HYDRAULICS AND HYDRAULIC CONSTRUCTIONS

The main objective of the course is to provide the basic knowledge of hydraulics. After a preliminary part where the physical characteristics of the fluids are described with special reference to those that distinguish them from the solids, the course introduces the fundamental topic of hydraulics along with the necessary theoretical framework. The course also includes topics on hydrology and construction of aqueducts and sewers for civil settlements. Several lessons will be devoted to the solution of practical problems of hydraulics and hydraulic constructions.

Introduction to the course

Definition of fluid substance. The continuum hypothesis. Quantities and measurement units. Mass forces and surface forces. Stress tensor and its properties. Fluid properties: compressibility, thermal elasticity, surface tension, viscosity. Non-Newtonian fluids. Gas absorption.

Fluid statics
Stress in fluids at rest. Equation of the statics of fluids in differential form. Equation of static equilibrium in global form. Statics of incompressible fluids under the action of gravity force. Pressure measurements. Forces applied on flat surfaces. Forces applied on curved surfaces. Statics of fluids in a non-inertial reference frame.

Kinematics.

Generalities on the fluid kinematic. Eulerian and Lagrangian approaches. Velocity and acceleration. Visualization of the flow field. Trajectories. Streamlines. Smoke lines. Flux tubes. Types of fluid motions. Permanent flows. Unsteady flows. Uniform flows. Two-dimensional flows. Flow regimes. Laminar flows. Turbulent flows. Continuity equation in differential form. Continuity equation for a fixed control volume. Continuity equation for a current. Rotation and deformation rate of fluid elements.

Fluid dynamics: the momentum equation
Momentum equation in differential form. Euler equation. Boundary conditions. Momentum equation in global form.

Bernoulli's theorem
Equation of motion in streamlines coordinates. Pressure distribution. Bernoulli's theorem. Geometric representation of Bernoulli’s theorem. Energy implications of Bernoulli's theorem. Outflow phenomena. Venturi tube. Pitot tube. Extension of Bernoulli's theorem to real fluids. Head losses. Extension of Bernoulli's theorem to a current. Energy exchange between a current and a machine.

The equations of motion of viscous fluids
Constitutive equations of viscous fluids. The Navier-Stokes equations. Momentum equation of viscous fluids in global form.

Pressurized flows
Drag force exerted by a current on a pipe. Tangential stress. Laminar flow in a pipe of circular section. Poiseuille formula. Flow between flat parallel plates. Turbulent flow. The mean flow equation. Viscous and turbulent shear stresses. Application of the Buckingham theorem for the determination of the form of the resistance law. Darcy-Weisbach formula. Resistance index. Flow in smooth pipes. Resistance index in smooth pipes. Mean velocity distribution of a turbulent flow in a smooth tube. Flows in rough pipes. Resistance index in rough pipes. Notes on the velocity distribution in a turbulent flow in a rough tube. Moody chart. Practical formulas for the calculation of the flow resistances. Localized head losses. Dissipations of energy because of abrupt enlargement, sharp-edged inlet and outlet in a reservoir. Flows subject to negative pressure.

Practical problems regarding long pipes
Generality. Pipes with uniform distribution along the path. Problems of verification of the operation of long pipes systems. Design problems of long pipes systems. Choosing the most appropriate path for the laying of a pipeline.

Open channel flow
Generality. Gradually varied flows. Uniform flow. Energy characteristics of a current in a section. Critical flow. Subcritical and supercritical currents. Kinematic character of subcritical and supercritical currents. Channels with mild and steep slopes. Currents in permanent motion: the free surface profiles. Practical examples. Passage of a current over a bottom bump. Passage of a current between the stacks of a bridge.

Basic Hydrology
Generality. Sources of information: the Hydrographic Service. Detection and distribution of rainfall. High-intensity rains of short duration. Probability curves of rains of short duration. Runoff formation.

Aqueducts.

Generality. Water extraction (springs, groundwater, surface water). Requirements for water potability. Selection of the route of an aqueduct. Distribution network. Reservoirs.

Sewerage systems

Generality. Sewerage networks. Types of sewers. Computation of sewage flow rate and rain flow rate. Ultimate destination and treatment of waste waters.

1) D. Citrini, D. Noseda "Idraulica", CEA Milano, 1987.

2) G. Ippolito " Appunti di Costruzioni Idrauliche". Edizione aggiornata a cura di Giuseppe di Martino. Liguori Editore. 1993.

3) G. Alfonsi, E. Orsi "Problemi di Idraulica e Meccanica dei Fluidi" CEA Milano, 1984.

4) G. Pezzinga "Esercizi di Meccanica dei Fluidi" Aracne editrice, 2008.

5) Appunti forniti dal docente reperibili durante il corso sulla piattaforma Studium.