2.016 HW #5 Out: October 18, 2005 Due: October 25, 2005
1) Expand the following for i=1,2,3, j=1,2,3, and k=1,2,3, and write them in vector notation. Recall for tensor notation, letters that appear only once imply expansion r into a vector, and repeated l
2.016 HW #4 Out: October 4, 2005 Due: October 18, 2005
1) A sphere of volume V in a fluid of density is located at a point (0, L, 0) with respect to a certain coordinate system. In terms of this coordinate system, identify whether each of the 6x6 added ma
2.016 Homework #3
Prof. A. Techet; Fall 2005 Issued: September 27, 2005 Due: October 4, 2005 Problem 1: Unsteady Potential Flow and Added Mass a. Derive added mass around a sphere. Hint: if you print out the Added Mass Derivation handout, the math is all
2.016 Hydrodynamics Prof. Alex Techet Fall 2005 HW #2 Out: September 20, 2005 Due: September 27, 2005 Problem 1: Buoyancy (3 pts.) An AUV is designed as shown below. It has three, hollow, cylindrical canisters arranged in an upside down triangle. The cyli
2.016 Hydrodynamics Prof. Alex Techet Fall 2005 HW #1 Out: 13 Sept 2005 Due: 20 Sept 2005
Problem 1: Which of the following are isotropic? Why or why not? a) c) Temperature Shear stress b) Pressure d) Dynamic viscosity Problem 2: At a particular point in
Free-Surface Waves
2.016 Fall 2005
Prof. A. Techet
Dept. Mechanical Engineering
Ocean Waves
Photos removed for copyright reasons.
Wave Breaking
Photos removed for copyright reasons.
Breaking wave in a Laboratory
PIV under the interface
Plunging Breaker
W
Added Mass Force
Formulation
Prof. A. Techet
Added Mass Tensor
Vector Velocity
Accelerations:
Added Mass Forces and Moments
Tensor Notation
2
+ 1 3
1
2
_ 3
Einstein Summation
Sum up the terms for all i,j,k,l options:
For example take: j =1 for the Fo
2.016 Hydrodynamics
Reading #8
2.016 Hydrodynamics
Prof. A.H. Techet
1. Froude Krylov Excitation Force
Ultimately, if we assume the body to be sufficiently small as not to affect the pressure field due to an incident wave, then we can neglect diffraction
2.016 Hydrodynamics
Reading #7
2.016 Hydrodynamics
Prof. A.H. Techet Fall 2005
Free Surface Water Waves
I. Problem setup
1. Free surface water wave problem. In order to determine an exact equation for the problem of free surface gravity waves we will assu
2.016 Hydrodynamics
Reading #6
2.016 Hydrodynamics
Prof. A.H. Techet
Added Mass
For the case of unsteady motion of bodies underwater or unsteady flow around objects, we must consider the additional effect (force) resulting from the fluid acting on the str
2.016 Hydrodynamics
Reading #5
2.016 Hydrodynamics
Prof. A.H. Techet
Fluid Forces on Bodies
1. Steady Flow In order to design offshore structures, surface vessels and underwater vehicles, an understanding of the basic fluid forces acting on a body is need
2.016 Hydrodynamics
Reading #4
2.016 Hydrodynamics
Prof. A.H. Techet
Potential Flow Theory
"When a flow is both frictionless and irrotational, pleasant things happen." F.M.
White, Fluid Mechanics 4th ed.
We can treat external flows around bodies as invici
2.016 Hydrodynamics
Reading #3
2.016 Hydrodynamics
Prof. A.H. Techet
Introduction to basic principles of fluid mechanics
I. Flow Descriptions
1. Lagrangian (following the particle):
In rigid body mechanics the motion of a body is described in terms of the
2.016 Hydrodynamics
Reading #2
2.016 Hydrodynamics
Prof. A.H. Techet
Pressure effects
Fluid forces can arise due to flow stresses (pressure and viscous shear), gravity forces, fluid acceleration, or other body forces. For now, let us consider a fluid in s
2.016 Hydrodynamics
Reading #1
2.016 Hydrodynamics
Prof. A.H. Techet
Why study Marine Hydrodynamics?
The Earth's oceans are one of our least explored resources. About 70-75% of the Earth's surface is covered by water. The total area of water covering the
Massachusetts Institute of Technology
2.016 Hydrodynamics Fall 2005
Surface Waves Kinematics
Friday 14 October 2005, 9-11am *Ocean Engineering Towing Tank *
Introduction
This lab is in an investigation into some of the properties of surface gravity waves.
Object Impact on the Free Surface and Added Mass Effect 2.016 Laboratory Fall 2005 Prof. A. Techet Introduction to Free Surface Impact
Free surface impact of objects has applications to ocean engineering such as ship slamming hydrodynamics. The simplest g
2.016: Hydrodynamics
Alexandra H. Techet
Dept. of Mechanical Engineering Lecture 1
MIT Dept. Mechanical Engineering, 2005
What is Hydrodynamics?
Hydrodynamics v. Aerodynamics
Water is almost 1000 times denser than air!
Marine Hydrodynamics
Design of u
2.016 Hydrodynamics Fall 2005 Prof. A. Techet
Out: November 29, 2005 Due: December 6, 2005
1) Consider the following control volume around a propeller where we have defined a slipstream boundary, such that the streamline that separates the flow going thro
0.47 0.4 Strouhal Number (S) 0.3 0.2 0.1 0 40 102 Rough Surface Smooth Surface
103
104
105
106
107
Reynolds Number (UD/)
Figure by MIT OCW.
2) A fishnet is made of 1mm-diameter strings knotted together into 2cm x 2cm squares. Estimate the horsepower requi
2.016 HW #6 Out: November 1, 2005 Due: November 8, 2005
1) Concept questions: a. The majority of ocean waves are caused by what force? Discuss. b. On the "Motion of a Fluid Particle" slide in the Free-Surface Waves handout, two equations are given for the