# A correlation-based optical flowmeter for enclosed flows

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## Abstract

A low-cost flowmeter would be very useful in a wide variety of monitoring situations. This article discusses the development of such a flowmeter based on optical components and its testing with water in an enclosed flow system. The sensor consisted of two sets of LEDs and phototransistors spaced 4 cm apart, monitoring the optical properties of the fluid at upstream and downstream locations, respectively. A small amount of dye was injected into the flow, which caused a change in the optical properties of the fluid at both locations. The time required for this change to move from the upstream to the downstream locations was determined using the biased estimate of the cross-covariance between the upstream and downstream signals. The velocity was then calculated using this time difference and the known distance between the locations. Tests were conducted at fluid velocities from 0.125 to 4.5 m sˉ¹, and separate results were calculated using phototransistors located 45° and 180° from the LEDs. The mean percent error was between 5% and 0% for individual measurements using the 180° phototransistors at velocities from 0.5 to 4.5 m sˉ¹ and between 2% and -8% for measurements using the 45° phototransistors in the same velocity range. Error increased when the velocity was reduced to 0.5 m sˉ¹ and was greater than 20% at 0.125 m sˉ¹ for both sets of phototransistors. A regression model was developed to correct the velocity estimate. This regression model was validated by conducting an independent test of the sensor under the same conditions. After using the regression model for calibration, errors in the validation set were between 9.1% and -5% for the 180° phototransistors and between 10.5% and -3.6% for the 45° phototransistors for the entire velocity range tested (0.125 to 4.5 m sˉ¹). Finally, the cross-correlation coefficient for each measurement was calculated to determine the degree of similarity between the signals recorded by the phototransistors at the upstream and downstream locations. The cross-correlation coefficient was higher at lower velocities and higher for measurements using the 180° phototransistors.