Chapter: Standard Atmosphere
Question 1: At 12 km in the standard atmosphere, the pressure, density, and temperature are 1.9399 x 104 N/m2, 3.1194 x 10-1 kg/m3, and 216.66 K, respectively. Using these values, calculate the standard atmospheric values of pressure, density and temperature at an altitude of 18 km, and check with
Question 2: Consider an airplane flying at some real altitude. The outside pressure and temperature are 2.65 x 104 N/m2 and 200 K, respectively. What are the pressure and density altitudes?
Question 3: During a flight test of a new airplane, the pilot radios to the ground that she is in level flight at a standard altitude of 35,000 ft. What is the ambient air pressure far ahead of the airplane?
Question 4: Consider an airplane flying at a pressure altitude of 33,500 ft and a density altitude of 32,000 ft. Calculate the outside air temperature.
Question 5: At what value of the geometric altitude is the difference h - hg equal to 2 percent of h?
Question 6: Using Toussaint's formula, calculate the pressure at a geopotential altitude of 5km.
Question 7: The atmosphere of Jupiter is essentially made up of hydrogen, H2. For H2, the specific gas constant is 4157 J/(kg)(K). The acceleration of gravity of Jupiter is 24.9 m/s2. Assuming an isothermal atmosphere with a temperature of 150 K, and assuming that Jupiter has a definable surface, calculate the altitude above that surface where the pressure is one-half the surface pressure.
Chapter: Basic Aerodynamics
Question 1: Consider the incompressible flow of water through a divergent duct. The inlet velocity and area are 5 ft/s and 10 ft2, respectively. If the exit area is four times the inlet area, calculate the water flow velocity at the exit.
Question 2: In the above problem, calculate the pressure difference between the exit and the inlet. The density of water is 62.4 lbm/ft3.
Question 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.
Question 4: An instrument used to measure the airspeed on many early low-speed airplanes, principally during 1919-1930, was the venturi tube. This simple device is a convergent-divergent duct. (The front section's cross-sectional area A decreases in the flow direction, and the back section's cross-sectional 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 A1 and A2 denote the inlet and throat areas, respectively. Let p1 and p2 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 V1 is essentially the same as the freestream velocity, i.e., the velocity of the airplane through the air. With a knowledge of the area ratio A1/A2 (a fixed design feature) and a measurement of the pressure difference p1 - p2, the airplane's velocity can be determined. For example, assume A2/A1 = 1/4, and p1 - p2 = 80 lb/ft2. If the airplane is flying at standard sea level, what is its velocity?
Question 5: Consider the flow of air through a convergent-divergent duct, such as the venturi described in Prob. 4.4. The inlet, throat, and exit areas are 3, 1.5, and 2 m2, respectively. The inlet and exit pressures are 1.02 x 105 and 1.00 x 105 N/m2, respectively. Calculate the flow velocity at the throat. Assume incompressible flow with standard sea-level density.
Question 6: An airplane is flying at a velocity of 130 mi/h at a standard altitude of 5000 ft. At a point on the wing, the pressure is 1750.0 lb/ft2. Calculate the velocity at that point, assuming incompressible flow.
Question 7: Imagine that you have designed a low-speed airplane with a maximum velocity at sea level of 90 m/s. For your airspeed instrument, you plan to use a venturi tube with a 1.3:1 area ratio. Inside the cockpit is an airspeed indicator - a dial that is connected to a pressure gauge sensing the venturi tube pressure difference p1 - p2 and properly calibrated in terms of velocity. What is the maximum pressure difference you would expect the gauge to experience?
Question 8: A supersonic nozzle is also a convergent-divergent duct, which is fed by a large reservoir at the inlet to the nozzle. In the reservoir of the nozzle, the pressure and temperature are 10 atm and 300 K, respectively. At the nozzle exit, the pressure is 1 atm. Calculate the temperature and density of the flow at the exit. Assume the flow is isentropic and, of course, compressible.
Chapter: Airfoils, Wings, and Other Aerodynamic Shapes
Question 1: Consider a rectangular wing mounted in a low-speed subsonic wing tunnel. The wing model completely spans the test section so that the flow "sees" essentially an infinite wing. If the wing has a NACA 23012 airfoil section and a chord of 0.3 m, calculate the lift, drag, and moment about the quarter chord per unit span when the airflow pressure, temperature, and velocity are 1 atm, 303 K, and 42 m/s, respectively. The angle of attack is 8°.