_applied sciences_  
_Article_  
**Force Measurement with a Strain Gauge Subjected to Pure**  
**Bending in the Fluid-Wall Interaction of Open Water Channels**  
**[PERSON] 1,2, [PERSON] 3\({}^{\copyright}\) and [PERSON] 1,4\({}^{\copyright}\)**  
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stress is difficult to derive from the bulk flow characteristics, such as applying predefined velocity profiles or the shear stress distribution. Currently, there is a wide range of methods for direct and indirect measurement of shear stress in open channels. However, direct measurements of shear stress in the wall-fluid interface are less frequent. [PERSON] et al. [4] classify intrusive approaches (acoustic Doppler velocimeters, optical backscatter sensors, ultrasonic velocity profilers, and acoustic Doppler current profilers) and non-intrusive techniques (laser-induced fluorescence, particle image velocimetry, and laser Doppler velocimetry) to detect the magnitude of the flow disturbance by the experimental probe itself. Detailed reviews about methods to measure and estimate shear stress can be found in [PERSON] et al. [5]. Experimental setups range from large-scale measurements (e.g., [PERSON] et al. [6]) to highly controlled laboratory-based experiments (e.g., [PERSON] et al. [7] and [PERSON] et al. [8]). The direct measurement of shear stress requires sensitivity to small changes in flow velocity, generates minimal flow disturbance, especially in the vicinity of the bed, and maintains the principle of no sliding of the material in the bed [9; 10; 11]. The development of microsystems, nanotechnology, fluid dynamics, aerodynamics, biotechnology, and biomedical technology, among others, involves the application of devices suitable to measure forces from the force scale of millinewtons (mN) to micronewtons (\(\mu\)N). On one side, microelectromechanical sensors (MEMS) such as systems based on interferometry, oil films, and liquid crystal coatings have shown improvements in performance and accuracy relative to conventional techniques (hybrid MEMS) and have been used to measure skin friction [12]. On the other hand, multidimensional F/M MEMS are used to measure force and moment in robotics, electronics, and the development of medical equipment and smart devices [1]. The techniques employed for these measurements can be direct or indirect [13; 14]. Despite the usefulness of these sophisticated devices to measure forces induced by external loads, they are limited by their complex calibration and testing procedures, which are not sufficiently structured because of the miniaturization of sensors [12; 13; 14; 15; 16]. Electrical resistance strain gauges are one of the simplest and most frequently used passive transducers. They are usually bonded to one of the surfaces of the specimen to be tested to generate only axial tension and compression. They have been used as load or strain transducers of sophisticated devices since their manufacturing technology and encapsulation prevent them from suffering mechanical and environmental damage. Due to their small size, sensitivity, accuracy, simplicity, and low cost compared to sophisticated devices, strain gauges are broadly used in laboratories worldwide as sensing devices [16]. Nonetheless, no research has been found that explores the operating principle of strain gauges subjected to pure bending. This is because the bending effect is considered negligible concerning the tension-compression effect. In the fields of fluid dynamics and aerodynamics, the measurement of small forces involved in the fluid-wall interaction is required to analyze the stability of walls and fluids. Consequently, there is a lack of simple devices for measuring forces of small magnitude, in the order of mN, that can be employed to measure flows of water in open and closed systems.