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Unformatted text preview: FLIGHT MECHANICS Exercise Problems CHAPTER 4 Problem 4.1 • Consider the incompressible flow of water through a divergent duct. The inlet velocity and area are 5 ft/s and 10 ft 2 , respectively. If the exit area is 4 times the inlet area, calculate the water flow velocity at the exit. Solution 4.1 s ft A A V V V A V A m / 25 . 1 4 1 5 2 1 1 2 2 2 2 1 1 1 = = = = = ρ ρ Problem 4.2 • 4.2 In the above problem calculate the pressure difference between the exit and the inlet. The density of water is 62.4 Ibm/ft 3 . Solution 4.2 2 2 2 1 2 3 2 2 2 1 1 2 / 7 . 22 2 25 . 1 5 94 . 1 / 94 . 1 2 . 32 4 . 62 2 2 1 2 1 ft lb p p ft slug V V p p VdV dp v v p p =  = = =  = = + ∫ ∫ ρ ρ ρ Problem 4.3 • Consider an airplane flying with a velocity of 60 m/s at a standard altitude of 3 km. At a point on the wing, the airflow velocity is 70 m/s. Calculate the pressure at this point. Assume incompressible flow. Solution 4.3 H.W. Problem 4.4 • An instrument used to measure the airspeed on many early lowspeed airplanes, principally during 1919 to 1930, was the venturi tube. This simple device is a convergent  divergent duct (The front section's crosssectional area A decreases in the flow direction, and the back section's crosssectional area increases in the flow direction. Somewhere in between the inlet and exit of the duct, there is a minimum area, called the throat.) Let A 1 and A 2 denote the inlet and throat areas, respectively. Let p 1 and p 2 be the pressures at the inlet and throat, respectively. The venturi tube is mounted at a specific location on the airplane (generally on the wing or near the front of the fuselage), where the inlet velocity V, is essentially the same as the freestream velocity that is, the velocity of the airplane through the air. With a knowledge of the area ratio A 2 /A 1 (a fixed design feature) and a measurement of the pressure difference p 1 p 2 the airplane's velocity can be determined. For example, assume A 2 /A 1 =1/4 and p 1 p 2 = 80 Ib/ ft 2 . If the airplane is flying at standard sea level, what is its velocity? Solution 4.4 H.W. Problem 4.5 Consider the flow of air through a convergentdivergent duct, such as the venturi described in Prob. 4.4. The inlet, throat, and exit areas are 3, 1.5, and 2 m 2 respectively. The inlet and exit pressures are 1.02 x 10 5 and 1.00 x 10 5 N/m 2 , respectively. Calculate the flow velocity at the throat. Assume incompressible flow with standard sealevel density. Solution 4.5 ( 29 s m V A A V A A p p V A A V V V p V p / 22 . 102 1 2 3 225 . 1 10 ) 00 . 1 02 . 1 ( 2 5 . 1 3 1 ) ( 2 2 2 2 5 1 2 1 2 2 3 1 3 1 1 3 1 1 3 2 3 3 2 1 1 =   = =  = = + = + ρ ρ ρ Note that only a pressure change of 0.02 atm produce this high speed Problem 4.6 An airplane is flying at a velocity of 130 mi/h at a standard altitude of 5000 ft. At a mi/h at a standard altitude of 5000 ft....
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 Spring '09
 MMEC
 Dynamics, Fluid Dynamics, Aerodynamics, Mach number, γ γ

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