We introduce solutions to the diffusion equation (Fick’s second law), which arises from Fick’s first law and continuity. Diffusion into semi-infinite half spaces as well as problems in finite spaces and the approach to equilibrium are addressed and solutions are given. The second part of the chapter describes fundamental, atomic scale aspects of diffusion in the solid state.

The powerful methods of dimensional analysis are introduced via the pi-theorem. The reader discovers that many of the results obtained in Chapters 3 and 4 can be arrived at using dimensional analysis alone. These include drag and pipe flow. Dynamical similarity is explained.

In this chapter we study the idealised, inviscid fluid. The central formula is Bernoulli’s equation, and its consequences are explored in a number of examples. Next we look at flow which is irrotational (vortex free) and develop potential theory, which in two dimensions can be treated very elegantly using complex analysis and the Cauchy–Riemann equations.

This chapter is mostly about solid mechanics: Cauchy stress, finite and infinitesimal strain, rotation. Velocity and acceleration are developed in both inertial and non-inertial fames. This is central to the education of the physicist and engineer, but the development leads to a derivation of the Navier–Stokes equations, which are central to fluid dynamics.

The equations of fluid dynamics and energy balance are arrived at from the starting point of the powerful Reynolds transport theorem. After writing down the four conservation laws – mass, energy, linear and angular momentum – their consequences when inserted into the transport equation are revealed, in particular Cauchy’s equations of motion, Navier–Stokes equations and the equation of energy balance. A number of prevalent examples are given, including Stokes’s formulae and the Darcy law. The chapter concludes with the theory of the boundary layer.

Here we begin fluid dynamics with the science of fluids at rest. This includes planetary science aspects of atmospheric and oceanic pressure, the forced and free vortex. Here also are introduced the three basic differential operators: grad, div and curl, which will be used throughout the book.

Heat transfer by conduction, convection and radiation are given a brief treatment. The connection with the previous chapter is emphasised since both involve the ‘heat equation’. The application of boundary conditions to the one-dimensional heat dissipation in a slab is presented. This chapter makes contact with Chapter 4 through a discussion of heat transfer across the boundary layer.

An introduction to the broad subject with a graphical outline of the fundamental equations to be encountered is presented. The reader is informed of any necessary mathematical prerequisites and the structure of the notation to be used is explained.

This chapter puts together fluid mechanics and heat and mass flow to describe chemical and materials processing in which diffusion and convection are combined. After setting up the central equations, special cases are introduced which can be described by equations in closed form; solutions are given.

In Chapter 2 the evolution of ship structures from the prehistoric period up to the present day is described. The aim of this chapter is to bring together the results of underwater archaeology with that of documents, images and models in order to underline the important stages in the evolution of waterborne craft, focusing on structural design and construction practice. The discussion concerning the prehistoric period deals mainly with Egypt and Greece. Fabrication methods used in antiquity are discussed (laced ships, mortise-and-tenon joint). A section is devoted to ship construction in Greece during the historical period (trieris and later ship types). This is followed by descriptions of ships built during the later Roman period and Byzantium covering the first ten centuries of the Christian era. Ship construction practice in Venice is discussed, followed by a discussion of ship construction in China. Evolution of ships in Western Europe included several ship types (cog, hulk, carrack, caravel and galleon). The impact of the introduction of iron and internal combustion engines is discussed. Theoretical developments in mechanics of materials and elasticity theory are discussed in relation to the practice of ship structural design during the 19th century and the first half of the 20th century. The chapter ends with a discussion of computer-based techniques and the introduction of reliability theory.

In this chapter the use of the finite element method in hull girder analysis and design is described. Quasi-static and vibration analysis of the hull girder are considered. The use of approximate simplified quasi-static analysis and of linear elastic finite element analysis using both 2D and 3D models are discussed. The implementation of FE models to the residual and ultimate strength is described and various approaches compared. FE models used in vibration response are considered and the matrix equations of dynamic equilibrium given. Free vibration and forced vibration response are discussed and vibration modes resulting from main engine excitation described. Rule requirements for the implementation of the FEM are discussed. The rational design of the hull girder using a classification society approach is described. Finite element codes used in ship structural analysis and design are mentioned and their capabilities compared. Two case studies are described in detail. The first of these concerns the use of nonlinear elasto-plastic analysis to determine the ultimate strength of a bulk carrier in the alternate hold loading condition. The second study presents a comparison of the dynamic response of single and double-skin bulk carriers involved in a collision incident.

This chapter provides an introduction to ship structures and includes descriptions of structural arrangements of the most important types of merchant ships and the properties of the materials used. This is followed by a discussion of the need to consider ship structures at different levels of analysis (top-down approach). The role of structural modelling, and in particular modelling applicable to global strength, is described. In the second part of the chapter an overview of current practice in ship structural design is presented, in which similarities between merchant and warship structural design are highlighted. The role of classification societies is described as well as that of the IMO Goal-Based-Standards. A comparison of classification society rules follows. The role of computer-based techniques is discussed. In the last section recommendations for good practice in ship structural design are provided.