The special effects are meant to give the viewer a realistic look at the motion of water or air. We have all seen special effects and visualizations of fluids in movies. Let’s first start with understanding these equations. We would now call such swirling motions vortices, and we have a systematic way of understanding the behavior of fluids through the Navier–Stokes equations. He often observed that water had a swirling motion, sometimes big and sometimes small, as shown in the sketch below. Leonardo da Vinci made several sketches of the motion of fluid and made a number of observations about how water and air behave. The motion of fluid flow has captured the interest of philosophers and scientists for a long time.
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