# Title 40

## SECTION 1065.642

### 1065.642 PDP, SSV, and CFV molar flow rate calculations.

§ 1065.642 PDP, SSV, and CFV molar flow rate calculations.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:

*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:

*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)(2)(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 g = 1.399 b = 0.8 Δ

*p*= 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 *C*d and other constants
you determined according to § 1065.640 and calculate *n* as
follows:

*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:

*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]