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MEASUR-Tools-Suite v1.0.11
The MEASUR Tools Suite is a collection of industrial efficiency calculations written in C++ and with bindings for compilation to WebAssembly.
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This calculator estimates gas flow rate and energy consumption in fuel-fired furnaces by measuring pressure drop across an orifice. The calculation uses orifice geometry, gas properties, operating conditions, and discharge coefficients to determine volumetric flow and thermal input. The method is based on standard industrial practice for orifice flow measurement in combustion systems.
The calculation follows a top-down approach:
Relevant formulas and symbol definitions are documented below.
Effective cross-sectional area of the orifice.
The orifice area is calculated using an empirical factor and the square of the orifice diameter. This factor accounts for the conversion from diameter in inches to effective area for volumetric flow calculations in standard cubic feet per hour.
\begin{equation}\label{eq:flow-calculations-orifice-area} A = k_{area} \cdot d_{orifice}^2\end{equation}
| \(A\) | Orifice area \([\unit{ \squareInch}]\) |
| \(k_{area}\) | Orifice area factor (1300) - empirical constant for flow calculations, see physics::us::kOrificeAreaFactor \([\unit{ \unitless}]\) |
| \(d_{orifice}\) | Orifice diameter \([\unit{ \inch}]\) |
Discharge coefficient corrected for diameter ratio effects.
When the orifice diameter is smaller than the pipe diameter, the discharge coefficient must be adjusted to account for the velocity of approach and contraction effects. If the diameters are equal, no adjustment is needed.
\begin{equation}\label{eq:flow-calculations-adjusted-discharge-coeff} C_{d,adj} = \begin{cases} \frac{C_d}{\sqrt{1 - \left(\frac{d_{orifice}}{d_{pipe}}\right)^4}} & \text{if } d_{orifice} < d_{pipe} \\ C_d & \text{otherwise} \end{cases}\end{equation}
| \(C_{d,adj}\) | Adjusted discharge coefficient \([\unit{ \unitless}]\) |
| \(C_d\) | Discharge coefficient \([\unit{ \unitless}]\) |
| \(d_{orifice}\) | Orifice diameter \([\unit{ \inch}]\) |
| \(d_{pipe}\) | Inside pipe diameter \([\unit{ \inch}]\) |
Normalized pressure drop term accounting for gas specific gravity.
The pressure drop term represents the driving force for flow through the orifice, normalized by the gas specific gravity. This accounts for the fact that lighter gases will flow faster for the same pressure drop.
\begin{equation}\label{eq:flow-calculations-pressure-drop} \Delta P_{norm} = \sqrt{\frac{\Delta P_{orifice}}{SG}}\end{equation}
| \(\Delta P_{norm}\) | Normalized pressure drop \([\unit{ \inchWaterColumn}]\) |
| \(\Delta P_{orifice}\) | Orifice pressure drop \([\unit{ \inchWaterColumn}]\) |
| \(SG\) | Gas specific gravity (relative to air) \([\unit{ \unitless}]\) |
Temperature correction factor for flow to standard conditions.
The temperature adjustment converts actual volumetric flow at operating temperature to standard conditions (60°F or 520°R). Gas volume is inversely proportional to the square root of absolute temperature.
\begin{equation}\label{eq:flow-calculations-convert-temperature} T_{gas} = T_{gas,F} + 459.67\end{equation}
\begin{equation}\label{eq:flow-calculations-temperature-adj} f_T = \sqrt{\frac{T_{std}}{T_{gas}}}\end{equation}
| \(f_T\) | Temperature adjustment factor \([\unit{ \unitless}]\) |
| \(T_{std}\) | Standard gas temperature (520) - see physics::us::kStandardGasTemperatureR \([\unit{ \degreeRankine}]\) |
| \(T_{gas}\) | Actual gas temperature in Rankine \([\unit{ \degreeRankine}]\) |
| \(T_{gas,F}\) | Actual gas temperature in Fahrenheit \([\unit{ \degreeFahrenheit}]\) |
| \(459.67\) | Fahrenheit to Rankine conversion factor - see physics::conversions::fahrenheitToRankine \([\unit{ \degreeRankine}]\) |
Pressure correction factor for flow to standard conditions.
The pressure adjustment converts actual volumetric flow at operating pressure (gauge) to standard atmospheric pressure. Gas volume is proportional to the square root of absolute pressure.
\begin{equation}\label{eq:flow-calculations-abs-gas-pressure} P_{gas,abs} = P_{gas,gauge} + P_{atm}\end{equation}
\begin{equation}\label{eq:flow-calculations-pressure-adj} f_P = \sqrt{\frac{P_{gas,abs}}{P_{atm}}}\end{equation}
| \(f_P\) | Pressure adjustment factor \([\unit{ \unitless}]\) |
| \(P_{gas,abs}\) | Absolute gas pressure \([\unit{ psia}]\) |
| \(P_{gas,gauge}\) | Gauge gas pressure \([\unit{ psig}]\) |
| \(P_{atm}\) | Atmospheric pressure (14.7) - see physics::us::kAtmosphericPressurePsi \([\unit{ psia}]\) |
Volumetric flow rate at standard conditions.
The flow rate is calculated by combining the orifice area, adjusted discharge coefficient, and all correction factors. This represents the gas flow rate at standard conditions (60°F, 1 atm).
\begin{equation}\label{eq:flow-calculations-flow-rate} \dot{V} = A \cdot C_{d,adj} \cdot \Delta P_{norm} \cdot f_T \cdot f_P\end{equation}
| \(\dot{V}\) | Volumetric flow rate \([\unit{ \scf\per\hour}]\) |
| \(A\) | Orifice area \([\unit{ \squareInch}]\) |
| \(C_{d,adj}\) | Adjusted discharge coefficient \([\unit{ \unitless}]\) |
| \(\Delta P_{norm}\) | Normalized pressure drop \([\unit{ \inchWaterColumn}]\) |
| \(f_T\) | Temperature adjustment factor \([\unit{ \unitless}]\) |
| \(f_P\) | Pressure adjustment factor \([\unit{ \unitless}]\) |
Thermal energy input over operating period.
