In the realm of fluid mechanics, flow regimes characterize the distinct behaviors exhibited by fluids in motion. At one extreme, we encounter steady motion, a scenario where fluid velocity remains uniform at each point over time. This regime is often characterized by smooth, predictable trajectories. In contrast, turbulence introduces a state of di

Engineering design relies heavily on the principles and concepts of mathematics. Through fundamental calculations to complex simulations, mathematical models provide engineers with the tools to analyze, design, and optimize systems. A deep knowledge of mathematical principles is essential for solving engineering problems and constructing innovative