## Fluid Machinery – (block A-D)

LEARNING OUTCOMES: This course aims at providing the fundamentals of fluid dynamics applied to fluid machines. More in detail, it deals with the fluid dynamics equations applied to energy-consuming and energy-producing machines, characterized by both axial and radial flows. It also deals with the understanding of systems connected to fluid machines.

KNOWLEDGE AND UNDERSTANDING: The student will be able to develop simple but useful calculations of fluid machines in terms of flow, work and power, along with solving practical problems of interest. The student will also learn the basics of the control of fluid machines with respect to the flow rate, work exchanged and power output or input The knowledge developed will help the student for both the design of fluid machines and of the systems connected to the machines.

APPLYING KNOWLEDGE AND UNDERSTANDING: The student will apply the knowledge and understanding developed to the analysis of practical problems. This would imply critical knowledge in terms of size and power output/input; the same thing will be done for the systems connected to the machine.

MAKING JUDGEMENTS: The student will have to prove his critical awareness with respect to the simplifying assumptions useful to describe and calculate fluid machines, as well as his critical awareness of the correct order of magnitude of performance parameters while dealing or designing fluid machines.

COMMUNICATION SKILLS: The student will prove, mostly during the oral test, his capacity of describing the operation and functioning of fluid machines, convening of the knowledge developed.

LEARNING SKILLS: The student will get familiar with the schematization of practical problems, mostly during the development of his skills for the written test. This mainly concerns fluid machines (e.g. wind turbines, steam turbines, hydraulic turbines, hydraulic pumps, gas compressors, etc) and the systems connected to the machines (e.g. hydraulic power plants, pumping systems, air distribution systems, etc).

DETAILED SYLLABUS

Introduction

Classification of machines. Turbines, compressors, volumetric, rotary machines and their applications to industrial practical cases. Analysis of performance: power, specific work, efficiency.

Basics of fluid mechanics

Material and spatial description of the flow field. Translation, deformation and rotation. Reynolds’ transport theorem. Principles of conservation and balance (mass, momentum, energy, entropy) in differential form. Mass, momentum, thermal and mechanical energy in stationary and rotating frames of reference.

Basics of fluid mechanics applied to turbomachinery

Integral balances in turbomachines (mass, momentum, moment of momentum, energy) and basic applications.
Gas dynamics equations, speed of sound, Mach number. Applications to nozzles in supersonic conditions, normal shock waves.

Velocity diagrams coupled to stator and rotor blades for energy producing and consuming machines. Moment of Momentum balance. Energy transfer and different expressions of the Euler work. Trothalpy, degree of reaction, utilization for a turbine.

Applications

Scaling and similitude: dimensionless parameters, specific speed and diameter, Cordier curve. Scaling and similitude for compressible flow machines.

Axial turbines: stage analysis, flow and loading coefficients, reaction ratio, special cases of 0 and 0.5 reaction ratio designs. Off-design operation and performance maps.

Axial compressors: stage analysis, flow and loading coefficients, reaction ratio. De Haller design criterion and its effect on blade design. Off-design operation and performance maps.

Centrifugal compressors: analysis of velocity diagrams, effect of blade shape on performance maps, stability and efficiency. Slip factor. Vaneless and vaned diffuser. Flow control (variable speed, IGV and throttling).

Centrifugal pumps operation into systems: definition of head and volumetric flow rate. Head-flow rate performance map and effects on velocity diagrams, blade design and efficiency. System head curves for simple and multi-branched open-ended and closed-circuit systems. Friction factor and expression of dimensional friction losses. Flow control by variable speed and throttling.

Cavitation: physical description; effects of system design on cavitation, Net Positive Suction Head, suction specific speed.

TEXTBOOKS AND MATERIAL

S. Korpela. Principles of Turbomachinery, Wiley 2019.

Karassik et al., Pump handbook, McGraw Hill.

Powerpoint slides and videos are available on the MS-team website.

## Engineering Economics

OBJECTIVES

LEARNING OUTCOMES
The aim of the course is to provide students with basic knowledge about microeconomic models (demand and supply functions, market structures, consumers and producers’ choices, perfectly competitive markets and monopolistic markets), as well as about investment analysis (comparison and choice between investment alternatives, basing on the most used parameters like Present Worth, Internal Rate of Return and payback period).

KNOWLEDGE AND UNDERSTANDING
Knowledge and understanding of the topics of the course will be developed mostly through active participation in didactic activities during classes.

APPLYING KNOWLEDGE AND UNDERSTANDING
The ability to apply knowledge and understanding is developed by encouraging active participation of students to classes, by questioning students during classes, by flipped classroom situations and by facilitating educational conversations.

MAKING JUDGEMENTS
The ability to make judgments on the topics of the course will be developed through theoretical and practical classes and by involving students in analysing the results obtained in simulations and exercises.

COMMUNICATION SKILLS
Communication skills, acquired knowledge and ability to make judgments on the topic of the course will be tested through the exam. During exams, students will face theoretical as well as practical questions.

LEARNING SKILLS:
Learning skills will be sustained by the teacher with the possibility of having appointments in which students can ask questions to solve doubts – both theoretical and practical – coming from individual study.

COURSE SYLLABUS

Microeconomics
• use of microeconomic theory; positive and normative economic analysis; why to study microeconomics; what is a market
• market mechanism; demand and supply curves; elasticity, both in the short and in the long run
• consumer’s preferences, utility function, budget line and consumer’s optimal choice
• production function, production isoquant, production in the short and in the long run
• cost structures in the short and in the long run and their determinants, optimal production choice
• profit maximization, marginal revenues and marginal costs, conditions for a perfectly competitive market
• average and marginal revenues in a monopolistic market, production decision making in a monopolistic market

Investment analysis
• time value for money, interest and interest rate, simple and compound interests
• nominal and effective interest rates
• economic equivalence and financial factors
• difference between investments and loans, investment projects, investment alternatives
• the “not to invest” alternative and the MARR
• choice between investment alternatives: PW, AE, FW, IRR, payback period

Lecture notes and practical classes are integral part of the program, as well as elements coming from discussions during classes.
Please note that lecture notes do not cover the program, but are meant to integrate and complete what is explained on suggested textbooks.