Questions and Answers of Fundamentals Of Aerodynamics

Consider a hypersonic vehicle with a spherical nose flying at Mach 20 at a standard altitude of 150,000 ft, where the ambient temperature and pressure are 500◦R and 3.06 lb./ft2, respectively. At
Consider a high-speed vehicle flying at a standard altitude of 35 km, where the ambient pressure and temperature are 583.59 N/m2 and 246.1 K, respectively. The radius of the spherical nose of the
Consider a flat plate at zero angle of attack in a hypersonic flow at Mach 10 at standard sea level conditions. At a point 0.5 m downstream from the leading edge, the local shear stress at the wall
Starting with Equations (1.7), (1.8), and (1.11), derive in detail Equations (1.15), (1.16), and (1.17). N' == TE -TE * (P, cos 0 + T₁ sine) ds, + ² (p, cos 0 — , sine) ds;
Consider a light, single-engine, propeller-driven airplane similar to a Cessna Skylane. The airplane weight is 2950 lb and the wing reference area is 174 ft2. The drag coefficient of the airplane CD
The purpose of this problem is to give you a feel for the magnitude of Reynolds number appropriate to real airplanes in actual flight. a. Consider the DC-3 shown in Figure 1.1. The wing root chord
For the design of their gliders in 1900 and 1901, the Wright brothers used the Lilienthal Table given in Figure 1.65 for their aerodynamic data. Based on these data, they chose a design angle of
Consider the Space Shuttle during its atmospheric entry at the end of a mission in space. At the altitude where the Shuttle has slowed to Mach 9, the local heat transfer at a given point on the lower
In Example 2.1, the statement is made that the streamline an infinite distance above the wall is straight. Prove this statement. The subsonic compressible flow over a cosine-shaped (wavy) wall is
Consider the existence of a forward-facing axial aerodynamic force on an airfoil. Can a forward-facing axial force exist on a flat plate at an angle of attack in a flow? Thoroughly explain your
Consider a venturi with a small hole drilled in the side of the throat. This Chole is connected via a tube to a closed reservoir. The purpose of the venturi is to create a vacuum in the reservoir
The Kutta-Joukowski theorem, Equation (3.140), was derived exactly for the case of the lifting cylinder. In Section 3.16 it is stated without proof that Equation (3.140) also applies in general to a
Consider the streamlines over a circular cylinder as sketched at the right of Figure 3.26. Single out the first three streamlines flowing over the top of the cylinder. Designate each streamline by
Consider the flow field over a circular cylinder mounted perpendicular to the flow in the test section of a low-speed subsonic wind tunnel. At standard sea level conditions, if the flow velocity at
Prove that the flow field specified in Example 2.1 is not incompressible; i.e., it is a compressible flow as stated without proof in Example 2.1. and where u = Voo v = h 2π [1 + 127 - l 2π.χ (cos
Starting with Equation (4.35), derive Equation (4.36). ["(dll.) = Poc Vso [^2y (4) d - V∞ - M₁E = - * 5 (dL) = LE (4.35)
Starting with Equations (4.35) and (4.43), derive Equation (4.62). MLE = - [ 5 (dL) =-PxV₂0 [°* &Y (₁ 0 0 == Voo 51 ξγ(ξ) dξ (4.35)
For the NACA 2412 airfoil, the lift coefficient and moment coefficient about the quarter-chord at −6° angle of attack are −0.39 and −0.045, respectively. At 4° angle of attack, these
For the airfoil in Problem 4.11, calculate the value of the circulation around the airfoil.Data from Problem 4.11:Consider again the NACA 2412 airfoil discussed in Problem 4.10. The airfoil is flying
The question is often asked: Can an airfoil fly upside-down? To answer this, make the following calculation. Consider a positively cambered airfoil with a zero-lift angle of −3°. The lift slope is
The airfoil section of the wing of the British Spitfire of World War II fame (see Figure 5.19) is an NACA 2213 at the wing root, tapering to an NACA 2205 at the wing tip. The root chord is 8.33 ft.
