Aerodynamics test on “Kelvin’s Circulation Theorem and the Starting Vortex”.
1. Is thin sheet of intense vorticity is unstable at downstream?
a) True
b) False
Answer: a
Clarification: As flow moves to the downstream, this thin sheet of intense vorticity is unstable, and it tends to roll up and form a picture similar to a point vortex. This vortex is called the starting vortex and is similar to the point vortex.
2. Is inviscid incompressible fluid has constant density?
a) False
b) True
Answer: a
Clarification: According to the kelvin’s circulation theorem an inviscid incompressible fluid of constant density be in motion in the presence of a conservative body force g per unit mass. Let c (t) denote a closed circuit that consists of the same fluid particles as time proceeds.
3. Is ‘C’ denotes a dyed circuit, composed of same fluid particles?
a) False
b) True
Answer: b
Clarification: In kelvin’s circulation theorem the C denotes a dyed circuit, composed of the same fluid particles as time proceeds, the result is not true in general if C is a closed curve fixed in space then the C does not denote the dyed circuit.
4. Is kelvin established his result subject to weaker conditions?
a) True
b) False
Answer: a
Clarification: The condition of incompressibility and constant density are not essential to unstable the intense vorticity over the sheet, hence kelvin established his results subject to a weaker condition. To which vortex are formed.
5. Is kelvin circulation does not require the dyed circuit?
a) True
b) False
Answer: a
Clarification: The kelvin circulation theorem does not require the fluid region to be simply connected, it does not require the dyed circuit C to be placed by a surface S lying wholly in the fluid, this condition is only applied to the vortex shedding off an airfoil.
6. Is circulation remains constant around the C?
a) True
b) False
Answer: a
Clarification: The inviscid equation of motion enter the proof only in helping to evaluate a line integral round C, so if viscous forces happened to be important elsewhere in the flow that is off the curve C, this would not affect the conclusion that the circulation remains constant round C.
7. Is starting vortex is essential to generate the lift on an airfoil?
a) True
b) False
Answer: a
Clarification: The shedding of a starting vortex is essential to the generation of lift on an airfoil according to the kelvin’s theorem. Kelvin’s theorem states that after airfoil starts moving, the viscous forces and vorticity will be confined to the thin boundary layer, a thin wake and the rolled-up core of the starting vortex.
8. Is circulation around the closed circuit is zero?
a) True
b) False
Answer: a
Clarification: A dyed circuit, which is large enough to have been clear of all these regions since the start of the motion. As the original state was one of rest, the circulation round that circuit will still be zero for time t. Therefore if we sketch in a line an instantaneous line in space at time t such that the curve encloses the airfoil but not the starting vortex.
9. How the circulation around the airfoil?
a) Positive
b) Negative
c) Constant
d) Slightly varies
Answer: b
Clarification: A positive circulation round an airfoil, this implies that there must be negative circulation round the airfoil. This has been observed experimentally. The vortex shedding continues until the circulation round the airfoil is sufficient to make the main irrotational flow smooth at the trailing edge.
10. Is fluid is initially in irrotational motion?
a) True
b) False
Answer: a
Clarification: An inviscid incompressible fluid of constant density move in the presence of a conservative body force. Then if a portion of the fluid is initially in irrotational motion, that portion will always be in the irrotational motion.
11. Is time rate of change of circulation around a closed curve is zero?
a) True
b) False
Answer: a
Clarification: The time rate of change of circulation around a closed curve consisting of the same fluid elements is zero, change in circulation with respect to time is zero, along which its supporting discussion is called kelvin’s circulation theorem.