Introduction to Fluid Mechanics

Universidad Carlos III de Madrid

Course Description

  • Course Name

    Introduction to Fluid Mechanics

  • Host University

    Universidad Carlos III de Madrid

  • Location

    Madrid, Spain

  • Area of Study

    Aerospace Engineering

  • Language Level

    Taught In English

  • Prerequisites

    Calculus I & II, Linear Algebra, Physics I & II

  • Course Level Recommendations


    ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

    Hours & Credits

  • ECTS Credits

  • Recommended U.S. Semester Credits
  • Recommended U.S. Quarter Units
  • Overview

    Course: Introduction to Fluid Mechanics
    Course Number: 251 - 15329
    ECTS credits: 6

    Calculus I & II, Linear Algebra, Physics I & II


    Fundamental and applied knowledge of the laws that determine the fluid motion and their application to problems of interest in engineering.


    1. Introduction to Fluid Mechanics
      1.1. Solids, liquids and gases.
      1.2. The fluid as a continuum: Fluid particles.
      1.3. Density, velocity and internal energy.
      1.4. Local thermodynamic equilibrium.
      1.5. Equations of state.

    2.  Flow kinematics
      2.1  Coordinate systems
      2.2 Eulerian and Lagrangian descriptions. Uniform flow. Steady flow. Stagnation points.
      2.3 Trajectories. Paths. Fluid lines, Fluid surface, Fluid Volume.
      2.4 Streamlines, stream surface and stream tubes
      2.5 Material derivative. Acceleration
      2.6 Circulation and vorticity.
      2.7 Irrotational flow. Velocity Potential
      2.8 Stream function
      2.9 Local flow deformation. Strain-rate tensor
      2.10 Convective flow
      2.11 Reynolds transport theorem.

    3. Conservation Laws
      3.1. Continuity equation in integral form
      3.2 Volume and surface forces
      3.3 Stress tensor. Navier-Poisson law
      3.4 Forces and moments on submerged bodies
      3.5 Momentum equation in integral form
      3.6 Angular momentum equation in integral form
      3.7 Heat conduction
      3.8 Energy equation in integral form. Formulation in terms of enthalpy and entropy.

    4. Conservation equations in differential form: Navier-Stokes equations.
      4.1 Continuity equation
      4.2 Momentum equation
      4.3 Energy equation. Internal energy and kinetic energy equations. Enthalpy and entropy equations.
      4.4 Initial and boundary conditions
      4.5 Bernoulli's equation.

    5. Fluid statics
      5.1 Equilibrium equations
      5.2 Hydrostatics
      5.3 Forces and moments on submerged bodies. Archimedes' Principle.
      5.4 The standard atmosphere

    6.  Dimensional analysis
      6.1 Dimensions of a physical magnitude
      6.2 Physical quantities with independent dimensions
      6.3 The Pi theorem
      6.4 Nondimensionalization of the Navier-Stokes equations; Dimensionless numbers in Fluid Mechanics
      6.5 Physical similarity. Partial similarity. Applications.

    7. Viscous flow
      7.1 Uni-directional viscous flow in channels and pipes: Poiseuille and Couette flows
      7.2 Uni-directional unsteady flows: Rayleigh's problem and Stokes' flow
      7.3 Flows dominated by viscosity in ducts and channels of slowly varying cross section
      7.4 The pipe entrance region
      7.5 Introduction to hydrodynamic lubrication. The wedge effect.


    The methodology will combine lecture classes for presentation of the fundamentals with problem solving sessions.
    The laboratory sessions, to take place in the computer room, will consist of a crash course on CFD methods to enable students to use FLUENT for solving realistic flow problems. The evaluation of the laboratory sessions will be based on an individual CFD project in which the student will be asked to address the optimized design of a simple flow system.


    Continuous evaluation will consist of two parts:
    (i) exercises and tests to be solved in groups or individually, during classes, or other activities (at least 3 activities) that will count 30% of the total mark.  
    (ii)laboratory practices, that will be assessed with a questionnaire that will be handed in at the end of each laboratory session, and that will count 10% of the total mark.
    Percentage of continuous evaluation assessment (exercises, tests, laboratory): 40
    -The final examination is will count for 60% of the total mark of the lecture course.
    Help sessions and tutorial classes will be held prior to the final exam.
    Percentage of end-of-term-examination: 60
    The minimum mark for the end-of-term exam is at least 4 out of 10.
    Final mark must be at least 5.

    The final mark is obtained in the following way:

    CFD LAb (20%)
    Part I exam (Midterm exam) (40%)
    Part II exam(40%)
    Course grade = 0.20xLAB + 0.40xP1 + 040xP2
    The continuous assessment allows to pass the course provided a Course grade equal or greater than 5.0 is achieved (a minimum 4.0 in each of the exams is required).

        G. K. Batchelor. An Introduction to Fluid Dynamics. Cambridge University Press. 1967
        L. D. Landau & E. M. Lifshitz. Fluid Mechanics. Pergamon Press. 1987
        P. A. Lagerstrom. Laminar Flow Theory. Princeton University Press. 1996

Course Disclaimer

Courses and course hours of instruction are subject to change.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.


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