Flow, level & control


good this is forms the basis of all the performance claims. It is a figure rarely quoted other than by certified calibration houses. No calibration, even fully traceable ones, can be absolute as there is an uncertainty on every single measurement all the way back to the National Standards. The very best calibration houses claim an uncertainty of ±0.02 per cent but more typical is ±0.1 per cent. This is the base value on which all the other accuracy statements are founded. If the uncertainty here is ±0.2 per cent the flow meter cannot be specified as being more accurate than that, even if the repeatability and linearity are less than ±0.1 per cent, as the uncertainty of the calibration equipment and methodology is the overriding determinant.


Repeatability


Repeatability is the ability of a flow meter to give the same result on repeated runs with the same operating conditions. Titan’s small turbine flow meters are successfully employed in batching processes and dispensing applications particularly within the food and beverage, chemical and laboratory sectors, as they have excellent repeatability (±0.1 per cent). This is not to be confused with accuracy or


linearity. Without excellent repeatability, a turbine flow meter cannot achieve good performance. Normally, multiple points are taken at each calibration point to check the repeatability of the device although these are not always reported on the calibration certificate. A highly repeatable flow meter that can be calibrated in-situ is ideal for batching applications where any process offset can also be reliably accounted for.


accuRacy


Accuracy is the term used to specify the true reading of an instrument (high accuracy), or indeed the deviation from the absolute truth (low accuracy). Accuracy is generally used as a qualitative term, giving an indication of the quality of the instrument. The accuracy figure stated should include linearity, repeatability and calibration uncertainty. The following images illustrate the relationship between repeatability and accuracy:


FSD lineaRity


This meter shows a reasonable reading. Plotted in this form (Figure 1) the indicated flow versus the actual flow shows almost a straight line. The meter is specified as ±2 per cent of full-scale accuracy with a full-scale range of 100 l/min. So a ±2 litre per minute tolerance applies over the whole operating range, even minimum flow. If the number of pulses per litre for the same meter is plotted against the flow rate a different story becomes clear (Figure 2).


maximum acceptable limit at full flow but drops outside the ±2 per cent of reading specification at around 17 litres per minute. A typical calibration graph (Figure 5) issued by


a manufacturer would normally show the permissible errors over the flow range. In this case the meter specification is zero to one l/min, ±0.5 per cent of reading. In practice, this meter exceeds the specification having a linearity of +0.28 per cent – 0.1 per cent and a repeatability of better than ±0.1 per cent.


Using the same meter, the plot in Figure 2


illustrates the increased error of reading at low flow rates. We can liken a ±1 per cent FSD specification to using an indicator with only 0-100 resolution digital display. All of the readings are in one unit steps so at full flow the meter is measuring ±1 litre per minute. The same is true at 1 litre per minute which could be zero or two, i.e. ±1 l/min equivalent to one per cent FSD linearity. One litre per minute accuracy at both 100 or 1 l/min. Although a 100:1 flow range and a 1 per cent FSD linearity is not normally claimed, this example provides a good illustration of the potential problem. Even a 10:1 flow range with one per cent FSD would give a 10 per cent permissible error at the specified minimum flow i.e. 10 l/min ±1 l/min.


This indicator analogy also demonstrates the lineaRity


Linearity is usually defined by stating the maximum deviation of the reading over a stated range (e.g. ±1 per cent of flow rate). It is the ability of the flow meter to remain within specified limits over its entire flow range determined by its design. The standard way of expressing linearity is


error of reading. A frequently used alternative in some industry sectors is percentage of full-scale deflection or FSD. The following charts illustrate examples of FSD and of reading linearity.


Instrumentation Monthly October 2021


importance of associated instrumentation and displays which is not discussed here.


OF ReaDing lineaRity


The graph plotted in Figure 3 uses the same flowmeter data as the FSD illustration above. In this case the error lines are shown as a percentage of reading. It is clear that the example flowmeter “drops out” of the required accuracy between 10 and 20 l/min for an of reading accuracy of ±2 per cent. The graph in Figure 4 better illustrates the


true situation with the same flowmeter used in Figure 1. The flow meter is close to the


cOncluSiOn


Whereas turbine flow meters, such as Titan’s Beverage flow meter and 800 series, offer the high level of repeatability and reliability required for accurate batch delivery systems, the Atrato and Metraflow ultrasonic flow sensors and the larger oval gear flow meters are highly accurate over wider flow ranges, especially with viscous liquids such as oils. Neil Hannay, senior R&D engineer at Titan


Enterprises, suggests: “When customers are deciding on appropriate flow meters to suit their application, they need to be aware of the difference between FSD and ‘of reading’ accuracy as often suppliers do not specify which accuracy is being quoted for. As discussed here, linearity reading has a significant impact on the flowmeter performance, particularly at the low end of its flow range.”


Titan Enterprises www.flowmeters.co.uk 23


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