Venturi Flowmeter Calculation for Liquid Flow |
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Topics: Introduction Equations Discharge Coefficients Error Messages References
Introduction
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 10^{5} to 10^{6}
as discussed below.
Equations
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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.
Discharge Coefficients
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The following graph shows how C varies with Re:
The graph is formed from the following data provided in ISO (1991)*:
Cast Iron Convergent (also known as "As Cast" or "Rough Cast") | ||||||
Re_{D} | 4x10^{4} | 6x10^{4} | 1x10^{5} | 1.5x10^{5} | 2x10^{5} to 1x10^{6} | |
C | 0.957 | 0.966 | 0.976 | 0.982 | 0.995 [1] | |
Machined Convergent | ||||||
Re_{d} | 5x10^{4} | 1x10^{5} | 2x10^{5} | 3x10^{5} | 5x10^{5} | 2x10^{5} to 1x10^{6} [2] |
C | 0.970 | 0.977 | 0.992 | 0.998 | 0.995 | 0.995 |
Welded Sheet Metal (or Welded Sheet Iron) Convergent | ||||||
Re_{D} | 4x10^{4} | 6x10^{4} | 1x10^{5} | 2x10^{5} to 2x10^{6} | ||
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]: Re_{D }(not Re_{d})=2x10^{5} to 1x10^{6} 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
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"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 Re_{d} or Re_{D}.
"Re_{D} out of range", "Re_{D} will be too high",
"Re_{D} will be too low", "Re_{d} and Re_{D} out of
range", or "Re_{d} , Re_{D} 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 Re_{d} or Re_{D},
depending on the type of venturi. Re_{d} is Reynolds number based on d
(throat diameter) and Re_{D} 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
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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.)