29897 - Fluidodynamics

Learning outcomes

At the end of the course the student should have the necessary knolwedge to analyze and design systems involving static and moving  fluids such as:
-manometers, flowmeters, rheometers, water turbines, reservoirs, pipelines, control valves, centrifugal pumps, settlers, safety valves

In particular, the student must know the main dimensionless parameters involved in fluid dynamics, the basic laws and constitutive equations for newtonian and non newtonian fluids.

Course contents

PREREQUISITES (SUGGESTED):

CALCULUS, PHYSICS; THERMODYNAMICS, NUMERICAL METHODS

Fluid flow variables, systems of units.

Dimensional analysis: Buckingham theorem, Kelvin method. Application to scale-up procedures.

The integral momentum balance and its applications: determination of the force exerted by fluid streams on solid surfaces, the ejector. The integral balance of angular momentum.

Fluidstatics: the stress tensor for a fluid, Pascal's law. Pressure distribution in incompressible and compressible fluids: adiabatic and isothermal pressure profiles in air. The buoyant force and its expression. Equilibrium of submerged and partially submerged bodies. Manometers. Force exerted by incompressible fluids on plane solid surfaces.

Continuum kinematics: Eulerian and Lagrangian systems. The local mass balance and the local momentum balance. The constitutive relation between the stress tensor and velocity gradient in newtonian fluids. Navier-Stokes equation.

Analytical solutions to the NS Equation: Couette and Poiselle laminar flow in plane and cylidrical pipes: velocity and stress profiles.

Dimensional analysis approach to the general solution of flow problems: Fanning friction factor, Reynolds number and the correlations between them for smooth and rough pipes: correlations of Blasius, Colebrook, Churchill, Moody diagram. The Bernoulli equation. Total and kinetic head. Friction losses and their evaluation in internal flow. Problems of internal flow in pipelines and hydraulic networks.

Determination of flowrate in Venturimeters, Pitot tubes, orifices.

Rheological behavior of non Newtonian fluids: the Bingham and power law fluid.

External flow: the drag coefficient and its correlation with the Reynolds number. Applications to the determination of terminal velocity and viscosity measurement.

Centrifugal and volumetric pumps, pump head, characteristic curve for a centrifugal pump. Working point of a pump in an pipeline. Dimensional analysis applied to the case of centrifugal pumps. Cavitation and NPSH. Choice of a pump. Considerations on the regulation of flowrate.

Compressible fluid flow: the speed of sound, the Mach number, isoentropic flow of ideal gases in converging ducts. Lapple diagrams. Isothermal flow with friction in constant-section ducts.

Readings/Bibliography

• Notes provided by the Instructor (In Italian)
• Y. A. Çengel, J. M. Cimbala, "Meccanica dei fluidi", 2007, Mc Graw Hill, ISBN: 9788838663840
• R. Darby "Chemical Engineering Fluid Mechanics", 2nd Ed., Marcel Dekker, 2001.
• N. DeNevers, "Fluid Mechanics for Chemical Engineers" McGraw-Hill 2004.
• Fay, J.A.: "Introduction to Fluid Mechanics", MIT Press, 1995.

Teaching methods

Traditional classes and intermediate tests to be performed by the students in the classroom.

Assessment methods

One written exam, that requires the solution of problems using a personal computer, and one oral exam. Final grade is the arithmetic mean of the grades of the written and oral exam.

Teaching tools

Notes, numerical examples

Office hours

See the website of Maria Grazia De Angelis