Nozzle Differential Pressure Flow Meter Calculation

ISA 1932 Nozzle, Long Radius Nozzle, Venturi Nozzle. Uses ISO-5167 equation. Liquids

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 Volumetric Flow, Qv (m3/s): Mass Flow, Qm (kg/s): Solve for: Differential Pressure, Δp (Pa): Flowrate Differential Pressure. (Qv known) Differential Pressure. (Qm known) Throat Diameter. (Qv known) Throat Diameter. (Qm known) Throat Diameter, d (m): Pipe Diameter, D (m): Select Meter Type and Liquid: Ratio, d/D: Water at 70 F, 20 C Water at 40 F, 5 C Seawater at 60 F, 16 C SAE 30 oil at 60 F, 16 C User Defined Liquid Density (kg/m3): Nozzle (ISA 1932) Long Radius Nozzle Venturi Nozzle Kinematic Viscosity (m2/s): Discharge Coefficient, C: Select Units for each Variable: Reynolds No. based on d, Red: Qv in ft3/s or cfs Qv in ft3/min or cfm Qv in gal/min or gpm (U.S. gal) Qv in gal/hr or gph (U.S. gal) Qv in gal/day or gpd (U.S. gal) Qv in barrels/day Qv in m3/s Qv in m3/min Reynolds No. based on D, ReD: Qm in slug/s Qm in lb/s Qm in lb/hr Qm in kg/s Qm in kg/hr Pressure Loss, w (Pa): Pressure in psi Pressure in inch H2O (60F) Pressure in inch Mercury (60F) Pressure in millibars Pressure in N/m2 or Pa Pressure in mm Mercury (0C) Minor Loss Coefficient, Km: Diameters in inches Diameters in feet Diameters in cm Diameters in meters Throat Velocity, Vthroat (m/s): Density in slug/ft3 Density in lb/ft3 Density in kg/m3 Density in g/cm3 Density in N/m3 Pipe Velocity, Vpipe (m/s): Visc in ft2/s; Vel in ft/s; Area in ft2 Visc in m2/s; Vel in m/s; Area in m2 Throat Area, Athroat (m2): http://www.LMNOeng.com Pipe Area, Apipe (m2): © 2015 LMNO Engineering, Research, and Software, Ltd.

Units in Nozzle Flow Meter calculator: cm=centimeter, ft=foot, g=gram, gal=U.S. gallon, hr=hour, kg=kilogram, km=kilometer, lb=pound, m=meter, min=minute, N=Newton, Pa=Pascal, psi=lb/inch2, s=second

Introduction
Nozzles are used to determine a fluid's flowrate through a pipe. The ISA 1932 nozzle was developed in 1932 by the International Federation of the National Standardizing Associations (later succeeded by the International Organization for Standardization or ISO). The ISA 1932 nozzle is commonly used outside of the USA (ASME, 1971). The long radius nozzle is a variation of the ISA 1932 nozzle. The venturi nozzle is a hybrid having a convergent section similar to the ISA 1932 nozzle and a divergent section similar to a classical venturi tube flowmeter. The venturi nozzle shown above is called a "truncated" venturi nozzle because the divergent section does not extend smoothly to the pipe diameter (ISO, 1991). The divergent portion of a "non-truncated" venturi nozzle is longer and extends smoothly all the way to the pipe diameter. The discharge coefficients are the same for both types of venturi nozzles.

Differential pressure is the pressure difference P1 - P2 shown in the above diagrams. For exact geometry and specifications for nozzles, see ISO (1991) or ASME (1971). Nozzles are typically used in 5 to 50 cm diameter pipes. The ASME (American Society of Mechanical Engineers) and ISO have been working on guidelines for nozzles since the early 1900s. The organizations have the most confidence in nozzle accuracy when the Reynolds number is in the range of 104 to 107 as discussed below. The calculation above is for liquids. Gas flow calculations have an additional factor called expansibility.

Equations
The calculations on this page are for nozzles carrying a liquid as described in ISO (1991) and ASME (1971). The ISO reference has a more complete discussion of nozzles than the ASME reference, so the ISO equations are used in our calculations.

k = Equivalent Roughness of the pipe material [L].  Click for k values.

w is the static pressure loss occurring from a distance of approximately D upstream of the nozzle to a distance of approximately 6D downstream of the nozzle. It is not the same as differential pressure. Differential pressure is measured at the exact locations specified in ISO (1991) (shown in the above figures). Km is computed to allow you to design pipe systems with nozzles and incorporate their head loss. Head loss is computed as h=KmV2/2g where V is the pipe velocity.

