INTRODUCTION TO FLIGHT - PROBLEMS

Consider the low-speed flight of the Space Shuttle as it is nearing a landing. If the air pressure and temperature at the: nose of the shuttle are 1.2 atm and 300 K, respectively, what are the density and specific volume?

density = 1.41 kg/m^3

v = 071 m^3 /kg

Consider I kg of helium at 500 K. Assuming that the total internal energy of helium is due to the mean kinetic energy of each atom summed over all the atoms, calculate the internal energy of this gas. Note: The molecular weight of helium is 4. Recall from chemistry that the molecular weight is the mass per mole of g&

1.558 x 10^6 J

Calculate the weight of air (in pounds) contained within a room 20ft long, 15ft wide, and 8 ft high. Assume standard atmospheric pressure and temperature of 2116lb/ft2 and 59°F, respectively.

183 lb

Comparing with the case of Prob. 2.3, calculate the percentage change in the total weight of air in the room when the air temperature is reduced to -1 0°F (a very cold winter day), assuming the pressure remains the same at 2116 lb/ft2•

Problem 2.3 :Calculate the weight of air (in pounds) contained within a room 20ft long, 15ft wide, and 8 ft high. Assume standard atmospheric pressure and temperature of 2116lb/ft2 and 59°F, respectively.

15.6%

If 1500 Ibm of air is pumped into a previously empty 900 ft3 storage tank and the air temperature in the tank is uniformly 70°F, what is the air pressure in the tank in atmospheres?

22.3 atm

In Prob. 2.5, assume the rate at which air is being pumped into the tank is 0.5 lbm/s. Consider the instant in time at which there is 1000 Ibm of air in the tank. Assume the air temperature is uniformly 50"'F at this instant and is increasing at the rate of 1 °F/min. Calculate the rate of change of pressure at this instant.

Problem 2.5:If 1500 Ibm of air is pumped into a previously empty 900 ft3 storage tank and the air temperature in the tank is uniformly 70°F, what is the air pressure in the tank in atmospheres?

0.0076 atm/sec

Assume that, at a point on the wing of the Concorde supersonic transport, the air temperature is -10°C and the pressure is 1.7 x 104 N/m2 . Calculate the density at this point.

0.225 kg/m^3

At a point in the test section of a supersonic wind tunnel, the air pressure and temperature are 0.5 x 10^5 N/m2 and 240 K, respectively. Calculate the specific volume.

v = 1.38 m^3/kg

Consider a flat surface in an aerodynamic flow (say a flat sidewall of a wind tunnel). The dimensions of this surface are 3ft in the flow direction (the x direction) and 1 ft perpendicular to the flow direction (they direction). Assume that the pressure distribution (in pounds per square foot) is given by p = 2116- 10x and is independent of y. Assume also that the shear-stress distribution (in pounds per square foot) is given by Tw = 90/(x + 9) 112 and is independent of y. In the above expressions, x is in feet, and x = 0 at the front of the surface. Calculate the magnitude and direction of the net aerodynamic force on the surface.

R = 6303.6

theta = 0.76 degrees

Consider an ordinary. helium-filled party balloon with a volume of2.2 ft3 . The lifting force on the balloon due to the outside air is the net resultant of the pressure distribution exerted on the exterior surface of the balloon. Us;ng this fact, Archimedes principle can be derived, namely that the upward force on the balloon is equal to the weight of the air displaced by the balloon. Assuming the balloon is at sea level, where the air density is 0.002377 slug/ft3 , calculate the maximum weight that can be lifted by the balloon. Note: The molecular weight of air is 28.8 and that of helium is 4

0.145 lb

In the four-stroke, reciprocating, internal combustion engine that powers most automobiles as well as most small general aviation aircraft, combustion of the fuel-air mixture takes place in the volume between the top of the piston and the top of the cylinder. (Reciprocating engines are discussed in Chap. 9.) The gas mixture is ignited when the piston is essentially at the end of the compression stroke (called top dead center), when the gas is compressed to a relatively high pressure and is squeezed into the smallest volume that exists between the top of the piston and the top of the cylinder. Combustion takes place rapidly, before the piston has much time to start down on the power stroke. Hence, the volume of the gas during combustion stays constant; that is, the combustion process is at constant volume. Consider the case where the gas density and temperature at the instant combustion starts are 11.3 kg/m3 :md 625 K, respectively. At the end of the constant volume combustion process, the gas temperature is 4000 K. Calculate the gas pressure at the end of the constant volume combustion. Assume that the specific gas constant for the fuel-air mixture is the same as that for pure air.

129 atm

In a gas turbine jet engine, the pressure of the incoming air is increased by flowing through a compressor; the air then enters a combustor that vaguely looks like a long can (sometimes called the combustion can). Fuel is injected in the combustor, bums with the air, and then the burned fuel-air mixture exits the combustor at a higher temperature than the air coming into the combustor. (Gas turbine jet engines are discussed in Chap. 9.) The pressure of the flow through the combustor remains relatively constant; that is, the combustion process is at constant pressure. Consider the case where the gas pressure and temperature entering the combustor are 4 x 106 N/m2 and 900 K, respectively, and the gas temperature existing the combustor is 1500 K. Calculate the gas density at (a) the inlet to the combustor and (b) the exit of the combustor. Assume the specific gas constant for the fuel-air mixture is the same as that for pure air.

15.49 kg/m^3

9.29 kg/m^3

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 4 times the inlet area, calculate the water flow velocity at the exit.

1.25 ft/s

In Prob. 4.1, calculate the pressure difference between the exit and the inlet. The density of water is 62.4 Ibm /ft3 .

Problem 4.1: 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 4 times the inlet area, calculate the water flow velocity at the exit.

22.7 lb/ft^2

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.

6.95 x 10^4 N/m^2

An instrument used to measure the airspeed on many early low-speed airplanes, principally during 1919 to 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 p 1 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, that is, the velocity of the airplane through the air. With a knowledge of the area ratio A2/A1 (a fixed design feature) and a measurement of the pressure difference p 1 - p2 , the airplane's velocity can be determined. For example, assume Ad A 1 = ~ and p 1 - p2 = 80 lb/ft2 . If the airplane is flying at standard sea level, what is its velocity?

67 ft/s

Consider the flow of air through a convergent-divergent duct, such as the venturi described in Pro b. 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 10^5 and 1.00 x 10^5 N/m2 , respectively. Calculate the flow velocity at the throat. Assume incompressible flow with standard sea-level density.

102.22 m/s

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.

216.8 ft/s

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?

3423 N/m^2

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 l atm. Calculate the temperature and density of the flow at the exit. Assume the flow is isentropic and, of course, compressible.

155 K

2.26 kg/m^3

Consider an airplane flying at a standard altitude of 5 km with a velocity of 270 m/s. At a point on the wing of the airplane, the velocity is 330 m/s. Calculate the pressure at this point.

4.19 x10^4 N/m^2

The mass flow of air through a supersonic nozzle is 1.5 lb m/s. The exit velocity is 1500 ft/s, and the reservoir temperature and pressure are !000°R and 7 atm, respectively. Calculate the area of the nozzle exit. For air, CP = 6000 ft · lb/(slug-R)

Ae = 0.0061 ft^2

A supersonic transport is flying at a velocity of 1500 mi/h at a standard altitude of 50,000 ft. The temperature at a point in the flow over the wing is 793.32°R. Calculate the flow velocity at that point.

V2 = 6.3 ft/s

A Boeing 747 is cruising at a velocity of 250 m/s at a standard altitude of 13 km. What is its Mach number?

M = 0.847