### Course Meeting Times

Lectures: 2 session(s) / week, 1.5 hour(s) / session

Recitations: 1 session(s) / week, 1 hour(s) / session

Labs: By arrangement

### Course Description

This subject was originally offered in Course 13 (Department of Ocean Engineering) as 13.021. In 2005, ocean engineering became part of Course 2 (Department of Mechanical Engineering), and this subject was renumbered 2.20.

The fundamentals of fluid mechanics are developed in the context of naval architecture and ocean science and engineering. The various topics covered are: Transport theorem and conservation principles, Navier-Stokes’ equation, dimensional analysis, ideal and potential flows, vorticity and Kelvin’s theorem, hydrodynamic forces in potential flow, D’Alembert’s paradox, added-mass, slender-body theory, viscous-fluid flow, laminar and turbulent boundary layers, model testing, scaling laws, application of potential theory to surface waves, energy transport, wave/body forces, linearized theory of lifting surfaces, and experimental project in the towing tank or propeller tunnel.

### Course Prerequisites

This course is traditionally taken by advanced undergraduate and first year graduate students in the Ocean Engineering Department. The typical capabilities of the students in the course is a very broad range due to its nature. However, a student should be very comfortable with calculus - in particular, vectors, integrals and derivatives. Complex math is not required however, some may be used during lecture. A previous fluids course is highly recommended.

### Texts

Newman, J. N. *Marine Hydrodynamics*. Cambridge, MA: MIT Press, 1977. ISBN: 9780262140263.

(Not required - however, readings are assigned.)

Sabersky, R. H., A. J. Acosta, E. G. Hauptmann, and E. M. Gates. *Fluid Flow*. 4th ed. Upper Saddle River, NJ: Prentice Hall, 1998. ISBN: 9780135763728.

### Fluid Mechanics Films

It is strongly recommended that you view the films described in the book *Illustrated Experiments in Fluid Mechanics*. Cambridge, MA: MIT Press, 1972. ISBN: 9780262640121.

### Grading

ACTIVITIES | PERCENTAGES |
---|---|

Quiz 1 (1.5 hours) | 20% |

Quiz 2 (1.5 hours) | 20% |

Final Exam (3 hours) | 30% |

Homework | 20% |

Lab Assignment | 10% |

### Educational Objectives and Subject Outcomes

Objective 1: Students will be able to apply basic principles of multi-variable calculus, Newtonian physics and classical fluid mechanics in general marine hydrodynamics problems.

- Outcome 1.1 - Understand basic features of Eulerian and Lagrangian descriptions of flow.
- Outcome 1.2 - Set up and solve basic mathematical problems involving transport theorem, mass and momentum conservation.
- Outcome 1.3 - Derive and analyze continuity equation and Euler’s equation.
- Outcome 1.4 - Derive and analyze Navier-Stokes equations (for Newtonian fluids).
- Outcome 1.5 - Derive and analyze kinematic and dynamic boundary conditions.
- Outcome 1.6 - Set up and solve basic mathematical problems involving treatment of gravity force.

Objective 2: Students will demonstrate knowledge and comprehension of basic principles of marine hydrodynamics.

- Outcome 2.1 - Define verbally and mathematically the basic principles of marine hydrodynamics including
- flow similitude and model testing (dimensional analysis, derivation of flow similarity parameters, principles of model testing, steady and unsteady forces around marine structure),
- ideal rotational and irrotational fluid flows (vorticity, vortical flow, simple potential flows, D’Alembert’s paradox and lift during circulation, unsteady motion and added mass),
- viscous and boundary layer flow (plane Couette flow, Poiseuille flow and Stokes’ boundary layer, flow separation, flow past a circular cylinder and a sphere, drag on a flat plate, laminar and turbulent boundary layers, turbulent flow and Reynolds’ stress),
- kinematics of surface waves (linear progressive waves, standing waves, and superposition, dispersion relationship, group velocity, and conservation of wave energy, two-dimensional ship waves and wave resistance, Froude-Krylov wave forces on a body),
- lifting surfaces (mechanism of life generation, linearized wing theory, two-dimensional foils).

