MEEG 432 Aerodynamics Fall 2014 Homework No. 2 Due: 7:00 p.m Thursday 2 October 1.(Review) Consider a 2-dimensional incompressible velocity field where the x and y components of velocity are given by u = cx and v = -cy where c is a constant. (a) Obtain a stream function ψ for this flow and draw some streamlines in the four quadrants of the (x,y) plane. Label each streamline with the appropriate value of ψ. (b) Show that the vorticity for this flow is zero. (c) What is the circulation Γ around the contour x 2 + y 2 =1? How do you know? (d) Find the velocity potential for this flow. (e) Show, for this flow, that the streamlines are perpendicular to the equipotentials. 2. Anderson problem 2.3 3. (a) A two-dimensional object is placed in an infinite stream. The velocity profiles are as shown. Find an expression for the drag force (per unit length) on the object, in terms of U,h and the constant density ρ. You may assume that the pressure is equal to its free-stream value at the two stations where the velocity profiles are shown. (b) Assuming that the fluid is air at sea-level conditions, U = 200 ft/s, and h = 10 ft, find the drag force per foot in lbs. U 2h U U/4 6h 4. Please attach your typed one-page outline of the term paper that you would like to write giving the title and 6 or 7 items corresponding to the subtopics that you intend to treat. Also indicate some sources of information. There is no grade for this outline. I will make suggestions to help you. See handout for list of topic suggestions.

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MEEG 432 AerodynamicsFall 2014

Homework No. 2 Due: 7:00 p.m Thursday 2 October

1.(Review) Consider a 2-dimensional incompressible velocity field where thex andy componentsof velocity are given byu = cx andv = −cy where c is a constant.

(a) Obtain a stream functionψ for this flow and draw some streamlines in the four quadrants of the(x, y) plane. Label each streamline with the appropriate value ofψ.

(b) Show that the vorticity for this flow is zero.

(d) Find the velocity potential for this flow.

(e) Show, for this flow, that the streamlines are perpendicular to the equipotentials.

2. Anderson problem 2.3

3. (a) A two-dimensional object is placed in an infinite stream. The velocity profiles are as shown.Find an expression for the drag force (per unit length) on theobject, in terms ofU, h and theconstant densityρ. You may assume that the pressure is equal to its free-streamvalue at the twostations where the velocity profiles are shown.

(b) Assuming that the fluid is air at sea-level conditions,U = 200 ft/s, andh = 10 ft, find the dragforce per foot in lbs.

U/4 6h

4. Please attach your typed one-page outline of the term paper that you would like to write givingthe title and 6 or 7 items corresponding to the subtopics thatyou intend to treat. Also indicate somesources of information. There is no grade for this outline. Iwill make suggestions to help you. Seehandout for list of topic suggestions.