Unit 5: Brief introduction to the methods of characteristics - Practice Quiz

1 The method of characteristics is especially useful for solving which type of flow equation?

2 In a two-dimensional supersonic flow, characteristic lines are closely associated with which lines?

3 For a Mach number , the Mach angle is given by which relation?

4 What is integrated along characteristic lines in the method of characteristics?

5 The Prandtl-Glauert rule is primarily used to estimate which effect?

6 In the Prandtl-Glauert correction, the factor for subsonic flow is defined as:

7 According to the Prandtl-Glauert rule, the compressible pressure coefficient is related to the incompressible value by:

8 The Goethert rule is mainly associated with transforming which flow problem?

9 Ackeret's theory applies most directly to which type of airfoil flow?

10 In Ackeret's theory, the pressure coefficient produced by a small surface turning angle is proportional to:

11 According to linearized Ackeret theory, the lift-curve slope of a thin airfoil is:

12 Which phenomenon contributes to drag in Ackeret's supersonic airfoil theory?

13 The linear small-perturbation potential equation for two-dimensional compressible flow is commonly written as:

14 For , the linear small-perturbation equation is classified as:

15 For , the linear small-perturbation equation is classified as:

16 Why are nonlinear terms important in transonic small-perturbation theory?

17 Which graph is commonly used to show how airfoil lift changes with angle of attack?

18 What usually happens to the lift coefficient when an airfoil exceeds its stall angle?

19 Which instrument is commonly used to measure aerodynamic forces on an airfoil in a wind tunnel?

20 The pressure coefficient on an airfoil surface is obtained primarily from measurements of:

21 A two-dimensional supersonic flow has Mach number and local flow angle . What are the directions of the two characteristic lines relative to the horizontal?

22 A uniform supersonic flow with Prandtl–Meyer angle passes around a convex corner that turns the flow through . What is the downstream Prandtl–Meyer angle?

23 At the intersection of two characteristics, the compatibility invariants are and . What are the local values of and ?

24 Why can a continuous compression region in a supersonic flow eventually develop into a shock wave?

25 An incompressible calculation gives for an airfoil. Using the Prandtl–Glauert rule, what is at ?

26 An airfoil has an incompressible lift coefficient of . What lift coefficient does the Prandtl–Glauert rule predict at ?

27 Why should the Prandtl–Glauert and linearized Goethert rules not be applied very close to Mach 1?

28 For the same small panel inclination, linearized supersonic similarity gives . What is ?

29 A panel in a Mach 2 flow turns the surface into the flow by . Using Ackeret's relation, what is the approximate pressure coefficient on the compression panel?

30 According to Ackeret's thin-airfoil theory, what is the lift coefficient of a symmetric airfoil at and ?

31 A symmetric double-wedge airfoil has a small panel angle of rad and flies at Mach 2 with zero angle of attack. Using , what is its wave-drag coefficient?

32 For a thin symmetric airfoil in linearized supersonic flow, where is the aerodynamic center predicted to lie?

33 The linearized two-dimensional potential equation is . How is this equation classified at ?

34 For , what is the coefficient of in , and what is the equation type?

35 Why must a nonlinear disturbance term be retained in the transonic small-disturbance equation?

36 Two geometrically related slender bodies obey hypersonic small-disturbance similarity with parameter . If one has and thickness ratio , what thickness ratio is required at ?

37 Pressure measurements over an airfoil show nearly constant values and along the chord. Neglecting surface-slope corrections, what lift coefficient is obtained by pressure integration?

38 Wind-tunnel data give at and at . What is the experimental lift-curve slope in the linear range?

39 Which combination of measured features most strongly indicates that an airfoil has entered stall?

40 Wind-tunnel measurements show that the pitching-moment coefficient about the quarter-chord remains nearly constant as angle of attack changes within the linear range. What does this indicate?

41 In a two-dimensional, steady, irrotational supersonic flow, let be defined by , where is the flow angle and is the Mach angle. Which compatibility relation applies along ?

42 At an interior point of a planar supersonic flow, an incoming characteristic carries , while an incoming characteristic carries . What are the local values of and ?

43 Why can the planar invariants not be transferred unchanged to axisymmetric supersonic nozzle design?

44 A compression wave steepens into an oblique shock inside a characteristic mesh. What is the correct treatment of the shock?

45 An incompressible linearized calculation gives at a point on a thin airfoil. Using the Prandtl-Glauert rule at , what is the predicted compressible value?

46 For linearized subsonic flow, define . Which Goethert transformation correctly relates the compressible flow around to an incompressible flow around a transformed profile ?

47 For the same thin airfoil and incidence, the Prandtl-Glauert rule is used at and . What ratio does it predict for the lift coefficients ?

48 The Prandtl-Glauert correction diverges as . What is the physically appropriate interpretation of this singularity?

49 A surface turns a uniform flow through a small compression angle rad at . According to Ackeret's relation, what is the local pressure coefficient?

50 A symmetric double-wedge airfoil has half-angle rad and incidence rad at . Using linearized supersonic theory, which pair is predicted?

51 For a symmetric thin airfoil of arbitrary thickness distribution in linearized supersonic flow, which statement about incidence-generated lift is correct?

52 At zero incidence, a thin airfoil has upper and lower surface slopes and . Which expression gives its wave-drag coefficient in Ackeret's theory?

53 Consider the steady two-dimensional small-disturbance equation . Which classification and physical implication are correct?

54 A transonic small-disturbance model is written as What condition identifies the local sonic line in this model?

55 For , what are the characteristic slopes of in the physical plane?

56 Two geometrically similar slender bodies satisfy hypersonic small-disturbance similarity with , where is a characteristic slope. For equal , what pressure-coefficient scaling follows?

57 A low-Reynolds-number airfoil has a laminar separation bubble near its suction peak. What is the most likely combined effect of adding a transition trip upstream of the bubble?

58 Why can profile drag near the minimum-drag condition be measured more reliably by a downstream wake survey than by integrating surface pressure taps alone?

59 Two geometrically similar airfoil tests have the same Reynolds number and negligible Mach number, but their drag polars do not collapse. Which uncontrolled difference is most capable of causing this result?

60 During slow pitch-up and pitch-down tests near static stall, an airfoil shows different values at the same angle of attack despite negligible compressibility. What is the most defensible interpretation?