Fluid mechanics


The target of the course is to provide the basics of the mechanics of liquids and gases and the applications of fluid mechanics. The course presents several topics that are relevant for the professional education of a civil or environmental engineering.


Basic knowledge of calculus, physics and theoretical mechanics.

- Properties of fluids: density, specific weight, viscosity. Surface forces. Compressibility of liquids and gases.
- Static of fluids
The hydrostatic equation for compressible and incompressible fluids. Piezometric measurements. Capillary rise in piezometric tubes. Hydrostatic thrusts on a plane and curved surface. Global equilibrium method.
- Kinematics of fluids
Eulerian and Lagrangian frameworks. Streamlines and trajectories. Conservation principles. Reynolds theorem. Mass conservation in integral and differential forms.
Deformation and rotation tensors. Irrotational flows.
- Fluid dynamics
Navier-Stokes equations. Euler, Froude and Reynolds dimensionless numbers.
- Dynamics of the ideal fluid.
Euler equations. Bernoulli theorems. Potential flows. Two-dimensional applications of potential flows: uniform translation, source point, hydraulic doublet, flow around a cylinder.
- Flows through orifices, nozzles and diffusers.
Flows over weirs of different shape and flows under gates.
- Applications of momentum conservation.
Hydrodynamic thrust on a bend of a pipe, on a nozzle, on an inclined wall and on a U-shaped profile. Pelton turbine. Francis turbine. Propeller propulsion, jet propulsion, Lift on a wing. Cavitations.
- Conservation of mechanical energy in integral form. Application to ducts with and without mobile parts. Head of a hydraulic machine.
- Creeping and Laminar flows:
flows between two parallel plates, flow in a circular pipe.
- Turbulent flows:
characteristics of the turbulent flow; statistically stationary turbulence. Reynolds equations. The problem of closure. Integral scales and microscales. Boussinesq diffusive model. Wall turbulence; Mixing length theory of Prandtl.
- Boundary layer
Definitions, von Karman integral relations; laminar boundary layer: simplified solutions without pressure gradient drag coefficients. Turbulent boundary layer: smooth wall, internal and external region: viscous sublayer, logarithmic sublayer. Prandtl-von Karman Logartihmic law. Power law and friction factors. Rough wall.
- Uniform flows in cylindrical pipes.
Velocity and shear stresses distributions. Friction factor; Darcy-Weissbach equation; equivalent roughness. Moody diagram. Empirical uniform flow equations. Non-circular ducts and hydraulic radius.
- Boundary layer in presence of pressure gradient
Boundary layer separation; Localized energy losses.
- Network of pipelines
Pipes in series and in parallel; pipes networks: linearized solution methods. Siphons. Problems connected with the altimetry of the pipes.
- Discharge and velocity measurements instruments
Pitot tube, propeller current meters, acoustic, electric and optical meters. Venturi meters, orifice meters and nozzles. Other instruments.
- Open-channel flows:
Uniform flow, specific energy. Celerity of propagation of a small surface perturbation. Gradually varying channel flow.. The hydraulic jump. Narrowing and sills.
- Unsteady flow in pipes
Anelastic description: emptying of a reservoir, mass oscillations. Flow in a U-shaped pipe. Water hammer: propagatory approach. Propagation of a small pressure perturbation.

Teaching Methods
Lectures and practice exercise sessions. Personal preparation is required. A visit in the hydraulic lab is planned.

Verification of learning
3 hours written examination and an oral examination. The result of the written examination is valid for two consecutive oral examining periods. If a student passes the written examination on two consecutive occasions, the higher score will be valid for the final result. Students may withdraw from the written examination at any time before the end of the examination. The completed examination is corrected in the presence of the student. If a student is not present for the correction the examination will not be given a pass grade.

An on-line textbook written by prof. Armanini is available.
Other text books:
Altri testi di possibile consultazione:
A. Ghetti, Idraulica. Ed. Cortina;
Cengel, Cimbala; Meccanica dei Fluidi, II ed.;
Mossa, Petrillo, Idraulica. Casa Ed. Ambrosiana;
Marchi, Rubatta,Meccanica dei Fluidi, UTET.

More Information
The program of the course is widely taught in technical faculties in Italy and abroad.


For a detailed list of contents see here