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1.	Which condition is to be met for occurrence of stagnation point on a conical surface at an angle of attack with free stream? (Vθ, Vϕ are cross flow velocities)(a) Vθ + Vϕ = 1(b) Vθ + Vϕ = 0(c) Vθ^2 + Vϕ^2 = 0(d) (Vθ + Vϕ)^2 = 1I got this question in semester exam.I would like to ask this question from Cones at Angle of Attack in portion Three-Dimensional Flow of Aerodynamics
Answer» Right option is (c) Vθ^2 + Vϕ^2 = 0 Explanation: While working with three – DIMENSIONAL flow over a cone kept at an angle of attack with the free stream, we look at the cross – flow plane to analyze the STREAMLINES. The velocity on this plane is called cross – flow velocity. Stagnation point on the cone is SITUATED where the condition Vθ^2 + Vϕ^2 = 0 is met. In the figure, the shaded portion is the X – y plane of the cone with the outer black boundary being the SHOCK wave. The blue lines are the streamlines with different entropies. Point A is the vortical singularity and point S is the stagnation point.

2.	When the angle of attack of the cone with free stream flow is greater than the shock wave angle where is the vortical singularity present?(a) On the windward surface(b) Away from the surface(c) Inside the conical surface(d) On the leeward surfaceI have been asked this question in unit test.I would like to ask this question from Cones at Angle of Attack in division Three-Dimensional Flow of Aerodynamics
Answer» The correct option is (b) Away from the SURFACE Best explanation: When the angle of attack of the cone with free stream FLOW is more than the SHOCK wave angle, the flow converges at a point that is not on the surface, rather it is SLIGHTLY away. When the angle of attack is less than the shock wave angle, the vortical singularity lies on the WINDWARD surface.

3.	There is a large gradient of entropy near the surface of the cone.(a) True(b) FalseI got this question in an interview for job.This is a very interesting question from Cones at Angle of Attack topic in section Three-Dimensional Flow of Aerodynamics
Answer» The correct option is (a) True Easiest explanation: On the top SURFACE of the CONE, the streamlines with different entropies come together and meet at a point known as VORTICAL singularity. This leads to an ENTROPY layer on or above the surface of the cone depending on the relation between angle of attack and shock wave angle. This layer leads to a large GRADIENT of entropy normal to the streamlines.

4.	What happens when the cross – flow velocity becomes supersonic?(a) Embedded shock waves on windward side(b) Embedded shock waves on the leeward side(c) Expansion shock waves on the windward side(d) Oblique shock waves on the leeward sideThe question was posed to me in my homework.This interesting question is from Cones at Angle of Attack topic in section Three-Dimensional Flow of Aerodynamics
Answer» RIGHT option is (B) Embedded shock waves on the leeward side The explanation: When the cross – FLOW velocity (Vθ, Vϕ) increases and Vθ^2 + Vϕ^2 becomes greater than the square of free – STREAM velocity i.e. the cross – flow velocity becomes supersonic, then there is formation of embedded shock waves on the leeward portion of the cone.

5.	When does embedded shock wave appear on the cone kept at an angle?(a) Angle of attack = half cone angle(b) Angle of attack > half cone angle(c) Angle of attack < half cone angle(d) Shock wave angle = 90 degreesI have been asked this question in semester exam.Question is from Cones at Angle of Attack in chapter Three-Dimensional Flow of Aerodynamics
Answer» Correct answer is (b) Angle of ATTACK > half cone angle The best explanation: Embedded shock waves appear over the leeward SURFACE of the cone when the cross – flow velocity increases thus becoming supersonic. These waves are prevalent only when the angle of attack is greater than the half – cone angle and are USUALLY weak in NATURE.

6.	For a cone at an angle of attack, what is the shock wave a function of?(a) Polar angle(b) Azimuth angle(c) Angle of attack(d) Conical ray distanceThis question was addressed to me in my homework.I want to ask this question from Cones at Angle of Attack in section Three-Dimensional Flow of Aerodynamics
Answer» Right choice is (b) Azimuth ANGLE For explanation: Shock wave angle is the angle formed between the shock wave and the axis of the CONICAL surface. This angle is a function of azimuth angle ϕ and varies for EVERY different meridian PLANE. Streamlines that move through various points on the shock wave UNDERGO various changes in entropy around the shock since the shock wave angle of the shock wave is different.

