AAE251 HW 5

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Dec 6, 2023

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1 Name Team Number AAE 251: Introduction to Aerospace Design Homework 5—Wind Tunnels, Lift, and Drag Due Tuesday February 22 nd , 11:59 PM ET on Gradescope Instructions Show all the work and clearly box your final answer. You will not receive full credit for a correct final answer if you don’t show your work. You must use the template provided. Anything that you want the graders to grade must be written legibly within the boxes provided to you. There are multiple steps involved to complete your submission on Gradescope. You can follow the step-by-step guide posted on Brightspace. Select the relevant pages of your final answer for each question in your Gradescope submission.

2 Question 1 (5 points) Consider a low-speed open-circuit subsonic wind tunnel with an inlet-to-throat area ratio of 12. The tunnel is turned on, and the pressure difference between the inlet (the settling chamber) and the test section is read as a height difference of 10cm on a U- tube mercury manometer. The density of air is 1.225kg/m ! and that of liquid mercury is 1.36 × 10 " kg/m ! . Calculate the velocity of the air in the test section. Answer 1:

3 Question 2 (8 points) You are testing a model wing of constant chord length in a low-speed subsonic wind tunnel, spanning the test section. The wing has an NACA 2412 airfoil and a chord length of 0.6 m. The parameters for the full scale and wind tunnel models are as follows: Parameters Full Scale Model Wind Tunnel Model Mach number 0.25 0.25 Density 0.019 kg/m 3 0.034 kg/m 3 Temperature 216.65 K 68.6 K Speed of sound 295 m/s 166 m/s Drag 95.6 N To be computed Assume that we can relate dynamic viscosity to temperature as follows: / #$%& ()%%*+ ,-&*+ / .)++ /01+* ,-&*+ = 1 2 #$%& ()%%*+ ,-&*+ 2 .)++ /01+* ,-&*+ 3 ! " (a) Compute the chord length of the wind tunnel model of the airfoil. (4 points) Answer 2a:

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4 (b) Calculate the drag per unit span on the wind tunnel model of the box. (3 points) Answer 2b:

5 (c) If the wing is at an angle of attack 4 = − 2 ° , calculate the lift coefficient 7 + . (1 point) Answer 2c:

6 Question 3 [8 points] You are designing a glider and use a scaled model for the wing to be tested in a wind tunnel. The model wing has a surface area of 1 m 2 and a wingspan of 5 m. The wind tunnel test conditions result in a test section airspeed of 30 m/s. The lift generated is measured by a weight balance, and the resulting lift is enough to overcome 15.45 kg. Assume the viscosity to be / = 1 .8 × 1 0 34 kg m 35 s 35 , and air density test section : = 1.225kg/m ! . Calculate the following: (i) Reynold’s number in the test section. (2 points) (ii) Lift Coefficient of the model wing. (3 points) (iii) If the glider is to fly at conditions of : = 0.526 kgm 3! , / = 1.527 × 10 34 kg m 35 s 35 and at a velocity of 50 m/s, calculate its wing span. (3 points) Answer 3:

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7 Question 4 [5 points] You decide to take your glider wing to another wind tunnel. Recall from Question 1, that the pressure difference across the inlet and exit of a wind tunnel is given by a certain manometer reading, Δℎ . The given wind tunnel has a specification 0 ≤ Δℎ ≤ 120 mm , and an inlet to test section area ratio of 10. Assume the density of mercury is 1.36 × 10 " kg/m ! , and that of air is 1.225 kg/m ! , and that the flow is incompressible. If the inlet air velocity is 25 m/s, compute the maximum velocity in the wind tunnel test section. Answer 4: