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Unified Engineering Fall 2003 Fluids Problems F21–F
F21. As shown in class, the nonlifting irrotational flow past a circular cylinder can be represented by superimposing the uniform freestream flow and a doublet. An alternative representation is proposed using a source sheet placed on the cylinder surface as shown. The proposed sheet strength distribution about the cylinder is �(�) = − 2 V� cos �. There is no vortex sheet, so on the surface, � = 0.
actual freestream+doublet model freestream + source sheetmodel (known) (proposed)
You are to determine whether the new model is correct.
a) Determine the velocity at point A from the known exterior surface velocities for the cylinder. V� (�) = − 2 V� sin � , Vr = 0
Using the sheet jump relations,
�Vn = � , �Vs = �
determine the interior velocity at point B.
b) Again using the known exterior V� (�), Vr result at point C, use the sheet jump condition to determine the velocity at point D.
c) Compare velocities at B and D. What appears to be the fictitious velocity inside the cylinder?
d) Is the source sheet jump �Vn = � consistent with the exterior and interior normal flows everywhere on the cylinder surface? Is the proposed source-sheet model correct?
A B?
C D
F22. A long rectangular wing has span b and chord c, and hence the wing area is S = bc.
a) The wing airfoil has certain lift and drag coefficients c� and cd which are constant across the span. Determine how these relate to the wing’s overall CL and CD. (Hint: Determine L^ and D , then get L and D, then from these determine CL and CD ).
The wing airfoil has a drag polar which can be approximated by
cd � 0. 01 + 0. 015 c^3 �
in the range c� = 0. 1... 1 .2. The propulsive power P needed to overcome drag D at flight speed V� is given by P = D V�
c^ P
l
cd
b) Determine the form of the P (V�) relation in level flight, and plot it for the range c� =
- 1... 1 .2. Any constant multiplicative factors on the P and V� axes are not important – only the shape of the curve is of interest. Hint: Simplest approach is to plot P (c�) versus V (c�) with c� as a dummy parameter.
(Note: Using only the airfoil’s cd ignores other contributions such as induced drag, which become especially significant at low flight speeds!)
V
Problem M In addition to chapters 4-7 of Ashby and Jones Engineering Materials, you may also find the chapters on polymers in Ashby and Jones, Engineering Materials 2, helpful (this is a green covered book, available in the Aero-Astro library).
a) Define the term polymer and list three engineering polymers.
b) Define a thermoplastic and a thermoset.
c) Distinguish between a cross-linked and a non-cross-linked polymer.
d) What is the glass transition temperature?
e) Explain the change in moduli of polymers at the glass transition temperature.
f) What is the range of temperature in which TG lies for most engineering polymers?
g) How would you increase the modulus of a polymer?
