Mathematical Methods and Fluid Mechanics - Block 2

Block 2 again contains a further 4 units and starts by investigating the motion of a fluid that is assumed to be incompressible (its volume cannot be reduced) and inviscid (there is no internal friction). Unit 5 - Kinematics of fluids introduces the equations of streamlines and pathlines, develops the concept of a stream function as a method of describing fluid flows, and formulates Euler s equation of motion for an inviscid fluid. Unit 6 - Bernoulli's equation analyses an important equation arising from integrals of Euler s equation for the flow of an inviscid fluid. It relates pressure, speed and potential energy, and is presented in various forms. Bernoulli s equation is used to investigate phenomena such as flows through pipes and apertures, through channels and over weirs. Unit 7 - Vorticity discusses two important mathematical tools for modelling fluid flow, the vorticity vector (describing local angular velocity) and circulation. The effects of viscosity on the flow of a real (viscous) fluid past an obstacle are described. Unit 8 - The flow of a viscous fluid establishes the Navier-Stokes equations of motion for a viscous fluid, and investigates some of their exact solutions and some of the simplifications that can be made by applying dimensional arguments.