MATH3072
Advanced Fluid Dynamics
Modelling fluid flow requires us first to extend vector calculus to include volumes that change with time. This will allow us to rephrase Newton’s second law of motion, that the force is equal to the time derivative of the linear momentum, in a way that can be applied to materials that flow and do not have a constant shape, i.e. to fluids. The final resulting equations are called the Navier-Stokes equations and are at the foundation of all fluid studies, from the microscopic motion of a bacterium to the hypersonic flow around a missile. In this module we will just touch on the simplest of the cases model by them: exact solutions of steady flows, water in a sloping channel, or of time dependent flows, driven by pulsating pressure (like blood flow). We will conclude by studying one of the most intriguing aspects of fluid dynamics, namely surface tension, the phenomenon responsible for the round shape of rain drops or soap bubbles. We will study its physical origin and how to model it in the context of the Navier-Stokes equations; we will finish by considering some fluid configurations where surface tension plays a dominant role (e.g. the capillary effect and soap bubbles).