For the conditions given in Problem 4.15, a more reasonable calculation of the skin friction coefficient would be to assume an initially laminar boundary layer starting at the leading edge, and then
Consider a finite wing with an aspect ratio of 6. Assume an elliptical lift distribution. The lift slope for the airfoil section is 0.1/degree. Calculate and compare the lift slopes for (a) a
Repeat Problem 5.6, except for a lower aspect ratio of 3. From a comparison of the results from these two problems, draw some conclusions about the effect of wing sweep on the lift slope, and how the
In Problem 1.19 we noted that the Wright brothers, in the design of their 1900 and 1901 gliders, used aerodynamic data from the Lilienthal table given in Figure 1.65. They chose a design angle of
Consider the Supermarine Spitfire shown in Figure 5.19. The first version of the Spitfire was the Mk I, which first flew in 1936. Its maximum velocity is 362 mi/h at an altitude of 18,500 ft. Its
If the elliptical wing of the Spitfire in Problem 5.9 were replaced by a tapered wing with a taper ratio of 0.4, everything else remaining the same, calculate the induced drag coefficient. Compare
Consider the Spitfire in Problem 5.9 on its landing approach at sea level with a landing velocity of 70 mi/h. Calculate the induced drag coefficient for this low-speed case. Compare your result with
Prove that three-dimensional source flow is irrotational.
Repeat Problem 7.10, considering the flow of Problem 7.11Data from Problem 7.10:Calculate the percentage error obtained if Problem 7.9 is solved using (incorrectly) the incompressible Bernoulli
Bernoulli’s equation, Equation (3.13), (3.14), or (3.15), was derived in Chapter 3 from Newton’s second law; it is fundamentally a statement that force = mass × acceleration. However, the terms
At a given point in a flow, T = 300 K, p = 1.2 atm, and V = 250 m/s. At this point, calculate the corresponding values of p0, T0, p∗, T ∗, and M∗.
When the Apollo command module returned to earth from the moon, it entered the earth’s atmosphere at a Mach number of 36. Using the results from the present chapter for a calorically perfect gas
The stagnation temperature on the Apollo vehicle at Mach 36 as it entered the atmosphere was 11,000 K, a much different value than predicted in Problem 8.17 for the case of a calorically perfect gas
Prove that the total pressure is constant throughout an isentropic flow.
Consider the supersonic flow over a flat plate at an angle of attack, as sketched in Figure 9.35. As stated in Section 9.7, the flow direction downstream of the trailing edge of the plate, behind the
Consider a two-dimensional duct with a straight horizontal lower wall, and a straight upper wall inclined upward through the angle θ = 3◦. The height of the duct entrance is 0.3 m. A uniform
Repeat Problem 9.18, except with θ = 30◦. Again, we will use these results to compare with a quasi-one-dimensional calculation in Problem 10.16. The reason for repeating this calculation is to
Consider a Mach 3 flow at 1 atm pressure initially moving over a flat horizontal surface. The flow then encounters a 20 degree expansion corner, followed by a 20 degree compression corner that turns
The purpose of this problem is to explain what causes the dramatic white cloud pattern generated in the flow field over the F/A-18C Hornet shown on the cover of this book. This problem is both a
Return to Problem 9.18, where the average Mach number across the two-dimensional flow in a duct was calculated, and where θ for the upper wall was 3◦. Assuming quasi-one dimensional flow,
Return to Problem 9.19, where the average Mach number across the two-dimensional flow in a duct was calculated, and where θ for the upper wall was 30◦. Assuming quasi-one-dimensional flow,
A horizontal flow initially at Mach 1 flows over a downward-sloping expansion corner, thus creating a centered Prandtl-Meyer expansion wave. The streamlines that enter the head of the expansion wave
Consider a centered expansion wave where M1 = 1.0 and M2 = 1.6. Using the method developed in Problem 10.17, plot to scale a streamline that passes through the expansion wave.Data from Problem
In Problem 11.8, the critical Mach number for a circular cylinder is given as Mcr = 0.404. This value is based on experimental measurements, and therefore is considered reasonably accurate. Calculate
Using the same flight conditions and the same value of the skin-friction coefficient from Example 12.3, and the results of Problem 12.6, calculate the maximum lift-to-drag ratio of the flat plate
Consider a flat plate at an angle of attack in a viscous supersonic flow; i.e., there is both skin friction drag and wave drag on the plate. Use linear theory for the lift and wave-drag coefficients.
The result from Problem 12.6 demonstrates that maximum lift-to-drag ratio decreases as the Mach number increases. This is a fact of nature that progressively causes designers of supersonic airplanes
Consider a flat plate at an angle of attack in an inviscid supersonic flow. From linear theory, what is the value of the maximum lift-to-drag ratio, and at what angle of attack does it occur?
Equation (12.24), from linear supersonic theory, predicts that cd for a flat plate decreases as M∞ increases? Does this mean that the drag force itself decreases as M∞ increases? To answer this