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EMCH 578 Introduction to Aerodynamics

EMCH 744 Aerodynamics and Flight Mechanics

Mid Term Exam

March 4th, 2015 (4:25 pm – 5:45 pm)

Total time: 1 hour 20 minutes

Name: Graduate/Undergraduate

(Show all steps of your work) Total points 100 for Undergraduate, Total points 125 for Graduate Students, Circle the appropriate student level section at the top.

Score

Prob 1 25 pts Prob 2 25 pts Prob 3 25 pts Prob 4 25 pts Prob 5 25 pts Total 100/125 points

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1) Consider two different flows over geometrically similar airfoil shapes, one airfoil being twice the size of the other. The flow over the smaller airfoil has free stream properties given by Tα = 200K, ρα =1.23 kg/m3, and Vα= 100 m/s. The flow over the larger airfoil is described by Tα = 800K, ρα =1.739 kg/m3, and Vα= 200 m/s. Assume that both the dynamic viscosity and speed of sound are proportional to / . Are the two flows dynamically similar? (25 points)

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2) The velocity field for the fully developed viscous flow in duct (Hagen Poiseuille flow) is as

follows: = − , = 0, = 0

Where the pressure gradient along the x direction is a constant and h is the height/diameter

of the duct. Is the flow rotational or irrotational? Why? For a duct flow does the Bernoulli’s equation hold true? (25 points)

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3) A long pipe (with a reducer) section is attached to a large tank (as shown in Figure). The diameter of the tank is 5.0 m, the diameter of the pipe is 20 cm at station 1 and 10 cm at station 2. The effects of viscosity are such that the velocity (u) maybe considered constant across the cross section at the surface (s) and at station 1, but varies with the radius at station 2 such that, = (1 − ), where Uo is the velocity

at the center line, R2 is the radius of the pipe at station 2, and r the radial coordinate. If the density of the liquid is 0.85 g/cm3and the mass flow rate is 10 kg/s, what are the velocities at s and 1 and what is the value of Uo? (25 points)

Figure: Problem 3

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4) Velocity profiles are measured at the upstream end (surface 1) and at the downstream end (surface 2) of a rectangular control volume as shown in the figure. If the flow is incompressible, two dimensional, and steady, what is the total volumetric flow rate across the horizontal surfaces (surfaces 3 and 4)? (25 points)

Figure: Problem 3

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5) For an irrotational flow, show that Bernoulli’s equation (consider Bernoulli’s equation without the body force term) holds between any points in the flow, not just along a streamline. (25 points) (Question 5 is only for graduate students)

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Reference values ρSL= 1.2250 kg/m3 (0.002377 slug/ft3), pSL =1.01325 x 105 N/m2 (2116 lb/ft2)

and μSL = 1.7894 x 10-5 N-s/m2 (3.737 x 10-7 lb-s/ft2), TSL = 288.15 K.