Exercises 2

Question 1

What real life circumstances justify using the inviscid model in which viscous effects
are ignored

Answer 1

In situations of very high Re #, when dissiaption can be ignored and stress is reduced to pressure, the viscous effects are limited to a very thin layer around the surface of interest, which is called the boundary layer. If there is NO separation, outside this area the flow behaves like an inviscid fluid and therefore, is safe to make this assumption, which greatly simplifies the calculations.

Question 2

Suppose you may describe a fluid via an inviscid model. Why is it that, in order to find
a solution to your governing equation you must specify something beyond Euler’s
equation, such as a condition of incompressibility or compressibility

Answer 2

Because when solving an iviscid problem, Euler’s equation will only solve for the velcoity, what is left to determine is the scalar quantity of pressure, so another law is needed (like incompressibility) which describes the medium in quesiton.

Question 3

What is special about typical inviscid incompressible aerodynamic problems that
allows their description via a scalar function (the potential) rather than the full vector
velocity?

Answer 3

There is typically the assumption that the air far ahead of an aircraft will be moving with uniform velcoity. Therefore, we can assume that that fluid upstream will also not be rotating (persistance of irrotationality). This way the problem is simplified to determining pressure and the velocity potential (a scalar).

Question 4

What is the name of the generalization of Newton’s equations (applying to an isolated
point particle) that applies to a continuum fluid?

Answer 4

Euler’s equation

Question 5

How is the generalization of the energy conservation equation of classical mechanics
called in fluid dynamics?

Answer 5

Bernoulli’s equation

Question 6

We shall see that the assumption of an inviscid flow with uniform velocity far away
from an obstacle leads to the prediction of zero drag and also zero lift. What especially
important flow element must be introduced to overcome the zero lift curse?

Answer 6

A vortex. The vortex is shed by the airfoil and sets the fluid aorund the airofil in circulation. No vortex = no circulation = no net fluid rotation = no possible lift