acceleration (m/s²)
\(c_p\) is the specific heat capacity (kJ/kgK)
\(T_a\) is the ambient temperature (K)
- Parameters:
- Returns:
Entrainment coefficient (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_11.k_constant_smoke_layer_height(0.5, 1.2, 9.81, 1.0, 293.15)
Equation 2.12 - K Constant for Smoke Layer Height (Simplified)¶
Calculate entrainment coefficient using simplified correlation.
- ofire.fire_dynamics_tools.chapter_2.equation_2_12.k_constant_smoke_layer_height_post_substitution(rho_g)¶
Calculate k constant for smoke layer height using simplified Yamana-Tanaka correlation (Equation 2.12).
This function computes the entrainment coefficient k using a simplified version of the Yamana-Tanaka correlation with pre-substituted standard values.
\[k = \frac{0.076}{\rho_g}\]where:
\(k\) is the entrainment coefficient (dimensionless)
\(\rho_g\) is the hot gas density (kg/m³)
0.076 is derived from substituting standard atmospheric values
- Parameters:
rho_g (float) – Hot gas density (kg/m³)
- Returns:
Entrainment coefficient (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_12.k_constant_smoke_layer_height_post_substitution(0.5)
Equation 2.13 - Hot Gas Density¶
Calculate density of hot gas layer based on temperature.
- ofire.fire_dynamics_tools.chapter_2.equation_2_13.density_hot_gas_layer(t_g)¶
Calculate density of hot gas layer (Equation 2.13).
This function computes the density of the hot gas layer based on the ideal gas law, assuming atmospheric pressure and using the hot gas temperature.
\[\rho_g = \frac{353.0}{T_g}\]where:
\(\rho_g\) is the hot gas density (kg/m³)
\(T_g\) is the hot gas temperature (K)
353.0 is derived from \(\frac{P \cdot M}{R}\) at atmospheric conditions
- Parameters:
t_g (float) – Hot gas temperature (K)
- Returns:
Hot gas density (kg/m³)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_2.equation_2_13.density_hot_gas_layer(500.0)
Chapter 4¶
Chapter 4 - Estimating wall fire flame height, line fire flame height against the wall, and corner fire flame height.
This chapter contains equations for fire dynamics calculations including flame height correlations for different fire configurations. These equations are fundamental for fire safety engineering analysis and design.
Equation Modules¶
Equation 4.1 - Wall Fire Flame Height¶
This module contains calculations for determining flame height of fires adjacent to walls. Wall fires exhibit different characteristics compared to free-burning fires due to the restriction of air entrainment from one side.
- ofire.fire_dynamics_tools.chapter_4.equation_4_1.wall_fire_flame_height(q)¶
Calculates wall fire flame height (Equation 4-1).
This equation determines the flame height for fires adjacent to walls based on the heat release rate. The wall effect increases flame height compared to free-burning fires due to reduced air entrainment.
\[h_f = 0.034 \cdot q^{\frac{2}{3}}\]where:
\(h_f\) is the flame height (m)
\(q\) is the heat release rate (kW)
- Parameters:
q (float) – Heat release rate (kW)
- Returns:
Wall fire flame height (m)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_4.equation_4_1.wall_fire_flame_height(700.0) >>> print(f"{result:.2f} m")
Equation 4.2 - Line Fire Flame Height¶
This module contains calculations for determining flame height of line fires. Line fires occur when fuel is arranged in a linear pattern, creating different flame dynamics compared to point source or area fires.
- ofire.fire_dynamics_tools.chapter_4.equation_4_2.line_fire_flame_height(q)¶
Calculates line fire flame height (Equation 4-2).
This equation determines the flame height for line fires, which are fires that spread along a linear fuel source. Line fires have different flame characteristics compared to point source fires due to their geometry.
\[h_f = 0.017 \cdot q^{\frac{2}{3}}\]where:
\(h_f\) is the flame height (m)
\(q\) is the heat release rate (kW)
- Parameters:
q (float) – Heat release rate (kW)
- Returns:
Line fire flame height (m)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_4.equation_4_2.line_fire_flame_height(700.0) >>> print(f"{result:.2f} m")
Equation 4.3 - Corner Fire Flame Height¶
This module contains calculations for determining flame height of fires located in corners. Corner fires have air entrainment restricted from two sides, leading to different flame behavior compared to wall or free fires.
