This chapter introduces the mechanical property of a fluid when it is at rest. In the absence of shear force, fluid is balanced between pressure force and body force. A universal differential equation is derived to describe the pressure distribution in a static fluid. This equation, can be called hydrostatic equilibrium equation, is the key to solve any fluid static problems. Two typical situations are then discussed as applications of the hydrostatic equilibrium equation, one is static fluid under the action of gravity, the other is fluid under the action of inertial forces. Differences and similarities of fluids and solids in the transfer of force are discussed in the end. Atmospheric pressure at different heights is calculated in the “Expanded Knowledge” section.

This chapter briefly introduces the application of similarity theory and dimensional analysis in fluid mechanics. The concept of flow similarity is discussed at first to give the readers a brief idea what similarity means. Then some important dimensionless number is listed and discussed, which includes Reynolds number, Mach number, Strouhal number, Froude number, Euler number and Weber number. Next, the governing equations are transformed to a dimensionless form to shows how the dimensionless numbers act in the equations. In the end, some flow examples are provided to show the role of the dimensionless numbers.

In this chapter, viscous flow is discussed in detail. This kind of flow represents the most common flow in daily life and industrial production. Firstly, shearing motion and flow patterns of viscous Fluids is introduced, characteristics of laminar flow and turbulent flow is discussed. Secondly, Prandtl’s boundary-layer theory is introduced and boundary-layer equation is derived from the Navier-Stokes equation through dimensional analysis. Thirdly, some theory and facts for turbulent boundary layer are introduced. Fourthly, some shear flows other than boundary layer flow, such as pipe flow, jets, and wakes are briefly introduced. Boundary layer separation is the most important issue in engineering design, so it is introduced and discussed in a separate section in depth. The two top concerns, namely the flow drag and the flow losses are discussed in a separate section with examples and illustrations. Some further knowledge concerning turbulent flow is briefly discussed in the “expanded knowledge” section, such as the theory of homogeneous isotropic turbulent flow and the numerical computation of turbulent flows.

This chapter introduces inviscid flow and potential flow method. Characteristics of inviscid flow is introduced and the rationality of neglecting viscosity in many actual flow cases is discussed. Then the characteristics of rotational flow for inviscid flow is discussed. The three factors that may cause a fluid to change from irrotational to rotational are enumerated and explained, namely the viscous force, baroclinic flow, and non-conservative body force. For irrotational flow, velocity potential is introduced and several elementary flows are taken as an example to illustrate the computational methods for planar potential flow theory. In the end, complex potential is briefly introduced.

The chapter describes results of measurements during several ship trials, in which instrumented vessels were used to interact with ice. The main focus is the measurement of local ice pressures by strain-gauging of the ship hull. The results include ramming of ice features. A variety of results are analysed, including those from the Kigoriak, Polar Sea, Louis S. St.-Laurent, Oden, and Terry Fox. Analyses of high-pressure zones are presented and a novel method (the alpha-method) is presented for local design of vessels and structures.

The chapter commences with a description of various observations of time-dependent fractures in ice. In the medium scale tests, slow loading resulted in very large flaws, whereas fast loading resulted in many small fractures and spalls in the vicinity of the load application. Then, a summary of fracture toughness measurements on ice are summarized. The question of stress singularity at crack tips is raised, and to deal with this, Barenblatt’s analysis is introduced, based on linear elasticity. Schapery’s linear viscoelastic solution for this method is described, using the elastic-viscoelastic correspondence principle. The J integral forms the basis of the application to fracture, using the correspondence principle noted. A set of experiments on ice samples, beams with 4-point loading, was conducted. Tests with a range of loading rates, as well as constant-load tests, were conducted. Comparison of the results with theory was made. The results of Liu and Miller using the compact tension set-up were also considered. Good agreement with theory was found in all cases. Nonlinear viscoelastic theory of Schapery is also outlined.

The analysis of ice response to stress using finite elements is described, using multiaxial constitutive relationships, including damage, in a viscoelastic framework. The U-shaped relationship of compliance with pressure is part of this formulation. The results show that the layer of damaged ice adjacent to the indentor arises naturally through the formulation, giving rise to a peak load and subsequent decline. This shows that there can be “layer failure” in addition to failure due to fractures and spalling. Tests on extrusion of crushed ice are described together with a formulation of constitutive relationships based on special triaxial tests of crushed ice. The ice temperature measured during field indentation tests showed a drop in temperature during the upswings in load. This was attributed to localized pressure melting. Small scale indentor tests are described, which show clearly the difference between layer failure and spalling, as found using high-speed video and pressure-sensitive film. The question of scaling, as used in ice tanks, is addressed. Flexural failure can be scaled to some extent; scaling of high-pressure zones lies in the mechanics as developed in the book.

Viscoelastic theory is introduced, using ice as the material under consideration. Linear theory is first introduced, based on elasticity of the springs and on linear viscosity of the dashpots. The nonlinearity of the dashpots in modelling ice deformation is then introduced. The “crushed layer” and analysis by Kheisin and co-workers is outlined, based on linearly viscous modelling. Kelvin and Burgers models are introduced. Microstructural change is modelled using damage mechanics and state variables for material points. Stress and strain re-distribution arises from this aspect, as well as from nonlinearity with stress. Schaperys modified superposition principle is introduced.

Recent observations are summarized, in which it has been found that in compressive ice failure, zones of high-pressure form with pressures locally as high as 70 MPa. Various aspects of ice behaviour are summarized: creep, fracture, recrystallization, and the development of microstructurally modified layers of ice. Pressure melting is described, whereby the melting temperature decreases with accompanying hydrostatic pressure. The importance of fracture and spalling in the development of high-pressure zones is emphasized. The use of mechanics in analysis of ice failure is discussed.