Mass flow versus volumetric flow Introduction This application note describes the difference between mass flow in terms of volumetric flow at standard conditions (1013.25 hPa, 0 °C) and volumetric flow at nonstandard conditions. Mass flow is a dynamic mass per time unit measured in grams per minute (g/min). By referencing a volumetric flow (cm3/min) to its known temperature and pressure, an exact mass flow can be calculated. It is common in the industry to specify mass flow in terms of volumetric flow at standard (reference) conditions. Note: Attention must be paid regarding the stated reference conditions when flow sensors are specified in standard volumetric flow such as sccm or slpm. Standard temperature and pressure (STP) is usually defined as being at 0°C (273.15 K) and 1013.25 hPa (1 atm). However, standard temperature may also be specified as 20 °C or 25 °C. Sometimes these reference conditions may also be referred to as normal temperature and pressure (NTP). Special industrial branches may even have their own definitions, e.g. the gas industry may reference flow volume to a temperature of 70 °F. In accordance with these standards, First Sensors mass flow sensors are specified as having volumetric flow at calibration reference conditions of 1013.25 hPa and 0 °C. These conditions are referred to as standard conditions and calibration units for these sensors are sccm (standard cubic centimeters per minute) or slpm (standard liters per minute). E / 11153 / 1 1/4 www.first-sensor.com www.sensortechnics.com Mass flow versus volumetric flow 1. Calculating true mass flow from volumetric flow A volumetric flow at standard conditions translates to a specific mass flow rate. For example, 200 cm3/min of dry air at standard conditions of temperature and pressure (200 sccm) calculates to a mass flow of 0.258 g/min as will be shown below. Gas density is defined as: ρ= Definitions: • The ideal gas law, PV = nRT can be solved for the gas volume to get: (4) With equation (3) mass flow can be redefined as: • m = mP • ⋅V nRT (5) • For a volumetric flow rate of VS = 200 cm3/min at standard conditions of 273.15 K and 1 atm the true mass flow then calculates to • m = 0.258 g min • E / 11153 / 1 (3) • m = ρ⋅V Number of molecules of gas [mole] Universal gas constant [(cm3•atm)/(mole•K)] Absolute temperature [K] Gas density [g/cm3] Mass [g] Mass flow [g/min] Volumetric flow [cm3/min] Volumetric flow at standard conditions [cm3/min] nRT P mP nRT Mass flow is equal to density times volumetric flow rate: P = Pressure [hPa][atm] V = Volume [cm3] V= (2) Substituting equation (1) into equation (2) redefines gas density as: ρ= n = R = T = ρ = m = • m = • V = • VS = m V VS m n P R T = = = = = = 200 cm3/min 28.949 grams in 1 mole air 1 Mol 1 atm (1013.25 hPa) 82.1 (cm3•atm)/(mole•K) 273.15 K (0 °C) (1) 2/4 www.first-sensor.com www.sensortechnics.com Mass flow versus volumetric flow 2. Calculating volumetric flow from true mass flow First Sensors flow sensors are mass flow devices rather than volumetric ones. At a constant mass flow, these sensors will give a constant output voltage even if the measured air or gas volume changes due to pressure or temperature changes. Confusion may result when mass flow sensors are used with volumetric devices, such as rotameters. Accurate volumetric flow calculations for mass flow devices require consideration of both temperature and pressure ranges. In contrast to mass flow sensors, volumetric devices indicate different flow rates at varying temperatures and pressures. Simple calculations can be used to show the relationship between mass flow and nonstandard volumetric flow. For example, a 200 sccm flow sensor of the WBA series with a mass flow rate of 0.258 g/min (200 sccm) at standard pressure of 1013.25 hPa but nonstandard temperature of 25 °C has a 5 V output voltage, indicating a standard flow rate of 200 sccm. The rotameter, however, would indicate a nonstandard volumetric flow rate. By rearranging equation (5) the corresponding volumetric flow at nonstandard conditions of 25 °C can be calculated for the mass flow measured by the WBA sensor. • V= nRT • ⋅m mP (6) • V = 218.3 cm3 min • m m n P R T = = = = = = 0.258 g/min 28.949 grams in 1 mole air 1 mole 1 atm (1013.25 hPa) 82.1 (cm3•atm)/(mole•K) 298.15 K (25 °C) In this example the mass flow rate of 0.258 g/min at standard conditions, which corresponds to a volumetric flow of 200 sccm, translates to a nonstandard volumetric flow of 218.26 cm3/min for an increased gas temperature of 25 °C. This increase reflects the fact that as temperature rises, gas expands, placing more distance between gas molecules (see Fig. 1). More distance between molecules means less mass in a given volume. If mass flow is kept constant, and temperature increases, volume flow increases to pass the same amount of mass (molecules) across the sensor. Fig. 1: Increased volumetric flow due to temperature increase T2 > T1 , constant mass flow and pressure. E / 11153 / 1 3/4 www.first-sensor.com www.sensortechnics.com Mass flow versus volumetric flow 3. Calculating nonstandard from standard volumetric flow • The actual, nonstandard volumetric flow VX can be found • with standard volumetric flow VS (PS= 1013,25 hPa, TS= 0 °C) when the actual temperature and pressure of the measured gas (TX, PX) is known. If mass flow is held constant over temperature and pressure, then the following is true: • This method eliminates the use of gas density values at reference and actual conditions. Therefore, mPS • mPX • ⋅ VX = ⋅ VS nRTX nRTS Further definitions: • VS = Volumetric flow at standard conditions • VX TS TX PS PX • mS • mX = = = = = = = Volumetric flow at nonstandard conditions Temperature at standard conditions Temperature at nonstandard conditions Pressure at standard conditions Pressure at nonstandard conditions Mass flow at standard conditions Mass flow at nonstandard conditions • Solving for VX yields: • • VX = VS ⋅ PS TX ⋅ PX TS (7) The actual, nonstandard volumetric flow at 25 °C is found to be • VX = 218.3 cm3 / min • VS PS PX TS TX E / 11153 / 1 • mS = m X = = = = = 200 cm3/min 1 atm (1013.25 hPa) 1 atm (1013.25 hPa) 273.15 K (0 °C) 298.15 K (25 °C) 4/4 www.first-sensor.com www.sensortechnics.com