- Outcome 2.2 - Derive mathematically the basic principles of marine hydrodynamics including those listed in Outcome 2.1.
- Outcome 2.3 - Discuss in writing and orally basic principles of marine hydrodynamics including those listed in Outcome 2.1.

Objective 3: Students will be able to apply basic principles of marine hydrodynamics in simple mathematical problem solving involving marine structures/vehicles.

- Outcome 3.1 - Set up and solve simple mathematical problems involving marine hydrodynamic principles including those listed in Outcome 2.1.

Objective 4: Students will demonstrate basic knowledge of experimental methods and be able to conduct (physical) model tests of simple marine systems.

- Outcome 4.1 - Test steady and unsteady forces on ship hulls and marine structures using the water tunnel experimental system.
- Outcome 4.2 - Test kinematics of surface waves and wave forces on ships/structures using the towing tank experimental system.

Objective 5: Students will be able to design and analyze simple marine systems.

- Outcome 5.1 - Apply marine hydrodynamic principles in design and analysis of underwater vehicles and marine structures.
- Outcome 5.2 - Apply marine hydrodynamic principles in design and analysis of hydrofoils.

Objective 6: Students will be able to use computer software in analysis, modeling, and design of marine systems.

- Outcome 6.1 - Set up and solve hydrodynamics problems involving analysis, modeling, and design of marine systems using computer software such as P-Flow and AMASS.

Objective 7: Students will be able to communicate ideas in written and oral form.

- Outcome 7.1 - Create concise lab reports that clearly present verbal, mathematical, photographic, and graphical information.

Objective 8: Students will be able to work as part of a team on lab experiments.

- Outcome 8.1 - Communicate clearly in verbal and oral communications with team members.
- Outcome 8.2 - Organize tasks with team members so that work is completed in a timely manner by deadlines.

### Syllabus

0. Introduction

1. Basic Equations

- 1.1 Description of Flow
- 1.2 Mass and Momentum Conservation
- 1.3 Transport Theorem
- 1.4 Continuity Equation
- 1.5 Euler’s Equation
- 1.6 Newtonian Fluids
- 1.7 Navier-Stokes Equation
- 1.8 Boundary Conditions
- 1.9 Body Forces, Gravity

2. Similitude

- 2.1 Dimensional Analysis
- 2.2 Similarity Parameters

3. Ideal (Inviscid) Fluid Flow

- 3.1 Introduction
- 3.2 Vorticity, Kelvin’s Theorem
- 3.3 Potential Flow
- 3.4 Bernoulli’s Equation
- 3.5 Boundary Conditions
- 3.6 Stream Function
- 3.7 Simple Potential Flows
- 3.8 Method of Images
- 3.9 D’Alembert’s Paradox
- 3.10 Lift Due to Circulation
- 3.11 Unsteady Motion, Added Mass
- 3.12 Slender-Body Approx.

4. Real (Viscous) Fluid Flow

- 4.1 Flow Past a Sphere
- 4.2 Drag on a Flat Plate
- 4.3 Plane Couette Flow
- 4.4 Poiseuille Flow
- 4.5 Unsteady Flow over a Flat Plate
- 4.6 Laminar Boundary Layer
- 4.7 Turbulent Flow, Reynolds’ Stress
- 4.8 Turbulent Boundary Layer

5. Model Tests

- 5.1 Steady Flow
- 5.2 Unsteady Forces
- 5.3 Drag on a Ship Hull

6. Surface Waves

- 6.1 Introduction
- 6.2 Small Amplitude Waves
- 6.3 Plane Progressive Waves
- 6.4 Wave Dispersion
- 6.5 Mass Transport
- 6.6 Superposition
- 6.7 Group Velocity, Wave Energy
- 6.8 2D Ship Waves, Wave Resistance
- 6.9 3D Ship Wave Pattern
- 6.10 Wave Forces on a Body

7. Lifting Surfaces

- 7.1 Lift and Drag of a Foil
- 7.2 2D Lifting Surfaces, Linearized theory, Analysis and Design Problems
- 7.3 3D Lifting Surfaces
- 7.4 Propellers