Lecturer: Luigi Natale   Stefano Sibilla  

Course name: Hydraulics
Course code: 502524
Degree course: Ingegneria per l'Ambiente e il Territorio
Disciplinary field of science: ICAR/01
University credits: CFU 12
Course website: n.d.

Specific course objectives

The course is intended to give the basic notions of incompressible fluid statics and dynamics. At the end of the course, the student will be able to solve simple problems in applied hydraulics, such as determining hydrostatic forces on tank walls, friction drag in pipes, energy exchanges between hydraulic machines and fluid flows, dimensioning of pipe networks. Moreover, the student will acquire the knowledge to solve free surface flow problems and will be able to compute the water levels in artificial channels in uniform and gradually varied flow conditions.

Course programme

Properties of fluids
Fluidi as continuous systems, internal stresses in continua, physical properties of fluids, measurement units.

Hydrostatics
Hydrostatic equilibrium equation, pressure measurement, forces on plane and curved surfaces, equilibrium of buoyant bodies.

Hydrodynamics
Characteristics of fluid motion, continuity and momentum equations, substantial derivative, Euler equations for perfect fluid, Bernoulli equation, gradually varied flow.

Orifices and discharge measurement
Orifices on tank bottom and on vertical walls, sluice gates, sharp-crested weirs, Venturimeter, Pitot tube, other discharge measurement devices.

Viscous fluid flows
Bernoulli equation for viscous fluids. Boundary layer growth, uniform flow: Darcy – Weisbach formula, laminar and turbulent regimes, smooth and rough pipes, classical resistance laws in pipes: Chezy formula, Manning formula, practical formulas.

Head losses
Hydrodynamic equilibrium equation, headlosses for sudden diameter variation, for smooth diameter variation, in elbows, across a sluice gate.

Hydraulic machines
Pumps, turbines.

Pipes
Pipe flow under negative pressure, long pipes, pipe systems.

Uniform flow in open channels
Geometrical quantities which characterize free-surface flows. Discharge curve in uniform flow: Chezy, Manning and Gauckler–Strickler formulas. Discharge in closed conduits and in compound sections.

Steady gradually varied flow
Critical flow. Characteristics of sub-critical and super-critical flows. Mild and steep slope. Classification of flow profiles in a prismatic channel. Control sections: outlet in a reservoir, jumps, sluice gates, regulated and free entrance, slope change. Numerical solution of steady flow profiles.

Hydraulic jump
Classification and features of hydraulic jupms. Momentum conservation. Hydraulic jump location. Channel connecting two lakes.

Rapidly varied flow
Bed sills. Broad-crested weir. Channel contractions. Flow through bridge piers and consequent backwater effect. Channel junctions.

Course entry requirements

Calculus: function of several variables, limits, derivative and integral. Geometry: trigonometry, elementary algebra, elementary analytical geometry . Physics: principles and fundamental equations of Mechanics, energy, power. vector calculus.

Course structure and teaching

Lectures (hours/year in lecture theatre): 60
Practical class (hours/year in lecture theatre): 60
Practicals / Workshops (hours/year in lecture theatre): 12

Suggested reading materials

M. Gallati, S. Sibilla. Fondamenti di idraulica. Carocci.

Testing and exams