- ofire.fire_dynamics_tools.chapter_4.equation_4_3.corner_fire_flame_height(q)¶
Calculates corner fire flame height (Equation 4-3).
This equation determines the flame height for fires located in corners, where two walls meet. Corner fires have restricted air entrainment from two sides, resulting in higher flame heights compared to wall fires.
\[h_f = 0.075 \cdot q^{\frac{3}{5}}\]where:
\(h_f\) is the flame height (m)
\(q\) is the heat release rate (kW)
- Parameters:
q (float) – Heat release rate (kW)
- Returns:
Corner fire flame height (m)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_4.equation_4_3.corner_fire_flame_height(700.0) >>> print(f"{result:.2f} m")
Chapter 5¶
Chapter 5 - Estimating Radiant Heat Flux fom Fire to a Target Fuel.
This module contains fire dynamics calculations from Chapter 5.
Equation Modules¶
Equation 5.1 - Thermal Radiation from a Point Source¶
This module contains calculations for thermal radiation incident flux from a point source fire.
- ofire.fire_dynamics_tools.chapter_5.equation_5_1.thermal_radiation_point_source(q, r, x_r)¶
This equation calculates the thermal radiation incident flux from a point source at a given distance, accounting for the radiative fraction of the total heat release rate.
\[\dot{q}^{"} = \frac{\chi_r \cdot \dot{Q}}{4 \cdot \pi \cdot r^2}\]where:
\(\dot{q}''\) is the radiant heat flux (kW/m²)
\(\dot{Q}\) is the heat release rate of the fire (kW)
\(r\) is the radial distance from the center of the flame to the edge of the target (m)
\(\chi_r\) is the fraction of total energy radiated (dimensionless)
- Parameters:
- Returns:
Radiant heat flux (kW/m²)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_5.equation_5_1.thermal_radiation_point_source(750.0, 2.5, 0.3)
Chapter 9¶
Chapter 9 - Fire plume temperature calculations.
This module contains fire plume temperature calculations from Chapter 9.
Equation Modules¶
Equation 9.2 - Maximum Centerline Temperature Rise in Fire Plumes¶
Equation 9-2 - Maximum centerline temperature rise in fire plumes.
This module contains calculations for the maximum temperature rise along the centerline of a fire plume at a given height above the fire source.
- ofire.fire_dynamics_tools.chapter_9.equation_9_2.maximum_centerline_temperature_rise_plume(t_a, q_c, g, c_p, rho_a, z, z_o)¶
Maximum centerline temperature rise in a plume above a fire source (Equation 9-2).
This equation calculates the maximum temperature rise along the centerline of a fire plume at a given height above the fire source.
\[\Delta T_p = 9.1 \left(\frac{T_a}{g \cdot c_p^2 \cdot \rho_a^2}\right)^{1/3} \frac{\dot{Q}_c^{2/3}}{(z - z_0)^{5/3}}\]where:
\(\Delta T_p\) is the maximum centerline temperature rise (K)
\(T_a\) is the ambient temperature (K)
\(\dot{Q}_c\) is the convective heat release rate (kW)
\(g\) is the acceleration of gravity (m/s²)
\(c_p\) is the specific heat of air (kJ/kg·K)
\(\rho_a\) is the density of ambient air (kg/m³)
\(z\) is elevation above the fire source (m)
\(z_0\) is the hypothetical virtual origin of the fire (m)
- Parameters:
t_a (float) – Ambient temperature (K)
q_c (float) – Convective heat release rate (kW)
g (float) – Acceleration of gravity (m/s²)
c_p (float) – Specific heat of air (kJ/kg·K)
rho_a (float) – Density of ambient air (kg/m³)
z (float) – Elevation above fire source (m)
z_o (float) – Hypothetical virtual origin of the fire (m)
- Returns:
Maximum centerline temperature rise (K)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_9.equation_9_2.maximum_centerline_temperature_plume(288.0, 700.0, 9.8, 1.0, 1.2, 2.0, -0.25)
Equation 9.3 - Virtual Origin Height to Diameter Ratio¶
Equation 9-3 - Virtual origin height to diameter ratio.
