# Improving flowmeter calibration

## Instrumentation engineers should understand the common methods used in measuring viscosity and their effects on final flowmeter calibration data.

06/03/2016

Calibrating a flowmeter is an essential part of any well-controlled process. However, accurate meter calibration not only requires a precision calibrator but also an accurate method to measure viscosity. Other than indicating a viscosity value on the calibration data sheet, calibration labs do not always expose their viscosity measurement methods.

Background

Calibration is a comparison between the reading of a device and traceable standards. The process establishing this relationship is a set of interrelated measurements and operations, which provide the comparison. Flow measurement does not rely on a single parameter, nor does a flow-based calibration.

Measurement of the volume or mass flow of a fluid depends on establishing verifiable measurements representing all the variables. The flow measurement may be the quantity collected over time or the actual rate of flow.

The volume measured by the calibration standard may be different from the volume passed through the meter under test if temperature measurements are incorrect. Temperature affects fluid viscosity, density, and the bore diameter of the flowmeter under test. This combination of fluid variables, coupled with how accurately they are measured and their effects on the calibration standard, will influence the uncertainty of the final calibration results (see Figure 1).

Understanding viscosity

Viscosity is a measure of a fluid's internal or intermolecular resistance to shear stress, which influences the velocity profile in the pipe. When viewing a fluid flowing between two plates, the shear stress is the relationship between the forces exerted on the top plate to the area of the plate. Therefore, τ (shear stress) = F/A. Shear rate takes into account the height between the two plates combined with the velocity of the top plate, or γ (shear rate) = v/h. Dynamic viscosity is the shear stress (τ)/shear rate (γ). These equations apply to ideal or Newtonian fluids.

What are Newtonian fluids? These fluids have shearing stress that is related linearly to the rate of shearing strain. They are referred to as "true liquids" because their viscosity is not impacted by shear, such as those found in agitation or pumping. Most common fluids, such as water and hydrocarbons, are considered Newtonian fluids.

Some flowmeters are more sensitive to viscosity than others. But to some degree, they are all affected because viscosity changes the flow profile. Knowing the viscosity of a liquid is undeniably one of the most essential parts of a liquid flowmeter calibration.

Viscosity measurements can be accomplished by using several methods, which vary in equipment cost and measurement time. The most widely used instruments for measuring viscosities are glass capillary (ASTM D445), rotational (ASTM D2983), and Stabinger (ASTM D7042 equivalent to D445) viscometers. The Stabinger high-precision viscometer requires clean filter fluid to achieve superior accuracy (see Figure 2).

Flow calibration facilities cannot, and do not, use customer-specific liquid for each calibration. Not only would this be extremely time-consuming and less than environmentally friendly, it would also be cost-prohibitive and possibly hazardous. Therefore, calibration facilities use a solvent/oil blend with a measured kinematic viscosity that matches the customer's fluid. This is based on the Reynolds number relationship (Reynolds number, or Re, is a dimensionless quantity used to help predict similar flow patterns in different fluid flow situations).

Re = (ρ x V x D)/µ

Where Re is the Reynolds number, ρ is density, D is the piper diameter, and µ is dynamic viscosity.

The fluid viscosity value in a positive displacement (PD) flowmeter calibrator is generated using a temperature/viscosity table, which is developed by inputting the actual kinematic viscosity value at two diverse temperature points. Temperature sensors, built into the calibrator piping, supply the actual fluid operating temperature used to extract the viscosity value from the temperature/viscosity table. A real-time fluid temperature and viscosity value is then recorded for each data point collected over the entire calibration flow range of the meter. It is worth noting that in a closed-loop calibration system, the fluid increases in temperature as it is continuously circulated through the piping.

Therefore, the precision of the calibration relies on the accuracy of:

• The initial fluid viscosity measurement as determined by a viscometer
• The accuracy of the fluid temperature measurements during the calibration.

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