CairoUniversity
Faculty of Engineering
Aerospace Department / / First Year
Introduction to Aeronautics
Sheet (2) 2008-2009
The use of neat sketches is appreciated

For air, the gas constant R = 287.04 J/Kg.K

  1. Show that the expression ρV2/2 (called dynamic pressure) has SI-unit in N/m2.
  1. For air the dynamic viscosityμ = 1.789 x 10-5 Kg/m.s and density ρ = 1.225 kg/m3. What is the kinematic viscosityνof air? Whatis its units in SI units?
  1. A liquid compressed in a cylinder has volume of 1 liter at 1 MN/m2and a volume of 995 cm3at 2MN/m2. What is its bulk modulus of elasticity? What is the compressibility of the liquid?
  1. A fluid of viscosity coefficient μ = 0.0012 Kg/m.s flows over a surface with velocity profile given by

u = 750 y + 2.5 x 10-6 y3 m/s,

Calculate the boundary shear stress. y

u

Boundary

  1. Determine the viscosity of the fluid between the moving shaft and the fixed sleeve.

Clearance = 0.075 mm

7.5 cm

F=100N v = 0.15 m/s

30 cm

Problem 5

  1. A shaft 7.62 cm in diameter rotates concentrically in a bearing 7.67 cm in diameter and 30.3 cm long. The space between them contains oil. A torque of 3.8 N.m is required to maintain the shaft at a constant speed of rotation of 1000 rpm. Determine the viscosity coefficient of the oil.

7.67 cm

7.62 cm

30.3 cm

Problem 6

  1. At a certain height the barometric pressure is 830 mbar and the temperature is 277. Find the density of the air at this height.
  1. A car tire is filled with air at a gauge pressure of 2 atm inside a garage at 25 oC.What will be the gauge pressure in the tire at: (a) -15 oC (b) 40 oC. Assuming no charge in the volume of the tire (Assume also atmosphere pressure of 101325 N/m2)and take 1 atm = 1.01 bar.
  1. The high-pressure air storage tank of supersonic wind-tunnel has a volume of 30 m3. if air stored at a pressure of 30 bar and a temperature of 22 oC. What is the mass of air stored in the tank in Kg.
  1. A rigid tank initially contains air at 2.2 bar and 22 oC. An air compressor adds 4 Kg of air to the tank. The final conditions in the tank are 4.8 bar and 25 oC. Calculate the volume of the tank.
  1. A spherical balloon filled with helium at 6 oC and 1.5 bar has a 7.5 m diameter. What load can it support in atmospheric air at 6 oCand 1.01 bar? Neglect the balloon weight. (Rhelium = 2079 J/kg.K)
  1. The average gauge pressure and shear acting on the surfaces of a 1 m2flat plate at 7oangle of attackto a fluid stream are on uppersurface: pav = -1.2 kN/m2 and τav = 5.8x10-2 kN/m2: on lower surface: pav = 2.3 kN/m2 and τav = 7.6 x 10-2 kN/m2. Determine the lift and drag generated.

Prof. Dr. Gala B. Salem

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