This section describes the equations for calculating molar flow rates from various flow meters. After you calibrate a flow meter according to § 1065.640, use the calculations described in this section to calculate flow during an emission test.

(a) *PDP molar flow rate.* (1) Based on the speed at which you operate the PDP for a test interval, select the corresponding slope, *a*1, and intercept, *a*0, as calculated in § 1065.640, to calculate PDP molar flow rate,, as follows:

Where:
*f*nPDP = pump speed.
*V*rev = PDP volume pumped per revolution, as determined in paragraph (a)(2) of this section.
*p*in = static absolute pressure at the PDP inlet.
*R* = molar gas constant.
*T*in = absolute temperature at the PDP inlet.
(2) Calculate *V*rev using the following equation:

*p*out = static absolute pressure at the PDP outlet.
Example:
*a*1 = 0.8405 (m
3/s)
*f*nPDP = 12.58 r/s
*P*out = 99.950 kPa
*P*in = 98.575 kPa = 98575 Pa = 98575 kg/(m·s
2)
*a*0 = 0.056 (m
3/r)
*R* = 8.314472 J/(mol·K) = 8.314472 (m
2·kg)/(s
2·mol·K)
*T*in = 323.5 K
*n*
= 29.428 mol/s
(b) *SSV molar flow rate.* Calculate SSV molar flow rate, *n
*, as follows:

Where:
*C*d = discharge coefficient, as determined based on the *C*d versus *Re*# equation in § 1065.640(d)(2).
*C*f = flow coefficient, as determined in § 1065.640(c)(3)(ii).
*A*t = venturi throat cross-sectional area.
*p*in = static absolute pressure at the venturi inlet.
*Z* = compressibility factor.
*M*mix = molar mass of gas mixture.
*R* = molar gas constant.
*T*in = absolute temperature at the venturi inlet.
Example:
*A*t = 0.01824 m
2
*p*in = 99.132 kPa = 99132 Pa = 99132 kg/(m·s
2)
*Z* = 1
*M*mix = 28.7805 g/mol = 0.0287805 kg/mol
*R* = 8.314472 J/(mol·K) = 8.314472 (m
2·kg)/(s
2·mol·K)
*T*in = 298.15 K
*Re*# = 7.232·10
5
γ = 1.399
β = 0.8
Δp = 2.312 kPa
Using Eq. 1065.640-7:

*r*ssv = 0.997
Using Eq. 1065.640-6:

*C*f = 0.274
Using Eq. 1065.640-5:

*C*d = 0.990
*n
* = 58.173 mol/s
(c) *CFV molar flow rate.* If you use multiple venturis and you calibrate each venturi independently to determine a separate discharge coefficient, *C*d (or calibration coefficient, *K*v), for each venturi, calculate the individual molar flow rates through each venturi and sum all their flow rates to determine CFV flow rate, *n*
. If you use multiple venturis and you calibrated venturis in combination, calculate *n*
using the sum of the active venturi throat areas as *A*t, the square root of the sum of the squares of the active venturi throat diameters as *d*t, and the ratio of the venturi throat to inlet diameters as the ratio of the square root of the sum of the active venturi throat diameters (*d*t) to the diameter of the common entrance to all the venturis (*D*).

(1) To calculate *n
* through one venturi or one combination of venturis, use its respective mean Cd and other constants you determined according to § 1065.640 and calculate *n
* as follows:

Where:
*C*f = flow coefficient, as determined in § 1065.640(c)(3).
Example:
*C*d = 0.985
*C*f = 0.7219
*A*t = 0.00456 m
2
*p*in = 98.836 kPa = 98836 Pa = 98836 kg/(m·s
2)
*Z* = 1
*M*mix = 28.7805 g/mol = 0.0287805 kg/mol
*R* = 8.314472 J/(mol·K) = 8.314472 (m
2·kg)/(s
2·mol·K)
*T*in = 378.15 K
*n*
= 33.690 mol/s
(2) To calculate the molar flow rate through one venturi or a combination of venturis, you may use its respective mean, *K*v, and other constants you determined according to § 1065.640 and calculate its molar flow rate *n*
during an emission test. Note that if you follow the permissible ranges of dilution air dewpoint versus calibration air dewpoint in Table 3 of § 1065.640, you may set *M*mix-cal and *M*mix equal to 1. Calculate *n*
as follows:

Where:
*V*stdref = volume flow rate of the standard at reference conditions of 293.15 K and 101.325 kPa.
*T*in-cal = venturi inlet temperature during calibration.
*P*in-cal = venturi inlet pressure during calibration.
*M*mix-cal = molar mass of gas mixture used during calibration.
*M*mix = molar mass of gas mixture during the emission test calculated using Eq. 1065.640-9.
Example:
*V*stdref = 0.4895 m
3
*T*in-cal = 302.52 K
*P*in-cal = 99.654 kPa = 99654 Pa = 99654 kg/(m·s
2)
*p*in = 98.836 kPa = 98836 Pa = 98836 kg/(m·s
2)
*p*std = 101.325 kPa = 101325 Pa = 101325 kg/(m·s
2)
*M*mix-cal = 28.9656 g/mol = 0.0289656 kg/mol
*M*mix = 28.7805 g/mol = 0.0287805 kg/mol
*T*in = 353.15 K
*T*std = 293.15 K
*R* = 8.314472 J/(mol·K) = 8.314472 (m
2·kg)/(s
2·mol·K)
*n*
= 16.457 mol/s
[81 FR 74177, Oct. 25, 2016, as amended at 86 FR 34557, June 29, 2021]