2.20 Marine Hydrodynamics Fall 2014

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Problem Set 2b

Assigned: Tuesday 09/11/14 Due: Tuesday 09/16/14

Exercise 2.6:

Supplemental Problems (http://web.mit.edu/2.20/www/supp_notes.html):

Ba1, Ba6, Ba 21

Exercise 2.7: (Choose the correct answer(s) to finish the statement):

1. The first KKT is valid for:

All flow

Incompressible flow only

Any control volume

Material volume only

2. The second KKT is valid for:

All flow

Incompressible flow only

Any control volume

Material volume only

3. Are the Euler equations, which are written as j

ij

ii

xF

Dt

vD

][,

valid for compressible or incompressible flows? Are they valid for Newtonian fluids,

Non-Newtonian fluids, both, or neither? Argue your conclusions clearly?

2.20 Marine Hydrodynamics Fall 2014

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(**) Exercise 2.8:

In a certain incompressible flow, the velocity field is given by

{

( )

( )

( )

What is the value of constant ?

(**) Exercise 2.9:

The stress tensor in a flow is given by , where . There is a mall surface with

area . The unit normal (into the surface) of the surface is given by ̂ ( ) √ . What

is the force acting on this surface?

Note: the normal vector given here is pointing into the surface.