Flow

The study of fluids i.e liquids and gases and their flow is one of the most baffling concepts of mathematical physics. Studying the predicted flow pattern of fluids depends on a number of factors like its density, gravity, and internal viscosity etc. Certain assumptions also have to be made such as assuming the liquid is in-viscous or it does not have any internal friction, that it has laminar flow and it is not turbulent etc. Most liquids do not obey these Utopian rules though and hence it becomes difficult to predict their flow. A certain dimensionless quantity called 'Reynold's number' is used to guess the flow pattern of fluids and consists of its pressure and mainly its internal resistance. One of the most important pioneers of fluid dynamics is Bernoulli, whose principle states that the faster the fluid flows, the lower its pressure is at that point. Liquids and gases flow via streamlines and the closer streamlines are at a point, the faster the liquid flows. An application of this is the Venturi effect, by which a spray paint gun works. Since pressure is decreased at the constricted point of the gun, paint rises up and is sprayed to overcome the loss in pressure. One of the most confusing aspects of fluid dynamics is the famous Navier-Stokes equation which is one of the unsolved Millenium math problems. Mathematicians have yet to find one fluid, gas or liquid which satisfies the equation and its variables of vector calculus.