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Unformatted text preview: MAE 103 FINAL EXAM (Closed Book, Closed Lecture Notes, 2page notes allowed) Please note : • There are 6 problems all together. CHOOSE 5 OUT OF 6 . If you solve all of them, I will grade first 5 only. • Show your work and your thought process even if you cannot complete a problem so that I can give you partial credit for your effort. However, scratch out those parts that you do not want me to read . Otherwise, some points may be taken off for wrong statements. Also, you will get no credit if your writing is illegible! • You may need the following information: – Geometric properties of a rectangle with its height a and width b : I xx = ba 3 / 12, I yy = ab 3 / 12, I xy = 0. – The center of pressure relative to the centroid: y cp = I xx sin θ h cg A , x cp = I xy sin θ h cg A , where θ is measured from the horizontal surface (e.g., θ = π/ 2 for a vertical plane). – Reynolds Transport Theorem: d d t B sys = ∂ ∂t integraldisplay cv ρb d V + integraldisplay cs ρb ( w · n ) d A . – absolute temperature: K = ◦ C + 273 in Kelvin, or ◦ R = ◦ F + 460 in Rankine. – 1 horse power (hp) = 550 ftlb/s. – gas constant for air, R air = 287 m 2 s 2 · K = 1716 ft 2 s 2 · ◦ R . – Moody chart and tables for isentropic flow and normal shock for a perfect gas with k =1.4. Name: 1 (20) 2 (20) 3 (20) 4 (20) 5 (20) 6 (20) Total: 1 1. (20pt) The rectangular submarine escape hatch of width w and length L will open when the constant pressure inside the chamber, p i , exceeds a critical value p i c . The hatch has negligible mass and it is hinged without friction at point A , which is a depth D below the surface. Find p i c in terms of w,L,D,ρ,g and θ . Note that the geometric properties needed to solve this problem are listed on the first page. g A L D θ Water density ρ Escape hatch Submarine chamber p i p a 2 2. (20 pt) A propeller is placed in a constant circular duct of diameter D as shown below. The flow is steady and the fluid has a constant density, ρ . The pressure p 1 and p 2 are uniform across the entry and exit areas, and the velocity profile are as shown. (a) Find U m in terms of U 1 . (b) Find the thrust T produced by the propeller on the fluid in terms of U 1 ,ρ,D,p 1 and p 2 . x r D p 1 ,U 1 p 2 ,U 2 = U m 2 r D Propeller Circular duct 3 3. (20 pt) A pipe is attached to a large water reservoir. The head loss in the pipe is equal to k ( V 2 p / 2 g ), where V p is the velocity in the pipe and k is a given constant. A nozzle is attached to the pipe and water issues from that nozzle into the atmosphere. The top of the reservoir is exposed to the atmosphere. The water level in the reservoir is maintained at a height h above the nozzle. The crosssectional area of the pipe is A p , and the ratio of the area of the jet to that of the pipe is r ( A j /A p = r ). Neglect nozzle losses and other losses....
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 Winter '09
 MAE103
 Fluid Dynamics, Aerodynamics, normal shock, perfect gas

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