The module "Idraulica Applicata" is the second module of "Idraulica" course. In this module, will become familiar with open-channel flow, mainly dealing with man-made channel problems. Students will learn qualitative trends of Gradually Varied Flow profiles and will numerically compute those profiles as a function of the flow characteristics and boundary conditions.
Course Prerequisites
Mathematical Analysis: functions of one or more real variables, limits, derivatives, integrals. Physics: measurement of physical quantities and units of measure. Principles and fundamental equations of mechanics. Energy. The energy conservation principle. Mathematical physics: scalars and vectors. Fundamental elements of vector calculus. Geometry of the masses.
Teaching Methods
Lessons (hours per year in the classroom): 32 Exercises (hours per year in the classroom): 24
Assessment Methods
The learning assessment involves carrying out a written test in which 3 problems will be proposed. The evaluation will consider both the procedure and the correctness of the obtained results. The positive result, if accepted, will be used for the average with the grade of the "Fondamenti di Idraulica" module for the calculation of the final grade of the "Idraulica" course (arithmetic average of the two modules, rounded up).
Texts
Lectures’ slides (for PowerPoint lectures only), exercises and solutions will be available on the course page on the KIRO platform. Additional references:
Gallati M., Sibilla S. (2009) Fondamenti di idraulica, Carocci editore, Roma.
Mossa M., Petrillo A.F. (2024) Idraulica, Casa Editrice Ambrosiana, Milano.
Citrini D., Noseda D. “Idraulica” Tamburini, Milano
AA.VV. “Sistemi di fognatura-Manuale di progettazione” (Capitolo 12), CSDU-Hoepli
Contents
Flow basic notions: the flow concept. Flow spatial and temporal characteristics. Continuity equations and momentum equations.
Free surface flows geometrical characteristics Geometrical characteristics of free surface flows for cross section. Geometrical characteristics of free surface flows for longitudinal profiles. Representation of natural open channels geometry.
Normal flow in free surface flow Normal flow. Free surface flow resistance and roughness coefficients. Flow rate versus normal depth. Flow rate versus normal depth for closed sections. Flow rate versus normal depth for composed sections. Verification and design problem under the condition of normal flow: graphical methods (specific and normalized flow rate versus normal depth) and numerical method (Bisection). Unstable normal flow (rapid flow).
Free surface flows energetic characteristics Specific-energy considerations. Water depth versus specific-energy with constant flow rate. Flow rate versus water depth with constant specific-energy. Critical state. Open channel flow: mild, critical and steep slope.
General considerations for the profiles of gradually varied flow Gradually varied flow equation. Gradually varied flow for five classes of channel slope (mild, critical, steep, horizontal and adverse), showing basic solution curves. Control sections.
Composite-flow profiles: solution curves between two regimes Passing through the critical depth. Hydraulic jump. Total force. Water depth versus total force with constant flow rate. Flow rate versus water depth with constant total force. Hydraulic jump placement.
Backwater profiles Backwater concept and its upstream/downstream propagation. Integration of the steady gradually varied flow equations in prismatic channel.
Open channel flow singularity Abruptly varied flow considerations. Characteristic scale (singularities scale and scale of steady flow profile). Properly filleted steps on the bottom. Flow measurement and control by weirs. Flow over wide weirs. Filleted and abrupt lateral contractions. Hydraulic jump modeler: sharp-crested weirs/ broad-crested weirs. Backwater caused by the bridge piers.