# Error Characteristic Analysis of Fluid Momentum Law Test Apparatus
## 1 Introduction  
Fluid mechanics is a basic science for studying fluid phenomena and related mechanical behaviors. Its application scopes cover aerospace engineering, mechanical engineering, power engineering, chemical engineering, biomedicine and other fields [1; 2; 3]. Fluid mechanics plays a broad and huge role in promoting scientific development, technological progress and industrial upgrading. The law of fluid momentum is one of the three basic laws of fluid mechanics as a basic theory explaining the relationship between fluid momentum change and force. The verification experiment of the law of constant flow of incompressible fluids, as the basic experiment to verify the theory of fluid momentum, is the core classic experiment of fluid mechanics [1; 4; 5]. The water jet impingement plate model method is a common experimental method to verify the law of fluid momentum. During the experiment, by changing the initial momentum of the jet, the force done on the plate and the momentum change of the jet were measured, and the momentum correction coefficient was solved to verify the law of conservation of momentum.  
The phenomenon of jet impacting on solids, as the physical basis of the momentum law verification experiment, is also a natural phenomenon widely existing in nature [6]. Analyzing the error characteristics of the momentum law verification experiment through the jet impact phenomenon will help improve the scientificity, accuracy and reliability of the error analysis, and provide a new path for the exploration of the error generation mechanism. Jet impact has a wide range of engineering application backgrounds, and its applications cover aerospace engineering, power engineering, mechanical engineering and mining engineering [7; 8; 9; 10]. The introduction of jet impact analysis into the fluid momentum law verification experiment will not only help improve the depth of momentum lawtheoretical research, but also play a significantly positive role for improving the engineering innovation and application expansion based on the law of momentum [11; 12; 13].  
Water jet impacting on a solid is a nonlinear dynamic process involving water hammer force, impact force (stagnation pressure), material deformation, damage and many other factors. It has the characteristics of large deformation, high strain rate, and transient processes that are difficult to observe and detect. [6; 10]. There are many researches on the theory and numerical calculation methods of water jet impact at home and abroad, but there are few studies on the specific impact process and error characteristics of the momentum law verification experiment based on the principle of water jet impact on a flat plate. The author and his team have studied the impact of water jet on a flat plate. A preliminary study on the action process of the model has been carried out, and the relevant experimental data on the condition of the initial momentum of the jet equal to 15.74 Kg-m/s is obtained. The analysis shows that the irregular vibration of the sensor in the non-jet direction is the main reason for the change of measurement error [14].  
This paper selects the momentum law experimental platform as the research object, establishes the numerical model of the water jet impingement momentum law experimental platform, uses the SPH-FEM coupling algorithm to analyze the jet impact on the plate, and obtains the jet load conditions at different speeds (different initial momentum). Based on the response characteristics of the sensor structure, the error characteristics of the momentum law experimental device are analyzed.