Unit 6 Bernoulli’s equation analyses an important equation arising from integrals of Euler’s equation for the flow of an inviscid fluid.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.The second block 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 4 Vector field theory relates line, surface and volume integrals through two important theorems – Gauss’ theorem and Stokes’ theorem – and formulates the equation of mass continuity for a fluid in motion.Unit 3 First-order partial differential equations extends the earlier version of the Chain Rule to cover a change of variables for functions of two variables, and shows how this leads to the method of characteristics for solving first-order partial differential equations.It concludes with an introduction to the method of power-series for solving initial-value problems. Unit 2 Ordinary differential equations starts by showing how changes of variables (involving use of the Chain Rule) can be applied to solve certain non-constant-coefficient differential equations, and leads on to the topics of boundary-value and eigenvalue problems.The basic equation of fluid statics is formulated and used to find the pressure distribution in a liquid and to provide a model for the atmosphere. Unit 1 Properties of a fluid introduces the continuum model and many of the properties of a fluid, such as density, pressure and viscosity.This is the foundation on which the rest of the module is built. The module is arranged in 13 units within four blocks. Fluid mechanics is essential to the meteorologist in studying the complicated flow patterns in the atmosphere. The flow of fluids through pipes and channels is also important to engineers. The flow of air over objects is of fundamental importance to the aerodynamicist in the design of aeroplanes and to the motor industry in the design of cars with drag-reducing profiles. The mathematical methods arise from (and are interpreted in) the context of fluid-flow problems, although they can also be applied in other areas such as electromagnetism and the mechanics of solids.īecause of its many applications, fluid mechanics is important for applied mathematicians, scientists and engineers. This module introduces the fundamentals of fluid mechanics and discusses the solutions of fluid-flow problems that are modelled by differential equations. The analysis of the forces in and motion of liquids and gases is called fluid mechanics. Familiar examples are air (a gas) and water (a liquid). In simple terms, we think of a fluid as a substance that flows.

Fluid mechanics example problems