How closely do most of us follow the normative model when we make probability judgments? Until the late 1960s, it was thought that even people with little experience did reasonably well at it intuitively (Peterson & Beach, 1967). Since then, psychologists have found that we do poorly at making probability judgments – in systematic ways. It is not just that our judgments are erroneous. Our judgments are erroneous because we attend to variables that we should ignore and ignore variables to which we should attend.

Turbomachines are the heart of all production jet engines and power generation gas turbines. This book discusses six basic types of turbomachines directly: axial flow compressors, axial flow pumps, radial flow compressors, centrifugal pumps, axial flow gas turbines, and axial flow hydraulic turbines. Two other basic types that are used in practice are not covered in this text because of their limited application in propulsion and power generation: radial inflow gas turbines and radial inflow hydraulic turbines. The basic derivations of the equations for each machine type are covered in this chapter rather than in the chapters in which the machines are discussed. As will be shown, the resulting fundamental equations apply to all types of turbomachines, regardless of categorization. Application of the equations with complementing internal velocity information is, however, different for the different turbomachines. Advanced details can be found in texts, including Stodola (1927), Howell (1945a, 1945b), Shepherd (1956), Vavra (1974), Dixon (1975, 1998), Osborn (1977), Balje (1981), Whittle (1981), Wallis (1983), Turton (1984), Hill and Peterson (1992), Logan (1993), Japikse and Baines (1994), Cohen et al. (1996), Hah (1997), and Wilson and Korakianitis (2014). Cumpsty and Greitzer (2004) present an interesting review of turbomachinery development. Furthermore, Denton and Dawes (1998), Elmendorf et al. (1998), LeJambre et al. (1998), Rhie et al. (1998), Adamczyk (2000), and Denton (2010) show how modern computational fluid dynamic (CFD) tools can effectively be used for the complex 3-D analysis and design of turbomachines and also cover some of the limitations. In the following three chapters the equations developed in this chapter will be used to find the operating characteristics of compressors and turbines.

The purposes of the diffuser or inlet are first to bring air smoothly into the gas turbine. Second, for a propulsion diffuser to slow the fluid and to increase the pressure, or for a power generation inlet to increase the fluid speed and to decrease the pressure. And third, to deliver a uniform flow to the compressor. As indicated by studies for cycle analyses in Chapter 3, gas turbine performance improves with increasing pressure to the burner. The first component the air encounters is the diffuser or inlet, and the second component is the compressor. Thus, if the diffuser or inlet incurs a large total pressure loss, the total pressure into the burner will be reduced by the compressor total pressure ratio times this loss. For example, if 2 psia are lost in the diffuser or inlet, for a large engine this can result in 50 psia less in the burner.

As discussed in Chapters 1–4, the purpose of the turbine is to extract energy from the fluid to drive the compressive devices. The actual operation of the turbine is in some respects similar to, but opposite that, of the compressor. That is, energy is extracted from the fluid and the pressure and temperature drop through the turbine. Typically, 70–80 percent of the enthalpy increase from the burner is used by the turbine to drive the compressor. For jet propulsion the remainder is used to generate thrust in the nozzle, while for a power generation unit the remainder is used to generate auxiliary power.

Part II was concerned with thinking about beliefs. Part III is about decision making, the thinking we do when we choose an action, including both the decisions that affect only the decision maker and the decisions that affect others, that is, decisions that raise moral questions. We shall also examine long-term planning, with special emphasis on the choice of personal goals. Part III is concerned mostly with inference rather than search – in particular, with how we infer a course of action from our goals and from evidence concerning the consequences of our options for achieving them.

Thinking is important to all of us in our daily lives. The way we think affects the way we plan our lives, the personal goals we choose, and the decisions we make. Good thinking is therefore not something that is forced upon us in school: It is something that we all want to do, and want others to do, to achieve our goals and theirs.

A promising approach to the problem of measuring utility and making difficult decisions is that of multiattribute utility theory (MAUT). The idea is to separate utility into attributes. Ideally, each attribute should correspond to a goal or value that is separate from those corresponding to the other attributes. This approach allows us to consider all relevant goals in the same way.