HYDRAULICS
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- Versione italiana
- Academic year
- 2019/2020
- Teacher
- ALESSANDRO VALIANI
- Credits
- 12
- Didactic period
- Secondo Semestre
- SSD
- ICAR/01
Training objectives
- The course is the first teaching of hydraulic engineering and treats the main concepts concerning the physical properties of fluids, the forces exerted by fluids in statics, the fluids motion and their interaction with solid boundaries and technical devices. The course treats also some typical technical problems, even if with a basic approach, such the design and operating principles of pressure pipes and open channels in uniform, steady and un steady flow.
The main purpose of the course consists of living to students the bases to face the study of the systems of forces acting on hydraulics devices and infrastructures, and to acquire the proper skills concerning the energy and momentum balances, governing the fluids motion in practical hydraulic engineering.
The main knowledge that should be acquired can be summarized as follows:
Physical mechanical properties of fluids, with a specific reference to incompressible fluids.
Fundamental equations of fluid statics, kinematics and dynamics of incompressible of weakly compressible fluids.
Differential and integral analysis in fluid mechanics problems.
Fundamental equations governing uniform, steady and un steady motion in pressure pipes.
Fundamental equations governing uniform, steady and un steady motion in artificial and natural open channel flows.
Basic concepts of seepage flows.
The main skills that should be acquired can be summarized as follows:
To evaluate hydrostatic forces acting over plane and curved surfaces.
To apply mechanical balances of mass, energy, momentum to simple systems of technical interest, to evaluate the dynamic forces of several devices and the mechanical energy exchanges between fluid flows and fixed or mobile surfaces.
To evaluate the flow resistances in external and internal flows, both laminar and turbulent.
To design and verify simple systems of pressure pipes in steady and un steady flow conditions.
To design and verify open channels in uniform and steady flows. Prerequisites
- A deep attention to this aspect is required. It is necessary to have understood and assimilated the contents of Mathematical Analysis I and General Physics, and it is strongly suggested to have understood and assimilated the contents of the courses of Mathematical Analysis II and Analytical Mechanics. More specifically, a proper skill in managing the following topics is required:
Differential and integral calculus;
Vector fields analysis (Gauss theorem, gradient, divergence, curl (Stokes) theorem;
Mechanical balances of forces and moments, of momentum and angular momentum, potential, kinetic and total mechanical energy;
Conservative and non-conservative force fields, work and energy;
Rigid body mechanics;
Mass geometry; area geometry. Course programme
- 120 hours of frontal lectures are planned, consisting of theoretical lectures, practical and numerical examples. 16 hours of practice exercises are provided for. These exercises are closely similar to those the students will find in the final written test. Numerical examples and practical aspects are deepened and explained.
The topics are the following.
INTRODUCTION and PHYSICAL PROPERTIES OF FLUIDS [4 h]
Definition of a fluid. Equation of state. Perfect gases, barotropic fluids, incompressibile fluids. Continuous model. Density and specific weight. Fluid compressibility. Surface tension. Dynamic and kinematic viscosity. Vapour pressure.
STRESS ANALYSIS [1h]
Cauchy Theorem. Stress tensor and its mathematical properties.
FLUID STATICS [15 h]
Isotropic pressure. Integral and differential equations. Piezometric head. Static forces against plane and curved surfaces, submerged and floating bodies.
FLUID KINEMATICS [3 h]
Pathlines, streamlines, streaklines. Material derivatives. Acceleration. Velocity gradients tensor.
CONTINUUM MECHANICS [3 h]
Reynolds theorem. Integral and differential equation of continuity. First and second integral and differential equation of motion.
INVISCID FLUID MECHANICS [10 h]
Euler Equations. Boundary conditions. Total head. Bernoulli’s theorem.
INTEGRAL EQUATIONS IN FLUID DYNAMICS [3 h]
Continuity equation. Discharge. Linear momentum balance and Angular momentum balance. One dimensional flows. Flow over orifices and weirs. External flows. Free jets. Dynamical forces. Hydraulic machinery.
DIMENSIONAL ANALYSIS [3 h]
Buckingham Theorem. Non dimensional quantities in fluid mechanics.
VISCOUS FLUID MECHANICS [5 h]
Stokes/Newton assumptions. Navier-Stokes equations. Boundary conditions. Viscous laminar flows in circular closed conduits. Friction slope and resistance coefficient.
UNIFORM FLOW IN CLOSED CONDUITS [2 h]
Velocity and stress distributions. Distributed head losses and resistance laws (Coolebrook/Moody).
