Unit FLUID MECHANICS
- Course
- Mechanical engineering
- Study-unit Code
- A005619
- Curriculum
- Energia
- Teacher
- Michele Battistoni
- Teachers
-
- Michele Battistoni
- Hours
- 54 ore - Michele Battistoni
- CFU
- 6
- Course Regulation
- Coorte 2025
- Offered
- 2026/27
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Sector
- ING-IND/08
- Type of study-unit
- Obbligatorio (Required)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Introduction; Basic Concepts; Properties of Fluids
Fluid Statics
Fluid Kinematics: Eulerian and Lagrangian description
Elementary Fluid Dynamics — Mass and Energy (Bernoulli) Conservation
Fluid Kinematics: Eulerian and Lagrangian description
Finite Control Volume Analysis
Differential Equations of Fluid Motion
Dimensional Analysis and Similitude
Viscous Internal Flows: Pipe Flows
Viscous External Flows: Flow Around Bodies, Drag and Lift, boundary layer.
Approximate Solutions of the Navier–Stokes Equation
Laminar and Turbulent flows
Compressible Fluid Flow - Reference texts
- Recommended:
Main book:
(ENG) Çengel, Cimbala – Fluid Mechanics – Fundamentals and Applications, McGraw-Hill
(ITA) Çengel, Cimbala – Meccanica dei Fluidi, McGraw-Hill
For additional support and exercises:
(ENG) Munson, Okiishi, Huebsch, Rothmayer – Fundamentals of Fluid Mechanics, Wiley
(ITA) Munson, Okiishi, Huebsch, Rothmayer – Meccanica dei fluidi, Città Studi Edizioni (De Agostini)
Other:
White F.M. – Fluid Mechanics –McGraw-Hill - Educational objectives
- The course aims to provide Mechanical Engineering students with the fundamental skills required to understand, model, and analyze fluid behavior under both static and dynamic conditions.
By the end of the course, the student will be able to:
Apply the principles of conservation of mass, momentum, and energy in both integral (macroscopic) and differential (microscopic) forms.
Solve engineering problems related to the calculation of hydrostatic forces, head losses in industrial hydraulic systems, and aerodynamic forces on submerged bodies.
Utilize dimensional analysis for the design and interpretation of experimental tests on scale models.
Understand elementary thermofluidodynamic phenomena related to compressible flows in nozzles and choked conditions (choking). - Prerequisites
- To successfully follow the course, a solid foundation in the following subjects is required:
Mathematical Analysis I and II: differential and integral calculus, ordinary differential equations, vector algebra, differential operators (gradient, divergence, curl), and the divergence and Stokes' (curl) theorems.
General Physics I (Mechanics): kinematics and dynamics of particles and rigid bodies, concepts of force, torque (moment), work, and energy. - Teaching methods
- The course consists of a total of 54 official teaching hours, structured in fixed weekly blocks:
Theoretical Lectures (36 hours): dedicated to explaining physical concepts, theoretical models, and the formal derivation of the governing equations.
Practical Classroom Exercises (18 hours): dedicated to the numerical and analytical application of the theory through the guided solution of engineering and academic problems selected from the reference textbooks. - Other information
- Learning verification modality
- Assessment of the acquired skills is carried out through an exam divided into two phases:
Written Exam (Duration approximately 3 hours): Solution of 3 independent numerical problems aimed at verifying the student's operational capability. Passing the written exam with a grade of at least 18/30 is a prerequisite for admission to the oral exam.
Oral Exam: An interview aimed at verifying the critical learning of the subject, the physical understanding of the phenomena, and the rigor in presenting the fundamental mathematical derivations. - Extended program
- 1) Introduction and Fluid Properties:
No-slip condition. Vapor pressure and cavitation. Viscosity and Newtonian fluids. Surface tension. Classroom exercise: Calculation of shear stresses in viscometers and fluid films (clearances).
2) Fluid Statics:
Hydrostatic pressure and manometers. Hydrostatic forces on submerged plane and curved surfaces. Archimedes' principle, buoyancy, and stability. Classroom exercise: Calculation of forces and moments on gates and dams.
3) Fluid Kinematics:
Lagrangian and Eulerian descriptions. Streamlines, streaklines, and pathlines. Vorticity, rotationality, and the strain-rate tensor. Reynolds Transport Theorem (RTT). Classroom exercise: Analytical determination of streamlines and material acceleration.
4) Bernoulli Equation and Integral Formulation of Energy:
Bernoulli equation: derivation, assumptions, and limitations. Hydraulic Grade Line (HGL) and Energy Grade Line (EGL). General energy equation for open systems, kinetic energy correction factor (a), and head losses. Classroom exercise: Energy balances in hydraulic systems and Venturi meters.
5) Integral Formulation of Momentum:
Conservation of mass and linear/angular momentum for fixed and moving control volumes. Momentum flux correction factor (ß). Classroom exercise: Calculation of anchoring forces on flanged bends, nozzles, and jet impingement on vanes.
6) Dimensional Analysis and Similitude:
Buckingham ¿ theorem and the method of repeating variables. Non-dimensional groups (Reynolds, Froude, Mach). Similitude and scale models. Integrated classroom exercise: Calculation of non-dimensional groups and operating conditions for scale models.
7) Differential Equations of Fluid Motion:
Differential continuity equation. Stream function. Derivation and physical meaning of the terms in the Navier-Stokes equations for incompressible fluids. Classroom exercise: Verification of admissible velocity fields and calculation of pressure gradients.
8) Approximate Solutions of the Navier-Stokes Equations:
Exact solutions for steady parallel flows (Couette and Poiseuille). Euler equations for inviscid flows. Irrotational flows and velocity potential. Classroom exercise: Analytical derivation of velocity profiles and flow rates between plates and inside conduits.
9) Internal Viscous Flows:
Laminar and turbulent regimes in pipes. Entrance region and fully developed flow. Major head losses (Darcy-Weisbach, Moody chart, Colebrook equation) and minor losses. Classroom exercise: Energy balance and hydraulic sizing of an industrial piping system.
10) External Viscous Flows and Boundary Layer:
Prandtl's boundary layer theory. Laminar (Blasius) and turbulent boundary layer on a flat plate. Characteristic thicknesses (nominal, displacement, momentum). Classroom exercise: Calculation of thicknesses and global wall shear stress on a flat plate.
11) Flow Around Bodies: Drag and Lift:
Drag forces (friction drag and pressure/shape drag) and lift forces. Boundary layer separation phenomenon. Drag and lift coefficients (C_D and C_L) for cylinders, spheres, and airfoils. Classroom exercise: Calculation of aerodynamic drag and lift forces.
12) Compressible Flows:
Speed of sound and Mach number. Stagnation state and properties. Isentropic flows in convergent and de Laval nozzles. Choked flow conditions (choking). Introduction to normal shock waves. Classroom exercise: Calculation of thermodynamic properties in de Laval nozzles. - Obiettivi Agenda 2030 per lo sviluppo sostenibile