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.
Where:
fnPDP = pump speed.
Vrev = PDP volume pumped per revolution, as determined in paragraph (a)(2) of this section.
pin = static absolute pressure at the PDP inlet.
R = molar gas constant.
Tin = absolute temperature at the PDP inlet.
= static absolute pressure at the PDP outlet.
Example:
a1 = 0.8405 (m3/s)
fnPDP = 12.58 r/s
Pout = 99.950 kPa
Pin = 98.575 kPa = 98575 Pa = 98575 kg/(m·s2)
a0 = 0.056 (m3/r)
R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)
Tin = 323.5 K
n = 29.428 mol/s
Where:
Cd = discharge coefficient, as determined based on the Cd versus Re# equation in § 1065.640(d)(2) .
Cf = flow coefficient, as determined in § 1065.640(c)(3)(ii) .
At = venturi throat cross-sectional area.
pin = static absolute pressure at the venturi inlet.
Z = compressibility factor.
Mmix = molar mass of gas mixture.
R = molar gas constant.
Tin = absolute temperature at the venturi inlet.
Example:
At = 0.01824 m2
pin = 99.132 kPa = 99132 Pa = 99132 kg/(m·s2)
Z = 1
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)
Tin = 298.15 K
Re# = 7.232·105
[GAMMA] = 1.399
[BETA] = 0.8
[DELTA]p = 2.312 kPa
Using Eq. 1065.640-7:
= 0.997
Using Eq. 1065.640-6:
= 0.274
Using Eq. 1065.640-5:
= 0.990
n = 58.173 mol/s
Where:
Cf = flow coefficient, as determined in § 1065.640(c)(3) .
Example:
Cd = 0.985
Cf = 0.7219
At = 0.00456 m2
pin = 98.836 kPa = 98836 Pa = 98836 kg/(m·s2)
Z = 1
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)
Tin = 378.15 K
n = 33.690 mol/s
Where:
Vstdref = volume flow rate of the standard at reference conditions of 293.15 K and 101.325 kPa.
Tin-cal = venturi inlet temperature during calibration.
Pin-cal = venturi inlet pressure during calibration.
Mmix-cal = molar mass of gas mixture used during calibration.
Mmix = molar mass of gas mixture during the emission test calculated using Eq. 1065.640-9.
Example:
Vstdref = 0.4895 m3
Tin-cal = 302.52 K
Pin-cal = 99.654 kPa = 99654 Pa = 99654 kg/(m·s2)
pin = 98.836 kPa = 98836 Pa = 98836 kg/(m·s2)
pstd = 101.325 kPa = 101325 Pa = 101325 kg/(m·s2)
Mmix-cal = 28.9656 g/mol = 0.0289656 kg/mol
Mmix = 28.7805 g/mol = 0.0287805 kg/mol
Tin = 353.15 K
Tstd = 293.15 K
R = 8.314472 J/(mol·K) = 8.314472 (m2·kg)/(s2·mol·K)
n = 16.457 mol/s
40 C.F.R. §1065.642