Discharge Coefficients
For each type of nozzle, a graph of Discharge Coefficient vs. ReD or d/D is shown. Each graph is followed by the equation used to form the graph. The equations are from ISO (1991).

ISA 1932 Nozzle Discharge Coefficient Equation:
C = 0.9900 - 0.2262(d/D)4.1 - [0.00175(d/D)2 - 0.0033(d/D)4.15][106/ReD]1.15
Valid for:   5 cm ≤ D ≤ 50 cm
and  0.3 ≤ d/D ≤ 0.44 having 7x104 ≤ ReD ≤ 107
and 0.44 ≤ d/D ≤ 0.8 having 2x104 ≤ ReD ≤ 107
and k/D ≤ 3.8 x10-4  generally for all d/D

Long Radius Nozzle Discharge Coefficient Equation:
C = 0.9965 - 0.00653[(106)(d/D)/ReD]0.5
Valid for:  0.2 ≤ d/D ≤ 0.8,  104 ≤ ReD ≤ 107,   5 cm ≤ D ≤ 63 cm
and k/D ≤ 10-3  generally.

Venturi Nozzle Discharge Coefficient Equation:
C = 0.9858 - 0.196(d/D)4.5
Valid for:  0.316 ≤ d/D ≤ 0.775,  1.5x105 ≤ ReD ≤ 2x106,
6.5 cm ≤ D ≤ 50 cm,  d ≥ 5 cm,  and   k/D ≤ 3.8x10-4  generally.

Values of k (equivalent roughness of pipe wall material) from ISO (1991):

 Material k (mm) Material k (mm) Material k (mm) Brass, copper, aluminum, plastics, glass.  Smooth without sediment: <0.03 Steel: Slightly rusted 0.1 to 0.2 Bituminized, new 0.03 to 0.05 New, seamless cold drawn <0.03 Rusty 0.2 to 0.3 Bituminized, normal 0.10 to 0.20 New, seamless hot drawn, rolled, or welded longitudinally 0.05 to 0.10 Encrusted 0.50 to 2 Galvanized 0.13 New, welded spirally 0.10 Heavy encrustation >2 Cast Iron: New 0.25 Encrusted >1.5 Rusty 1.0 to 1.5 Bituminized, new 0.03 to 0.05 Asbestos cement: Coated and not coated, new <0.03 Not coated, normal 0.05

Error Messages given by calculation
"All inputs must be positive". This is an initial check of user input.

"d, D, d/D, or ReD out of range". Results may or may not be computed. Valid values for C have not been determined for d, D, d/D, or Reynolds number (based on D) outside the ranges shown above. Note that C will be computed if it is not a function of an out of range variable. However, the calculated value of C is out of the range of the experiments used to form the ISO equations and is suspect.
• Try the simpler nozzle calculation on our Bernoulli page if your parameters are out of range. It is not as accurate, but won't give "parameter out of range" error messages.

References
American Society of Mechanical Engineers (ASME). 1971. Fluid meters: Their theory and application. Edited by H. S. Bean. 6ed. Report of ASME Research Committee on Fluid Meters.

International Organization of Standards (ISO 5167-1). 1991. Measurement of fluid flow by means of pressure differential devices, Part 1: Orifice plates, nozzles, and Venturi tubes inserted in circular cross-section conduits running full. Reference number: ISO 5167-1:1991(E).

LMNO Engineering, Research, and Software, Ltd.
7860 Angel Ridge Rd.   Athens, Ohio  45701  USA   Phone and fax: (740) 592-1890
LMNO@LMNOeng.com    http://www.LMNOeng.com

August 25, 2015: Made text fields narrower to show 8 significant figures rather than 16. Calculation still uses double precision internally.

To:

Other Flow Meter Calculations using standard methodologies:

Venturi (liquid)

Orifice for liquids (D<5cm)

Orifice for liquids (D>5cm)

Orifice for gases (D<5 cm)

Orifice for gases (D>5cm)

Simpler nozzle calculation (not as accurate but won't give "parameter out of range" messages):

Bernoulli page

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