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