# Research Progress and Engineering Applications of Viscous Fluid Mechanics
## 3 Application Areas of Engineering  
The theory of viscous fluid dynamics (or simply viscous fluid theory) plays a crucial role in the field of engineering. The theory not only provides engineers with tools to deeply understand and predict the behavior of various fluids but also directly contributes to the development of several industries in design, optimization, and innovation. In aerospace engineering, the theory of viscous hydrodynamics is of crucial importance for designing the aerodynamic shape of aircraft and optimizing airfoils [114, 115]. Through the in-depth study of viscous fluid dynamics, engineers are able to gain a deep understanding of aerodynamic effects such as aerodynamic drag and lift generation mechanisms. This knowledge helps to optimize the aerodynamic shape of the vehicle, reduce drag, improve flight efficiency, reduce fuel consumption, and thus extend range [116, 117, 118]. In automotive engineering, viscous fluid dynamics theory is widely used to improve the aerodynamic performance of vehicles. By gaining a deeper understanding of the complexity of air flow during vehicle operation, engineers can design and optimize body shapes, mirrors, and other streamlined components to reduce air resistance and improve the fuel efficiency and driving stability of vehicles [119, 120]. In marine engineering, the theory of viscous hydrodynamics is used to study the hydrodynamic performance of marine structures (e.g., platforms, buoys, etc.). By analyzing the motion characteristics of water flow on the surface of structures, engineers can optimize the design to improve the stability and wind and wave resistance of the structures to ensure that they can operate safely in extreme marine environments [121, 122, 123]. In the oil, gas, and chemical industries, the theory of viscous fluid mechanics plays an important role in the design and optimization of piping systems. Engineers need to have an in-depth understanding of the flow characteristics of fluids within pipelines to minimize energy loss, control pressure drops, avoid pipeline clogging, and ensure the stable and efficient transportation of fluids [124, 125, 126]. In biomedical engineering, the theory of viscous fluid dynamics is important for studying the flow of blood in the cardiovascular system. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**Precision of**} & \multirow{2}{*}{**Visualization**} & \multirow{2}{*}{**Time Cost**} & **Complexity** \\  & **Mathematical Results** & & & **Adaptability** \\ \hline Arithmetic & High & Mediocre & Relatively low & Low \\ Emulate & Relatively low & First-rate & High & High \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparative table of advantages and limitations of algorithms and simulations. For example, in the simulation model of heart valves, viscous fluid dynamics can simulate the flow of blood over the valves and evaluate the hydrodynamic properties of the valves when they open and close, which can help optimize the design and surgical plan of artificial heart valves [127; 128; 129]. In industrial production, the theory of viscous hydrodynamics is used to improve the efficiency and quality of coating technology and printing engineering. By precisely controlling the droplet impaction, expansion, and drying processes, engineers can improve the uniformity and durability of coatings, which in turn affects the final quality and appearance of the product. This theory has a wide range of applications in fields such as electronics and packaging materials [130; 131]. In environmental engineering, the theory of viscous hydrodynamics is applied to the design of wastewater treatment systems and water management programs. Through a deeper understanding of the complex behavior of water flow in the treatment process, engineers can optimize the design of treatment facilities, improve the treatment efficiency, and reduce the impact on the environment, thus protecting water resources and the ecological environment [132; 133; 134].