Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you will be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures, surface waves, and floating bodies in waves. Real-life applications are discussed and end-of-chapter problems help ensure full understanding. Students and practicing engineers will find this book an invaluable resource for developing problem-solving and design skills in a challenging ocean environment through the use of engineering mathematics.

Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you will be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures, surface waves, and floating bodies in waves. Real-life applications are discussed and end-of-chapter problems help ensure full understanding. Students and practicing engineers will find this book an invaluable resource for developing problem-solving and design skills in a challenging ocean environment through the use of engineering mathematics.

Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you will be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures, surface waves, and floating bodies in waves. Real-life applications are discussed and end-of-chapter problems help ensure full understanding. Students and practicing engineers will find this book an invaluable resource for developing problem-solving and design skills in a challenging ocean environment through the use of engineering mathematics.

Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you will be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures, surface waves, and floating bodies in waves. Real-life applications are discussed and end-of-chapter problems help ensure full understanding. Students and practicing engineers will find this book an invaluable resource for developing problem-solving and design skills in a challenging ocean environment through the use of engineering mathematics.

Gaining expertise in marine floating systems typically requires access to multiple resources to obtain the knowledge required, but this book fills the long-felt need for a single cohesive source that brings together the mathematical methods and dynamic analysis techniques required for a meaningful analysis, primarily, of large and small bodies in oceans. You will be introduced to fundamentals such as vector calculus, Fourier analysis, and ordinary and partial differential equations. Then you will be taken through dimensional analysis of marine systems, viscous and inviscid flow around structures, surface waves, and floating bodies in waves. Real-life applications are discussed and end-of-chapter problems help ensure full understanding. Students and practicing engineers will find this book an invaluable resource for developing problem-solving and design skills in a challenging ocean environment through the use of engineering mathematics.

This chapter introduces influence of density change on a flow, i.e., the compressible flow theory. Strictly speaking, any gas flow is both viscous and compressible. In tradition the influence of viscosity and compressibility are dealt with separately to make things easy. In this book, the chapter 6 deals with viscosity, and the chapter 7 deals with compressibility. Sound speed and Mach number are introduced in the beginning, then the equations for steady isentropic flow are derived with statics and total parameters introduced. Some gas dynamic functions are derived that use coefficient of velocity in replace of Mach number. Propagation mode of pressure waves are discussed next, and expansion and compression waves are introduced. Shock wave, as a strong compression wave, is discussed in depth. In the end, transonic and supersonic flow in a variable cross-section pipe is discussed, especially the characteristics of the flow in a Laval nozzle.

In this chapter, basic concepts in fluid mechanics are introduced. Firstly, the definition of a fluid is discussed in depth with the conclusion that a fluid is such a substance that cannot generate internal shear stresses by static deformation alone. Secondly, some important properties of fluids are discussed, which includes viscosity of fluids, surface tension of liquids, equation of state for gases, compressibility of gases, and thermal conductivity of gases. Lastly, some important concepts in fluid mechanics are discussed, which includes the concept of continuum and forces in a fluid. Within these discussions, fluid is compared to solid in both microscopic and macroscopic to reveal the mechanism of its mechanical property. Viscosity of fluid is compared to friction and elasticity of solid to give readers a better idea how it works microscopically. Forces is classified as body force and surface force for further analysis. Finally, continuum hypothesis is introduced to deem the fluid as continuously separable, which tells the reader that fluid mechanics is a kind of macroscopic mechanics that conforms Newtonian mechanics and thermodynamics.

In this chapter, the basic equations of fluid dynamics are derived and their physical significances are discussed in depth and in examples. Both integral and differential forms of the continuity equation, momentum equation, and energy equation are derived. In addition, Bernoulli’s equation, angular momentum equation, enthalpy equation and entropy equation are also introduced. Finally, several analytical solutions of these governing equations are shown, and the mathematical properties of the equations are discussed. Besides the fundamental equations, some important concepts are explained in this chapter, such as the shaft work in integral energy equation and its origin in differential equations, the viscous dissipation term in the differential energy equation and its relation with stress and deformation, and the method to increase total enthalpy of a fluid isentropically.

This chapter introduces the description of fluid motion, that is, the fluid kinematics. At first, the Lagrangian and Eulerian method is compared to emphasize that most problems in fluid mechanics is more suitable for Eulerian method. Secondly, the concepts of pathlines and streamlines are introduced. Next, Acceleration equation and substantial derivative are derived in Eulerian coordinates and their physical significance is discussed in depth and in examples. Reynolds transport theorem is then introduced and compared with substantial derivative to demonstrate that they are the same relation in integral and differential form respectively. Deformation of a finite fluid element is discussed in the next. Linear deformation, rotation, angular deformation equations are derived individually with equations and illustrations. These knowledges are the key to derive the differential equations of a flow, which will be introduced in chapter 4.

In this chapter, twenty-five carefully selected flow-related phenomena are analyzed, with the purpose of consolidating the understanding of the subject and strengthening the ability to link theory with practice. These flow phenomena include some interesting examples such as the principle of lift, the thrust of a water rocket, the mechanism of a faucet et al. Another type of the examples includes those with controversial explains in some popular science books or websites, such as the pressure of jet flow, the pressure change by a passing train, the reason why the water does not spill when a cup is upside-down et al.