7.	When the right – circular cone is kept at an angle of attack to the free – stream, what is it considered to be?(a) One – dimensional(b) Two – dimensional(c) Three – dimensional(d) Four – dimensionalThis question was addressed to me during an online interview.Origin of the question is Cones at Angle of Attack in section Three-Dimensional Flow of Aerodynamics
Answer» Right answer is (c) Three – dimensional Explanation: When the right – circular cone is KEPT at a ZERO angle of attack to the free – stream, it is KNOWN to be axisymmetric and is known to be a two – dimensional flow. But, when it is kept at an angle of attack, the flow no longer remains two – dimensional. The shock wave more or LESS remains the same but the flow becomes three – dimensional.

8.	How many variables is the flow field dependent on in case of flow over a cone at an angle of attack?(a) 1(b) 2(c) 3(d) 4The question was posed to me in an online interview.I would like to ask this question from Cones at Angle of Attack in chapter Three-Dimensional Flow of Aerodynamics
Answer» Right choice is (b) 2 The explanation is: For axisymmetric flow (flow over a cone at zero ANGLE of attack), the flow FIELD is only DEPENDENT on polar angle WHEREAS when the cone is kept at some angle of attack, the flow field is a function of both polar angle θ and the azimuth angle ϕ.

9.	For a supersonic flow over a right – circular cone at zero angle of attack, what are the flow properties a function of?(a) Polar angle(b) Azimuth angle(c) Mach number(d) Conical ray distanceThe question was asked in a job interview.The query is from Cones at Angle of Attack topic in section Three-Dimensional Flow of Aerodynamics
Answer» The correct option is (a) Polar angle Easiest explanation: When a right – CIRCULAR cone is kept at a ZERO angle of attack in a supersonic flow, the flow PROPERTIES are only a function of polar angle θ. It is independent of the azimuth angle ϕ and the distance from the VERTEX along conical ray.

10.	10 Flow over an elliptical cone at zero angle of attack, the fluid properties are a function of how many elements?(a) 1(b) 2(c) 3(d) 4I had been asked this question during an interview.My question comes from Cones at Angle of Attack in division Three-Dimensional Flow of Aerodynamics
Answer» CORRECT answer is (b) 2 Best explanation: UNLIKE right – circular cone kept at zero angle of attack with respect to the FREE stream, FLUID properties over an elliptical cone at zero angle of attack is dependent on two factors – Azimuth angle and polar angle.

11.	Vortical singularity exists at which part of the conical surface?(a) Leeward surface(b) Windward surface(c) Axis of the cone(d) Vertex of the coneThe question was asked in an interview for internship.My question is from Cones at Angle of Attack topic in portion Three-Dimensional Flow of Aerodynamics
Answer» Right option is (b) Windward surface For explanation: When a cone is at an ANGLE of ATTACK, the windward STREAMLINE is at ϕ = 0 deg and the leeward streamline is at ϕ = 180 deg. The flow through leeward streamline acquires an entropy of s1 which curves toward the windward surface thus wetting the ENTIRE cone. The flow through windward surface has an entropy of s2 as well as entropy s1 from the streamlines that curve upward to the windward side. This leads to the windward portion of the cone with two values of entropy which is known as a vortical singularity.

12.	Streamlines curl from the leeward to the windward surface along the conical surface when kept at an angle to the free stream.(a) True(b) FalseI got this question during an online interview.This question is from Cones at Angle of Attack topic in portion Three-Dimensional Flow of Aerodynamics
Answer» RIGHT option is (b) False Best EXPLANATION: The incoming STREAMLINES move along the CONICAL SURFACE curve from the windward surface which is the bottom portion of the cone to the leeward surface which is the upper portion of the cone.