Exercises 6

Question 1

What does the Euler formula say for e^iα?

Answer 1

That the flow field will rotate by an angle α

Question 2

What is the effect of multiplying a complex number by e^iβ?

Answer 2

The flow field will rotate an angle β counterclockwise

Question 3

What is the relation between the velocity potential and the complex velocity potential?

Answer 3

The velocity potential is part of the complex velocity potential w(z)=Φ+iΦ

Question 4

What is the basis of the Cauchy Riemann relations

Answer 4

The requirement that a function Φ(z) of complex variable z=x+iy to be analytic

Question 5

What can you say generally about the real and imaginary parts of an analytic function
f(z) of the complex variable z=x+iy?

Answer 5

They’re solution to laplace equation ()and therefore are harmonic solutions. This means that they are orthogonal to each other and they’re ????????

Question 6

Given a complex velocity potential
Φ(z), what is the most economic means to obtain
the velocity field?

Answer 6

dΦ/dt = u - iv

Question 7

Given a complex velocity potential
Φ(z), what is the most economic means to obtain
the stream function?

Answer 7

Im[Φ(z)]