29897 - Fluidodynamics

Learning outcomes

At the end of the course, the student will acquire the necessary knowledge to examine, in operational terms, various aspects of the transport of fluids, also making the choice of the necessary equipment, becaming familiar with the basics of fluid mechanics.

Course contents

The course will be taught in Italian.

 

Input Knowledge:

Mathematical knowledge: Methods of integration and derivation, ordinary differential equations, matrix algebra, vector and tensor calculus, trigonometry. Physics knowledge: physical quantities of a mechanical nature (force, acceleration, speed, pressure, etc..) and their representation, vectors and operations with vectors. Thermodynamic knowledge: mass and energy balance for a pure substance, equation of state of ideal gases, isothermal and adiabatic processes.

Numerical Analysis

 

1. Dimensional analysis

Dimensions and systems of units of measurement. Dimensional homogeneity of physical relationships. Buckingham's theorem. Steps of dimensional analysis (Kelvin's method). Dimensional analysis as a scale-up methodology and as a method to evaluate the orders of magnitude of simultaneous physical phenomena.

2. Integral momentum balance

Momentum balance in steady state conditions: a) Ejectors; b) Constrain Reactions: force exerted by fluids in motion on solid surfaces and reduction elements, on curves, on the blades of a Pelton turbine, on hydraulic barriers; c) Stationary propulsion. Momentum balance of momentum. Example: the Flixborough incident.

3. Fluid statics

Forces acting on a fluid particle, stress tensor in a fluid in motion and at rest. Pressure and pressure distribution in an incompressible fluid immersed in a gravitational field (hydrostatic): Stevino's law. Pressure distribution in an incompressible fluid immersed in a gravitational field subject to a uniformly accelerated overall motion. Pressure gauges: U-tube, "tank", inclined, 2-fluid differential. Other devices containing fluids at rest: hydraulic seal. Notes on surface tension: contact angle, capillary rise. Archimedes' principle - buoyant force, equilibrium of immersed bodies, notes on the stability of equilibrium. Force exerted on flat solid surfaces by fluids at rest.

4. Flow inside pipelines

Dimensional analysis for the viscous stress in the internal motion of pipelines. The Reynolds number and its link with the flow rate. Laminar and Stokes regime. Turbulent regime, rough pipes: Moody diagram. Churchill correlation. Integral balance of qdm for a one-dimensional current, Bernoulli equation, Bernoulli generalized theorem. Distributed and concentrated pressure drops. Pipe characteristics: nominal diameter, schedule number, commercial diameters for pipes, roughness. Project problems and pipeline verification. Numerical resolution algorithms in Excel for pipeline design and verification problems. Pipe Networks. Altimetric pipelines: line of loads. Flow meters: venturi, nozzle, drilled diaphragm, Pitot tube. Numerical resolution algorithms in Excel for flowmeter design and verification problems.

5. Fluid handling

Volumetric pumps and Centrifugal Pumps: dimensional analysis of the functioning of centrifugal pumps, characteristic curve and its variation with the number of revolutions and with the diameter. Characteristic speed. Cavitation and positive suction head (Net Positive Suction Head, NPSH). Pump-circuit coupling: determination of the operating point numerically in Excel. Project problem: choice of centrifugal pump (fixed Q). Flow rate regulation in a circuit with centrifugal pump. Flow control valves and valve characteristic curve (linear, equal percentage, parabolic, quick opening).

6. External Flow

Dimensional analysis of the problem. Evaluation of the friction coefficient CD in the external flow: DallaValle's correlation, Stokes' law. Falling sphere viscometer and terminal velocity of falling spherical particles. Sedimentators, particle separation apparatus. Sizing and verification issues.

7. Microscopic balances, analytical description of laminar flows and rheology

Lagrangian and Eulerian description of motion; local derivative and substantial derivative. Local momentum balance; expression for strain rate; expression of the stress tensor for Newtonian fluids. Velocity and effort profile in plane Couette motion and in plane and cylindrical Poiseuille motion. Viscosity; Non-Newtonian fluids: Bingham fluids, pseudoplastics, dilants, rotational viscometer.

 

Readings/Bibliography

Notes provided by the professor.

recommended books:

• Y. A. Çengel, J. M. Cimbala, "Fluid Mechanics Fundamentals and Applications", 2007, Mc Graw Hill,
• R. Darby "Chemical Engineering Fluid Mechanics", 2nd Ed., Marcel Dekker, 2001,
  

Other readings:

• N. DeNevers, "Fluid Mechanics for Chemical Engineers" McGraw-Hill 2004;
• Fay, J.A.: "Introduction to Fluid Mechanics", MIT Press, 1995.
• Marchi E., Rubatta A, "Meccanica dei fluidi: principi e applicazioni idrauliche", UTET 1981;
• Foraboschi F.P., "Principi di ingegneria chimica", UTET 1973.

Teaching methods

Lessons using blackboard and slides. Introduction of theory and resolution of exam exercises.

Projection of educational videos for the visualization of physical phenomena and engineering devices.

Solving problems by numerical method with the use of spreadsheets developed in the computer lab or built by the student at home via e-learning (video tutorials).

Exam exercises solved step-by-step

Assessment methods

The exam consists of a theoretical test with multiple-choice questions and a practical test with the resolution of exercises, carried out in sequence throughout the same day. There is a minimum threshold in both tests to pass the exam. The final grade is an average of the scores achieved in the two tests.

Theory test

The theory test consists of answering multiple choice questions on aspects of theory. For wrong answers a negative score is foreseen. The duration of the test is approximately 30 min.

Practice Test

The practical test consists in solving 4/5 exercises in about 150 min. You can use a scientific calculator and/or a laptop. You can use spreadsheets prepared independently using any software you like (Excel, Matlab, Mathematica etc.), and the solution algorithms illustrated in class and described in the video tutorials. You can consult the tables provided expressly for the exam. You can consult 1 handwritten form on an A4 sheet, single-sided.

Texts, handouts, video tutorials, tables other than those provided cannot be consulted, either digitally or on paper. It is forbidden to communicate in any form with other students or with the outside world during the entire test.

Attribution of grade and honors

The mark consists of the weighted average of the scores of the theoretical test (about 30%) and of the practical test (about 70%). Honors are awarded to the student who has obtained a score higher than 30/30 following the overall evaluation of the theoretical and practical test.

Test repetition

There are at least 6 annual exam sessions, of which at least three in the summer session, one in the autumn session and two in the winter session.

1) There are no extraordinary exam sessions outside the exam sessions

2) within 5 days from the date of publication of the exam result, a decision must be made whether to record the mark achieved, or to refuse and repeat the test (one time only)

3) in case of refusal, the entire test must be repeated (both theoretical and practical)

4) the second time the exam is passed, the mark is automatically recorded and the exam cannot be taken any further.

Teaching tools

Lecture notes provided by the teacher and downloadable for free on Virtuale.

Educational videos for visualizing physical phenomena and engineering devices.

Video tutorials for setting up problem solving spreadsheets.

Examples of solution of exercises with analytical and numerical method

Office hours

See the website of Matteo Minelli