**Units: **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/inch^{2}, s=second.

**Nozzle Diagrams**

**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 P_{1} - P_{2} 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 10^{4}
to 10^{7} 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.

**Varible Definitions**

[L]=Length units, [F]=Force units, [M]=Mass units, [T]=Time units.

A = Area [L^{2}], C = Discharge Coefficient, d = Throat Diameter [L], D = Pipe Diameter [L],
h = Head Loss [L],
k = Equivalent Roughness of Pipe Material [L],
K_{m} = Minor Loss Coefficient,
Δp = Differential Pressure [F/L^{2}], Q_{m} = Mass Flow Rate [M/T], Q_{v} = Volumetric Flow Rate [L^{3}/T], Re_{d} = Reynolds Number based on d, Re_{D} = Reynolds Number based on D, V = Velocity [L/T],
w = Pressure Loss [F/L^{2}],
ρ = Density [M/L^{3}], ν = Kinematic Viscosity [L^{2}/T].

k is used in discharge coefficient validity equations listed under each figure in next section. 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). K_{m} is
computed to allow you to design pipe systems with nozzles and incorporate their head
loss. Head loss is computed as h=K_{m}V^{2}/2g where V is the pipe
velocity.

**Discharge Coefficients**

For each type of nozzle, a graph of Discharge Coefficient vs. Re_{D} 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}][10^{6}/Re_{D}]^{1.15}

Valid for: 5 cm ≤ D ≤ 50 cm

and 0.3 ≤ d/D ≤ 0.44 having 7x10^{4 }≤
Re_{D} ≤ 10^{7}

and 0.44 ≤ d/D ≤ 0.8 having 2x10^{4 }≤
Re_{D} ≤ 10^{7}

and k/D ≤ 3.8 x10^{-4} generally for all d/D

Long Radius Nozzle Discharge Coefficient Equation:

C = 0.9965 - 0.00653[(10^{6})(d/D)/Re_{D}]^{0.5}

Valid for: 0.2 ≤ d/D ≤ 0.8, 10^{4 }≤ Re_{D} ≤
10^{7}, 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, 1.5x10^{5 }≤ Re_{D}
≤ 2x10^{6},

6.5 cm ≤ D ≤ 50 cm, d ≥ 5 cm, and
k/D ≤ 3.8x10^{-4} generally.

**Equivalent Roughness (k) Values**

Values are from ISO (1991).

Material |
k (mm) |
Material |
k (mm) |

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 |

Brass, copper, aluminum, plastics, glass. Smooth without sediment: |
<0.03 |

**Error Messages**

"All inputs must be positive". This is an initial check of user
input.

"d, D, d/D, or Re_{D} 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).

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