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Flow Calculation from Pressure Differential Devices

Symbols
Expansion Factor
Discharge Coefficient and Flow Coefficient
Flow Equation

When installation requirements and flow conditions from ISO 5167 are met, standardized flow devices can provide flow rate results with good accuracy.

The diameter ratio is defined

β = d/D     (1)

The Reynolds number, expressing the ratio between the inertia and viscous forces in the upstream pipe is

ReD = m/0.25 π μ1 D     (2)

Symbols

β
diameter ratio [-]
μ1
dynamic viscosity upstream of the flow device [Pa·s]
ε
expansion factor [-]
α
flow coefficient [-]
κ
isentropic exponent [-]
ρ1
density upstream of the flow device [kg/m³]
Δp
pressure difference across the flow device [Pa]
C
discharge coefficient [-]
D
upstream internal pipe diameter under working conditions [mm]
L'2
quotient for downstream tapping distance [-]
L1
quotient for upstream tapping distance [-]
ReD
Reynolds number with respect to D [mm]
d
diameter of the flow device (orifice or throat) under working conditions [mm]
m
mass flow [kg/s]
p1
absolute static pressure upstream of flow device [Pa]
p2
absolute static pressure at flow device [Pa]; required is p2/p1 ≥ 0.75

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Expansion Factor

The expansion factor takes into account the compressibility of the fluid.

Orifice plates

equation 9.3 (9.3)

Nozzles, Venturi nozzles, Venturi tubes

equation 9.4 (9.4)

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Discharge Coefficient and Flow Coefficient

The discharge coefficient is defined for an incompressible fluid flow and relates actual vs. theoretical flowrate.

Orifice plates

equation 9.5 (9.5)

Corner tappings: L1 = L'2 = 0
Flange tappings: L1 = L'2 = 25.4/D with D [mm]
D and D/2 tappings: L1 = 1; L'2 = 0.47

ISA 1932 Nozzles

equation 9.6 (9.6)

Long radius nozzles

equation 9.7 (9.7)

Venturi nozzles

equation 9.8 (9.8)

Classical venturi tubes with an »as cast« convergent section

equation 9.9 (9.9)

Classical venturi tubes with a machined convergent section

equation 9.10 (9.10)

Classical venturi tubes with a rough-welded sheet-iron convergent section

equation 9.11 (9.11)

Discharge coefficient and flow coefficient are related

equation 9.12 (9.12)

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Flow Equation

Where the discharge coefficient depends on the Reynolds number the mass flow can only be found by iteration.

equation 9.13 (9.13)

Symbols

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