Division (a)

Molar based approach. To calibrate an SSV flow meter the following steps shall be performed:

1. (i)

   The Reynolds number, Re ^#, for each reference molar flow rate, shall be calculated using the throat diameter of the venturi, d _t [equation (7-145)]. Because the dynamic viscosity, μ, is needed to compute Re^# , a specific viscosity model may be used to determine μ for calibration gas (usually air), using good engineering judgment [equation (7-146)]. Alternatively, the Sutherland three-coefficient viscosity model may be used to approximate μ (see Table 7.7):

   ${\mathrm{Re}}^{\#}=\frac{4\times M_{\mathrm{mix}}\times {ṅ}_{\mathrm{ref}}}{\pi \times d_t\times \mu }$

   (7-145)

   Where:

   d _t

2. diameter of the SSV throat [m]

M _mix

3. mixture molar mass [kg/mol]

ṅ _ref

4. reference molar flow rate [mol/s]

and, using the Sutherland three-coefficient viscosity model:

$\mu ={\mu }_0{\left(\frac{T_{\mathrm{in}}}{T_0}\right)}^{\frac{3}{2}}\times \left(\frac{T_0+S}{T_{\mathrm{in}}+S}\right)$

(7-146)

Where:

μ

5. Dynamic viscosity of calibration gas [kg /(m · s)]

μ ₀

6. Sutherland reference viscosity [kg /(m · s)]

S

7. Sutherland constant [K]

T ₀

8. Sutherland reference temperature [K]

T _in

9. Absolute temperature at the venturi inlet [K]

Table 7.7
Sutherland three-coefficient viscosity model parameters
Tabulated parameters only for the pure gases, as listed, shall be used. Parameters to calculate viscosities of gas mixtures shall not be combined.
Gasf1	μ 0	T0	S	Temp range within ± 2 % error	Pressure limit
	kg /(m · s)	K	K	K	kPa
Air	1,716 × 10– 5	273	111	170 to 1 900	≤ 1 800
CO2	1,370 × 10– 5	273	222	190 to 1 700	≤ 3 600
H2O	1,12 × 10– 5	350	1,064	360 to 1 500	≤ 10 000
O2	1,919 × 10– 5	273	139	190 to 2 000	≤ 2 500
N2	1,663 × 10– 5	273	107	100 to 1 500	≤ 1 600