The heat input is calculated by multiplying the volumetric flow rate by the heating value of the gas and the operating time. The result is converted from Btu to MMBtu. If the heating value is zero or negative, the heat input is zero.
\begin{equation}\label{eq:flow-calculations-heat-input} Q_{input} = \frac{\dot{V} \cdot HHV \cdot t_{op}}{CF_{MMBtu}}\end{equation}
| \(Q_{input}\) | Heat input over operating period \([\unit{ \MMBtu}]\) |
| \(\dot{V}\) | Volumetric flow rate \([\unit{ \scf\per\hour}]\) |
| \(HHV\) | Higher heating value of gas \([\unit{ \btu\per\scf}]\) |
| \(t_{op}\) | Operating time \([\unit{ \hour}]\) |
| \(CF_{MMBtu}\) | Conversion factor to convert from Btu to MMBtu (1,000,000 Btu/MMBtu) - see physics::conversions::kMMBtuToBtu \([\unit{ \btu\per\MMBtu}]\) |
Total gas volume consumed over operating period.
The total flow is calculated by multiplying the volumetric flow rate at standard conditions by the operating time. This represents the total volume of gas consumed during the operating period.
\begin{equation}\label{eq:flow-calculations-total-flow} V_{total} = \dot{V} \cdot t_{op}\end{equation}
| \(V_{total}\) | Total gas volume consumed \([\unit{ \scf}]\) |
| \(\dot{V}\) | Volumetric flow rate \([\unit{ \scf\per\hour}]\) |
| \(t_{op}\) | Operating time \([\unit{ \hour}]\) |
The following table shows the default specific gravity values. Provided for reference.
| Gas Type | Specific Gravity (unitless) |
|---|---|
| Air | 1.0 |
| Ammonia (Dissociated) | 0.3 |
| Argon | 1.38 |
| Butane | 2.02 |
| Endothermic Ammonia | 0.59 |
| Exothermic (Cracked Lean) | 1.0 |
| Exothermic (Cracked Rich) | 0.85 |
| Helium | 0.14 |
| Hydrogen | 0.07 |
| Natural Gas | 0.65 |
| Nitrogen | 0.96 |
| Oxygen | 1.11 |
| Propane | 1.52 |
The following table shows the default discharge coefficient values. Provided for reference.
| Section Type | Discharge Coefficient (unitless) |
|---|---|
| Square Edge | 0.5 |
| Sharp Edge | 0.6 |
| Venturi | 0.8 |
Modules | |
| Orifice Area Formula | |
| Effective cross-sectional area of the orifice. | |
| Adjusted Discharge Coefficient Formula | |
| Discharge coefficient corrected for diameter ratio effects. | |
| Pressure Drop Term Formula | |
| Normalized pressure drop term accounting for gas specific gravity. | |
| Temperature Adjustment Formula | |
| Temperature correction factor for flow to standard conditions. | |
| Pressure Adjustment Formula | |
| Pressure correction factor for flow to standard conditions. | |
| Flow Rate Formula | |
| Volumetric flow rate at standard conditions. | |
| Heat Input Formula | |
| Thermal energy input over operating period. | |
| Total Flow Formula | |
| Total gas volume consumed over operating period. | |
Files | |
| file | flow_calculations_energy_use.h |
| Flow calculations for energy use in fuel-fired furnaces. | |
Namespaces | |
| namespace | flow_calculations_energy_use |
| Flow calculations for energy use in fuel-fired furnaces. | |
Classes | |
| struct | flow_calculations_energy_use::FlowCalculationsEnergyUseResults |
| Results of the flow calculations energy use. More... | |
Functions | |
| FlowCalculationsEnergyUseResults | flow_calculations_energy_use::flowCalculationsEnergyUse (double specific_gravity, double orifice_diameter, double inside_pipe_diameter, double discharge_coefficient, double gas_heating_value, double gas_temperature, double gas_pressure, double orifice_pressure_drop, double operating_time) |
| Calculates flow rate, heat input, and total flow for a fuel-fired furnace using orifice flow equations. | |
| FlowCalculationsEnergyUseResults flow_calculations_energy_use::flowCalculationsEnergyUse | ( | double | specific_gravity, |
| double | orifice_diameter, | ||
| double | inside_pipe_diameter, | ||
| double | discharge_coefficient, | ||
| double | gas_heating_value, | ||
| double | gas_temperature, | ||
| double | gas_pressure, | ||
| double | orifice_pressure_drop, | ||
| double | operating_time | ||
| ) |
Implements standard orifice meter equations for combustion gas flow measurement. All parameters must be provided in U.S. customary units.
| [in] | specific_gravity | Specific gravity of gas (unitless) |
| [in] | orifice_diameter | Orifice diameter \([\unit{in}]\) |
| [in] | inside_pipe_diameter | Inside pipe diameter \([\unit{in}]\) |
| [in] | discharge_coefficient | Discharge coefficient (unitless) |
| [in] | gas_heating_value | Gas heating value \([\unit{Btu/scf}]\) |
| [in] | gas_temperature | Gas temperature \([\unit{\degreeFahrenheit}]\) |
| [in] | gas_pressure | Gas pressure \([\unit{psig}]\) |
| [in] | orifice_pressure_drop | Orifice pressure drop \([\unit{in. W.C.}]\) |
| [in] | operating_time | Operating time \([\unit{hr}]\) |
1.9.8