STEADY FLOW IN CLOSED CONDUITS [8 h]
Cross section variations. Concentrated head losses. Pipes in series and in parallel. Syphons. Pipe networks. Distributed releases of discharge. Practical examples. Pumping and turbine plants.
UNSTEADY FLOWS IN CLOSED CONDUITS [10 h]
Continuity and momentum equations. Un steady uniform flow. Waterhammer problem. Wave celerity. Simplified equations. General solution. Initial and boundary conditions. Closing and opening valves. Overpressures. Chained Allievi equations. Graphical method. Methods of characteristics. Boundary conditions.
UNIFORM FLOW IN OPEN CHANNELS [5 h]
Specific energy and critical depth. Subcritical and supercritical flows. Critical depth. Resistance to flow. Stage-discharge curves. Compound channels.
STATIONARY FLOW IN OPEN CHANNELS [15 h]
Prismatic channels. Free surface profiles. Boundary conditions. Bresse solution. Non prismatic channels. Hydraulic jump and its position. Obstacles, abrupt changes, weirs.
UNSTEADY FLOW IN OPEN CHANNELS [3 h]
Small undulations propagation without friction. Method of characteristics. Boundary conditions.
GROUNDWATER FLOWS [3 h]
Fluid and grains properties. Darcy law. One dimensional seepage in phreatic and artesian aquifers. Phreatic and artesian wells.
TURBULENT FLOWS [3 h]
Reynolds equations. Uniform flows in the average. Mixing length theory.
PLANE IRROTATIONAL FLOWS
Velocity potential for irrotational flows. Vector potential for constant-volume flows. Streamfunction. Plane, constant-volume, irrotational flows. Simple flows and their superposition.
BOUNDARY LAYERS [5 h]
Laminar flow past a flat plate. Scale problems and dimensional analysis. Blasius solution. Turbulent boundary layer past a flat plate. Integral simplified momentum balance and relative solution. Boundary layer separation. Drag of the circular cylinder and of the sphere.
TRAINING AND EXAMINATION STANDARD [16 h].
WRITTEN TEST (pre-appello) [3 h]. Didactic methods
- The lectures are organized as follows.
Frontal lectures concerning the described topics;
Practical examples, that are devoted to explain engineering applications of theoretical concepts;
Support to carry out practical exercises (including numerical computations), that are extracted from written tests of previous academic years. Learning assessment procedures
- The main purpose of the final examination consists of verifying the proper achievement of the previously defined training objectives.
The exam is divided into two parts, a written test and the oral examination, in different dates.
The written test (3 hours) consists of 3 exercises; each of them is evaluated as 1/3 of the total mark (30): 1) Static force on a curved surface; 2) Bernoulli’s theorem applications and dynamic forces computation using momentum balances; 3) computation of friction in pipes and solving simple hydraulic networks. A mark of 16/30 (at least) is required to sit the oral examination. The validity of the written text (if the mark is 18/30 at least) is twelve months. The validity of the written test, if the mark is less than 18/30, expires at the date of the following written text.
The oral examination is mainly based on the topics not addressed in the written test. Open channel flows and water hammer problems are always faced. Moreover, a theoretical topic is also touched. The final mark is not the simple mean between written part and oral part (anyway is never less than this mean), but is a synthetic mark, expressed as a fraction of 30. If the candidate retreats during the oral examination, he must repeat the written test just if his mark on such test is less than 18/30. Reference texts
- Reference text:
Lecture notes.
Written text examples: internet site of the course.
In-depth texts:
MONTEFUSCO L., Lezioni di Idraulica. Pitagora Editrice, Bologna, 2005.
MARCHI E., RUBATTA A., Meccanica dei fluidi. Principi ed applicazioni idrauliche. UTET, 1981.
MOSSA M., PETRILLO A. F., Idraulica, CEA, Milano, 2013.
CITRINI D., NOSEDA G., Idraulica. CEA, 1987.
ALFONSI G., ORSI E., Problemi di Idraulica e Meccanica dei fluidi. CEA, Milano, 1984.
GHETTI A., Idraulica, Ed. Cortina, Padova, Ultima ediz. .
LIGGET J.A., CAUGHEY D. A., FluidMechanics. An Interactive Text. ASCE Press, Reston, VA, 1998.
WHITE F. M., Fluid Mechanics, Mc Graw Hill Intern. Student Ed., 1979.
CENGEL Y.A., CIMBALA J. M., Meccanica dei fluidi, McGraw-Hill Education, Milano, 2015 (edizione italiana a cura di G. Cozzo e C. Santoro).