This module contains calculations for the virtual origin height to diameter ratio used in fire plume calculations.
- ofire.fire_dynamics_tools.chapter_9.equation_9_3.virtual_origin_over_diameter(d, q)¶
Virtual origin height normalized by fire diameter (Equation 9-3).
This equation calculates the ratio of virtual origin height to fire diameter for use in fire plume calculations.
\[\frac{z_0}{D} = -1.02 + 0.083 \frac{\dot{Q}^{2/5}}{D}\]where:
\(z_0\) is the virtual origin height (m)
\(D\) is the fire diameter (m)
\(\dot{Q}\) is the total heat release rate (kW)
- Parameters:
- Returns:
Virtual origin height to diameter ratio (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_9.equation_9_3.virtual_origin_over_diameter(2.2, 750.0)
Equation 9.4 - Effective Diameter of a Fire Source¶
Equation 9-4 - Effective diameter of a fire source.
This module contains calculations for the effective diameter of a fire source based on its area, assuming an equivalent circular fire source.
- ofire.fire_dynamics_tools.chapter_9.equation_9_4.effective_diameter(a_f)¶
Effective diameter of a fire source from its area (Equation 9-4).
This equation calculates the effective diameter of a fire source based on its area, assuming an equivalent circular fire source.
\[D = \left(\frac{4 \cdot A_f}{\pi}\right)^{1/2}\]where:
\(D\) is the effective diameter (m)
\(A_f\) is the fire area (m²)
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_9.equation_9_4.effective_diameter(4.0)
Chapter 18¶
Chapter 18 - Visibility calculations.
This module contains visibility calculations through smoke from Chapter 18.
Equation Modules¶
Equation 18.1 - Visibility Through Smoke¶
Equation 18-1 - Visibility through smoke.
This module contains calculations for visibility distance through smoke based on extinction coefficients and particulate mass concentrations.
- ofire.fire_dynamics_tools.chapter_18.equation_18_1.visibility(k, alpha_m, m_p)¶
Visibility through smoke (Equation 18-1).
This equation calculates the visibility through smoke based on the extinction coefficient and mass concentration of particulates.
\[S = \frac{K}{\alpha_m \cdot m_p}\]where:
\(S\) is the visibility (m)
\(K\) is proportionality constant (dimensionless)
\(\alpha_m\) is the specific extinction coefficient (m²/kg)
\(m_p\) is the mass concentration of particulates (kg/m³)
- Parameters:
- Returns:
Visibility (m)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_18.equation_18_1.visibility(8.0, 37000.0, 0.000006)
Equation 18.2 - Mass Concentration of Particulates¶
Equation 18-2 - Mass concentration of particulates.
This module contains calculations for mass concentration of particulates based on total mass and volume.
- ofire.fire_dynamics_tools.chapter_18.equation_18_2.concentration_particulates(m_p, v)¶
Mass concentration of particulates (Equation 18-2).
This equation calculates the mass concentration of particulates based on the total mass of particulates and the volume.
\[m_p = \frac{M_p}{V}\]where:
\(m_p\) is the mass concentration of particulates (kg/m³)
\(M_p\) is the total mass of particulates produced (kg)
\(V\) is the volume (m³)
- Parameters:
- Returns:
Mass concentration of particulates (kg/m³)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_18.equation_18_2.concentration_particulates(0.059, 90000.0)
Equation 18.3 - Mass of Particulates Produced¶
Equation 18-3 - Mass of particulates produced.
This module contains calculations for the total mass of particulates produced based on fuel mass and particulate yield.
- ofire.fire_dynamics_tools.chapter_18.equation_18_3.mass_particulates_produced(m_f, y_p)¶
Mass of particulates produced (Equation 18-3).
This equation calculates the total mass of particulates produced based on the fuel mass burned and particulate yield.
\[M_p = y_p \cdot M_f\]where:
\(M_p\) is the total mass of particulates produced (kg)
\(y_p\) is the particulate yield (dimensionless)
\(M_f\) is the mass of fuel burned (kg)
- Parameters:
- Returns:
Total mass of particulates produced (kg)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> result = ofire.fire_dynamics_tools.chapter_18.equation_18_3.mass_particulates_produced(2.0, 0.015)