# 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*<sub>1,</sub> and intercept, *a*<sub>0,</sub> as calculated in § 1065.640, to calculate PDP molar flow rate,, as follows:
Where:
*f*<sub>nPDP</sub> = pump speed.
*V*<sub>rev</sub> = PDP volume pumped per revolution, as determined in paragraph (a)(2) of this section.
*p*<sub>in</sub> = static absolute pressure at the PDP inlet.
*R* = molar gas constant.
*T*<sub>in</sub> = absolute temperature at the PDP inlet.
(2) Calculate *V*<sub>rev</sub> using the following equation:
*p*<sub>out</sub> = static absolute pressure at the PDP outlet.
*a*<sub>1</sub> = 0.8405 (m
<sup>3</sup>/s)
*f*<sub>nPDP</sub> = 12.58 r/s
*P*<sub>out</sub> = 99.950 kPa
*P*<sub>in</sub> = 98.575 kPa = 98575 Pa = 98575 kg/(m·s
<sup>2</sup>)
*a*<sub>0</sub> = 0.056 (m
<sup>3</sup>/r)
*R* = 8.314472 J/(mol·K) = 8.314472 (m
<sup>2</sup>·kg)/(s
<sup>2</sup>·mol·K)
*T*<sub>in</sub> = 323.5 K
*n*
= 29.428 mol/s
(b) *SSV molar flow rate.* Calculate SSV molar flow rate, *n
*, as follows:
Where:
*C*<sub>d</sub> = discharge coefficient, as determined based on the *C*<sub>d</sub> versus *Re*<sub>#</sub> equation in § 1065.640(d)(2).
*C*<sub>f</sub> = flow coefficient, as determined in § 1065.640(c)(3)(ii).
*A*<sub>t</sub> = venturi throat cross-sectional area.
*p*<sub>in</sub> = static absolute pressure at the venturi inlet.
*Z* = compressibility factor.
*M*<sub>mix</sub> = molar mass of gas mixture.
*R* = molar gas constant.
*T*<sub>in</sub> = absolute temperature at the venturi inlet.
*A*<sub>t</sub> = 0.01824 m
<sup>2</sup>
*p*<sub>in</sub> = 99.132 kPa = 99132 Pa = 99132 kg/(m·s
<sup>2</sup>)
*Z* = 1
*M*<sub>mix</sub> = 28.7805 g/mol = 0.0287805 kg/mol
*R* = 8.314472 J/(mol·K) = 8.314472 (m
<sup>2</sup>·kg)/(s
<sup>2</sup>·mol·K)
*T*<sub>in</sub> = 298.15 K
*Re*<sub>#</sub> = 7.232·10
<sup>5</sup>
γ = 1.399
β = 0.8
Δp = 2.312 kPa
Using Eq. 1065.640-7:
*r*<sub>ssv</sub> = 0.997
Using Eq. 1065.640-6:
*C*<sub>f</sub> = 0.274
Using Eq. 1065.640-5:
*C*<sub>d</sub> = 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*<sub>d</sub> (or calibration coefficient, *K*<sub>v</sub>), 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*<sub>t</sub>, the square root of the sum of the squares of the active venturi throat diameters as *d*<sub>t</sub>, 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*<sub>t</sub>) 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<sub>d</sub> and other constants you determined according to § 1065.640 and calculate *n
* as follows:
Where:
*C*<sub>f</sub> = flow coefficient, as determined in § 1065.640(c)(3).
*C*<sub>d</sub> = 0.985
*C*<sub>f</sub> = 0.7219
*A*<sub>t</sub> = 0.00456 m
<sup>2</sup>
*p*<sub>in</sub> = 98.836 kPa = 98836 Pa = 98836 kg/(m·s
<sup>2</sup>)
*Z* = 1
*M*<sub>mix</sub> = 28.7805 g/mol = 0.0287805 kg/mol
*R* = 8.314472 J/(mol·K) = 8.314472 (m
<sup>2</sup>·kg)/(s
<sup>2</sup>·mol·K)
*T*<sub>in</sub> = 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*<sub>v</sub>, 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*<sub>mix-cal</sub> and *M*<sub>mix</sub> equal to 1. Calculate *n*
as follows:
Where:
*V*<sub>stdref</sub> = volume flow rate of the standard at reference conditions of 293.15 K and 101.325 kPa.
*T*<sub>in-cal</sub> = venturi inlet temperature during calibration.
*P*<sub>in-cal</sub> = venturi inlet pressure during calibration.
*M*<sub>mix-cal</sub> = molar mass of gas mixture used during calibration.
*M*<sub>mix</sub> = molar mass of gas mixture during the emission test calculated using Eq. 1065.640-9.
*V*<sub>stdref</sub> = 0.4895 m
<sup>3</sup>
*T*<sub>in-cal</sub> = 302.52 K
*P*<sub>in-cal</sub> = 99.654 kPa = 99654 Pa = 99654 kg/(m·s
<sup>2</sup>)
*p*<sub>in</sub> = 98.836 kPa = 98836 Pa = 98836 kg/(m·s
<sup>2</sup>)
*p*<sub>std</sub> = 101.325 kPa = 101325 Pa = 101325 kg/(m·s
<sup>2</sup>)
*M*<sub>mix-cal</sub> = 28.9656 g/mol = 0.0289656 kg/mol
*M*<sub>mix</sub> = 28.7805 g/mol = 0.0287805 kg/mol
*T*<sub>in</sub> = 353.15 K
*T*<sub>std</sub> = 293.15 K
*R* = 8.314472 J/(mol·K) = 8.314472 (m
<sup>2</sup>·kg)/(s
<sup>2</sup>·mol·K)
*n*
= 16.457 mol/s
[81 FR 74177, Oct. 25, 2016, as amended at 86 FR 34557, June 29, 2021]