# An Explanation of the Term Linearity

Continuing in our objective to describe flow meter terms to provide a better understanding of commercialized language, we have decided to attempt an explanation of linearity. The flowmeter’s ability to remain within its defined limits over the entire specified flow range is its linearity. The standard technique of expressing the term linearity is known as “of reading,” which can further be defined as is the expression of the percentage error within the meter’s operating range. In some sections of the industry, alternative definitions are also used, such as FSD linearity or Full Scale Deviation”.

Looking at the flow meter chart to the right, you can see that the actual flow versus the plot of the indicated flow is almost a straight line, which shows that the linearity of this device looks good. Because the flowmeter is indicated as ±2% of full scale accuracy, a ±2 liter per minute tolerance applies over minimum flow as well as over the whole operating range. A different picture of the device’s linearity is evident if we plot the number of pulses per liter for the flow rate.

What does a specification of ±2% FSD mean? It means that, at full flow of 100 liters per minute (lpm), there is a ±2 lpm error, as well as a ±2 lpm error at a lower flow of 50 lpm and 10 lpm. The actual flow rate at these lower points can be between 48 and 52 lpm or 8 and 12 lpm, respectively. This comes down to an error of ±4% at 50 lpm and a massive ±20% at 10 lpm, not to mention the error at 1 lpm. That is comparable to an analogue pressure gauge reading of 1 psi pressure on a 100 psi full scale. However, while this is a good illustration of a potential problem, most people will not normally claim a turn down ratio of 100:1 and 2% FSD linearity. In reality, at the specified minimum flow, a turn down ratio of 10:1 with a 2% FSD would give a 20% permissible error.

In the above demonstrations, we can compare the same flowmeter data in a standard “of reading” linearity plot. The error lines in this linearity graph are shown as the percentage of reading. Although it may be difficult to see, the black dashed line intersects the solid red lower limit line, indicating that the flowmeter “drops out” of the required accuracy at lower flows. The graph, which specifies the linearity percentage of the reading, better illustrates the true situation when the K-factor (number of pulses per liter) is plotted against the flow rate. While close to the maximum acceptable limit at full flow, the meter drops outside the ±2% reading specification when it falls around 20 liters per minute.

Hopefully, this explanation has brought a greater level of understanding to all of our readers. If not, feel free to ask us any questions you may still have.

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