Assignments

There are only two problems for this course. They are listed below.

 

Problem 1: Two-Dimensional Subsonic Flow Over Slender Bodies

Using regular perturbation methods, derive the partial differential equations and boundary conditions for the perturbation velocity potentials φn, n=0, 1, and 2.

Hint: For n=0, the PDE is: (1 - M20xx + φ0xy = 0

 

Problem 2: Slender Body in Subsonic Flow

Consider a subsonic flow over a slender axially body of profile section

$$R(x)=\frac{2tx(L-x)}{L^2}$$

where t is hte maximum thickness, L is the total length of the body,  and (t/L) <<1.

(a) Sketch the profile.

(b) Find the perturbation potential φ.

(c) Find the perturbation velocity component u=∂φ/∂x

(d) Find Cp.