Indirect measurement of the flow rate based upon a solution of an inverse coefficient problem

Purpose The purpose of this paper is to extend the possibilities of using the earlier developed indirect method of fluid flow rate measurement in circular pipes to the square-section channels with elbows installed. Design/methodology/approach The idea of the method is based on selecting such a value of the Reynolds number assumed as a coefficient in fluid flow equations, which fulfills with set accuracy the condition of equality between the measured and computed pressure difference at the end points of the secant of the elbow arch. The numerical calculus takes into consideration the exact geometry of the flow space and the measured temperature of the fluid, on the basis of which its thermo–physical properties are determined. To implement the proposed method in practice, a special test stand was built. The numerical computations were carried out using the software package FLUENT. Findings The results of calculations were compared with corresponding results of measurements achieved on the stand, as well as those found in the literature. The comparative analysis of the obtained numerical and experimental results shows a high grade of consistence. Practical implications The discussed elbow flow meter, implementing the extended indirect measuring method, can be applied to determine the flow rate of gases, as well as liquids and suspensions. Originality/value The indirect method used to measure the volumetric flow rate of the fluid is characterized by high accuracy and repeatability. The high accuracy is possible because of a very realistic mathematical model of the complex flow in the curved duct. The indirect method eliminates the necessity of frequent calibration of the flow meter. The discussed extended indirect measuring method can be applied to determine the flow rate of gases as well as liquids and suspensions. The fluid flow rate measurement based on the method considered in this paper can be particularly useful in newly designed as well as already operated ducts.