# 40 CFR 90.426 - Dilute emission sampling calculations

Where:

A

*WM*= Final weighted brake-specific mass emission rate for an emission (HC, CO, CO*2*, or NO*X*) [g/kW-hr]W

*i*= Average mass flow rate of an emission (HC, CO, CO*2*, NO*X*) from a test engine during mode i [g/hr]WF

*i*= Weighting factor for each mode i as defined in § 90.410(a).P

*i*= Gross average power generated during mode i [kW], calculated from the following equation,Where:

speed = average engine speed measured during mode i [rev./minute]

torque = average engine torque measured during mode i [N-m]

K

*Hi*= NO*X*humidity correction factor for mode i. This correction factor only affects calculations for tion factor only affects calculations for NO*X*and is equal to one for all other emissions. K*Hi*is also equal to 1 for all two-stroke engines.
(b)
The mass flow rate, W

*i*in g/hr, of an emission for mode i is determined from the following equation:Where:

Q

*I*= Volumetric flow rate [m^{3}/HR at stp].Density = Density of a specific emission (DensityHC, DensityCO, DensityCO

*2*, Density NO*X*) [g/m^{3}].DF

*i*= Dilution factor of the dilute exhaust during mode i.C

*Di*= Concentration of the emission (HC, CO, NO*X*) in dilute exhaust extracted from the CVS during mode i [ppm].C

*Bi*= Concentration of the emission (HC, CO, NO*X*) in the background sample during mode i [ppm].STP = Standard temperature and pressure. All volumetric calculations made for the equations in this section are to be corrected to a standard temperature of 20 °C and a standard pressure of 101.3 kPa.

Density

*HC*= 576.8 g/m^{3}Density

*NOX*= 1912 g/m^{3}Density

*CO*= 1164 g/m^{3}Density

*CO2*= 1829 g/m^{3}
(1)
The value of Density

*HC*above is calculated based on the assumption that the fuel used has a hydrogen to carbon ratio of 1:1.85. For other fuels Density*HC*can be calculated from the following formula:Where:

M

*HC*= The molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule [g/mole].R

*STP*= Ideal gas constant for a gas at STP = 0.024065 [m^{3}·mole]
(2)
The idealized molecular weight of the exhaust hydrocarbons, i.e., the molecular weight of the hydrocarbon molecule divided by the number of carbon atoms in the molecule, M

*HC*, can be calculated from the following formula:Where:

M

*C*= Molecular weight of carbon=12.01 [g/mole]M

*H*= Molecular weight of hydrogen=1.008 [g/mole]M

*O*= Molecular weight of oxygen=16.00 [g/mole]α = Hydrogen to carbon ratio of the test fuel

β = Oxygen to carbon ratio of the test fuel

(d)
The dilution factor, DF, is the ratio of the volumetric flow rate of the background air to that of the raw engine exhaust. The following formula is used to determine DF:

Where:

C

*DHC*= Concentration of HC in the dilute sample [ppm].C

*DCO*= Concentration of CO in the dilute sample [ppm].C

*DCO2*= Concentration of CO*2*in the dilute sample [ppm].
(e)
The humidity correction factor K

*H*is an adjustment made to measured NO*X*values. This corrects for the sensitivity that a spark-ignition engine has to the humidity of its combustion air. The following formula is used to determine K*H*for NO*X*calculations:K

*H*= (9.953 H 0.832)Where:

H = the amount of water in an ideal gas; 40 CFR 1065.645 describes how to determine this value (referred to as x

*H**2**O*).K

*H*= 1 for two-stroke gasoline engines.Where:

M

*FUEL*= Mass of fuel consumed by the engine during the mode [g]T = Duration of the sampling period [hr]

(i)
The mass of fuel consumed during the mode smpling period, M

*FUEL*, can be calculated from the following equation:Where:

G

*S*= Mass of carbon measured during the mode sampling period [g].R

*2*= The fuel carbon weight fraction, which is the mass of carbon in fuel per mass of fuel [g/g].
(j)
The grams of carbon measured during the mode, G

*S*, can be calculated from the following equation:Where:

HC

*mass*= mass of hydrocarbon emissions for the mode sampling period [grams].CO

*mass*mass of carbon monoxide emissions for the mode sample period [grams].CO

*2mass*= mass of carbon dioxide emissions for the mode sample period [grams].α = The atomic hydrogen-to-carbon ratio of the fuel.

[60 FR 34598, July 3, 1995, as amended at 70 FR 40450, July 13, 2005; 73 FR 59182, Oct. 8, 2008]

**Title 40 published on 2014-07-01**

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