Venturi Flowmeter Calculation for Liquid Flow

Compute flowrate, orifice diameter, or differential pressure.
Equations: ISO 5167

Other Flowmeter Calculations using standard methodologies:
  Nozzle for liquids   Orifice for liquids (D<5cm)  Orifice for liquids (D>5cm)
Orifice for gases (D<5 cm)  Orifice for gases (D>5cm)
Simpler venturi calculation (not as accurate but won't give "parameter out of range" messages): Bernoulli page
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Venturi Flowmeter


Topics:  Introduction    Equations    Discharge Coefficients    Error Messages    References

The classical Venturi tube (also known as the Herschel Venturi tube) is used to determine flowrate through a pipe.  Differential pressure is the pressure difference between the pressure measured at D and at d.  Other devices typically used to determine flowrate are orifices and nozzles, but the venturi tube has less head loss than either of these other methods due to its streamlined design.  For exact geometry and specifications for venturi tubes, see ISO (1991) or ASME (1971).  Venturis with cast iron entrance cones (the converging portion) are typically used in 4 to 32 inch (10 to 80 cm) diameter pipes.  Venturis with machined convergences are typically used in pipes having diameter less than 10 inches (25 cm) while venturis with a welded sheet metal convergence are used for larger pipes, typically up to 48 inch (1.2 m) diameter (ASME, 1971).  The ASME (American Society of Mechanical Engineers) and ISO (International Organization of Standards) have been working on guidelines for Venturi tubes since the early 1900s.  The organizations have the most confidence in Venturi tube accuracy when the Reynolds number is in the range of 105 to 106 as discussed below.

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

Venturi Equations
Variable Definitions

Discharge Coefficients                                            Top of Page
The following graph shows how C varies with Re:
Discharge Coefficient vs. Reynolds Number
The graph is formed from the following data provided in ISO (1991)*:

Cast Iron Convergent (also known as "As Cast" or "Rough Cast")
ReD 4x104 6x104 1x105 1.5x105   2x105 to 1x106
C 0.957 0.966 0.976 0.982   0.995 [1]
Machined Convergent
Red 5x104 1x105 2x105 3x105 5x105 2x105 to 1x106 [2]
C 0.970 0.977 0.992 0.998 0.995 0.995
Welded Sheet Metal (or Welded Sheet Iron) Convergent
ReD 4x104 6x104 1x105     2x105 to 2x106
C 0.96 0.97 0.98     0.985 [3]

Notes in above table:
* ISO 5167-1 states that only the last column of C values is part of the standard; the other values presented are from a smaller number of experiments and, in most cases, the venturi tubes had geometries which were not strictly in accordance with the ISO standard.   No limits on D or d/D are indicated for any C's except for the last column.
[1]: Valid for 5 cm <= D <= 25 cm and 0.4 <= d/D <= 0.75
[2]: ReD (not Red)=2x105 to 1x106 and 5 cm <= D <=25 cm and 0.4 <= d/D <= 0.75
[3]: Valid for 20 cm <= D <= 1.2 m and 0.4 <= d/D <= 0.7

LMNO Engineering fit curves through the data points to arrive at the above graph.   The fitted curves are used in the calculations and have the form:
C = a + b log(Re) + c  [log (Re)]2 + d [log(Re)]3 + ...
where a, b, c, d, ... are constants.  The number of constants was set equal to the number of data points plus 1.

Error Messages given by calculation                   Top of Page
"All inputs must be positive".  This is an initial check of user input.  No computations.
"d/D must be < 1".  This is an input check if both d and D are entered.  No computations.

"D or d/D out of range", "D out of range", or "d/D out of range".  Results are computed and printed, but D or d/D are out of the valid range where tests were conducted to determine C values.   Computations are completed since C does not depend directly on D or d/D; C is only a function of Red or ReD.

"ReD out of range", "ReD will be too high", "ReD will be too low", "Red and ReD out of range", or "Red , ReD will be out of range".  C is not computed and neither is the desired quantity.  However, some quantities are computed if they don't require C (e.g. pipe area from D).  Accurate values for C have been determined by ISO and ASME only within the published ranges of Red or ReD, depending on the type of venturi.  Red is Reynolds number based on d (throat diameter) and ReD is Reynolds number based on D (pipe diameter).

· Try the simpler venturi 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                                                            Top of Page
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).

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.

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(Modifications: July 24, 2005 - Deleted text references to gas flow. Previously our text discussion said the calculation is valid for both liquids and gases. However, the calculation is not valid for gases since the calculation does not account for gas expansibility.)