Code No: 44049

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD IIII B.TECH SEM SUPPLEMENTARY EXAMINATIONS FEBRUARY2010 - 2010 B.TechIIII Semester Supplimentary Examinations,February AERODYNAMICS - I Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ?????

i. A point vortex ii. A constant strength vortex panel iii. A linearly varying strength vortex panel

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1. (a) Explain difference between

Make a comparison of the 3 in judgment and bring out the conclusions.

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(b) A planar horse shoe vortex is placed symmetrically along OX on the X-axis With its BV aligned with Y-axis. Determine a general expression for the downwash in the plane of symmetry. [8+8] 2. (a) An airfoil is kept at 5 degrees angle of attack in a flow. The lift and drag coefficients are 3.0 and 0.2 respectively. Find the normal and axial forces.

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(b) The normal force is acting at the quarter chord point. Find the moment on the airfoil at the leading edge of the airfoil. [8+8] 3. (a) Explain in detail how the combination of a uniform and a doublet produces the flow over a circular cylinder. (b) Derive an expression for pressure coefficient over a circular cylinder.

[10+6]

4. (a) Lifting surface theory predicts better lift distribution on a wing with a low aspect ratio and of any type of given planform’. Can you demonstrate the verification of the statement?

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(b) Compare the formulation in (a) above with that in the classical lifting line theory with details. [8+8]

5. Define and derive the equation for the vorticity of a flow. Hence prove that the vorticity is equal to the curl of the velocity and twice the angular velocity. [16]

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6. (a) Derive Rthe fundamental equation of thin airfoil theory, (1/2π) [{γ(ξ)dξ}/{x−ξ?}] = V{α−(dz/dx)} where the integration is carried out from the leading edge to the trailing edge of a symmetrical airfoil. (b) State and explain the limitations of thin airfoil theory.

[12+4]

7. (a) Show that the transformation ζ= z + (b2 /z) =ξ+iη leads to ζ= (r + b2 /r)cosθ+i(r − b2/r)sinθ, where z is complex while ξ and η are real. (b) Hence show that ζ = f (z) transforms a circle a symmetrical airfoil if the origin of the circle is a (be, h) where b, h and e are constants. [6+10] 1

Code No: 44049

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8. How is downwash produced on a finite wing? Explain its effect on the wing.

[16]

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.TECH II SEM SUPPLEMENTARY EXAMINATIONS FEBRUARY - 2010 II B.Tech II Semester Semester Supplimentary Examinations,February 2010 AERODYNAMICS - I Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Starting from fundamentals, derive the expression for the angular velocity of a two dimensional flow. Hence derive the expression for irrotationality condition. [16]

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2. (a) A 2-d point source with a strength 50 units is located at T( 1.0,1.52). obtain the velocity potential φ (x,z) and velocity components (u.v) at P( 3.5,2.5). (b) What are the preliminary considerations prior to establish a numerical solution to a non lifting problem using “source panel method” technique. Hence describe types of boundary conditions to be satisfied by such a method. [8+8]

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3. Explain the Aerodynamics of a finite wing.

[16]

4. Why are different airfoils and wings required for subsonic aircraft and supersonic aircraft? Explain using neat sketches. Is it possible to have different airfoils for a supersonic aircraft while it flies in subsonic and supersonic regimes? [16]

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5. What is extended lifting line theory? Explain a numerical solution for a finite wing of given planform and geometric twist, with different airfoil sections at different spanwise stations. [16] 6. Derive Rthe fundamental equation of thin airfoil theory, (1/2π) [{γ(ξ)dξ}/{x−ξ}] = V{α−(dz/dx)}, where the integration is carried out from the leading edge to the trailing edge of an airfoil and prove that the lift coefficient is proportional to angle of attack for a cambered airfoil. [16]

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7. Consider a velocity field where the x and y components of velocity are given by u = cx and v = cy, where c is a constant. Assume the flow to be incompressible, calculate the stream function and velocity potential. Using the results, show that lines of constant φ are perpendicular lines of constant ψ. [16]

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8. A constant strength vortex panel of strength 50 units is located on the axis from X1=3.5 to X2=6.65. Determine the influence of this vortex panel at a point P (4.5, 4.5) to evaluate V (u, w). Develop the expressions used for determining (a) Velocity potential

(b) Velocity components.

[8+8] ?????

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD II B.Tech II Semester Supplimentary Examinations,February 2010 II B.TECH II SEM Semester SUPPLEMENTARY EXAMINATIONS FEBRUARY - 2010 AERODYNAMICS - I Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Write short notes on the following:

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(a) Effective angle of attack (b) Horse shoe vortex (c) Biot - Savart law.

[5+5+6]

2. (a) What is the physical significance of continuity equation?

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(b) Derive the Momentum equation of a flow, and explain how it varies for steady flow, iniviscid flow, and a steady inviscid flow. [8+8] 3. (a) Starting with the definition of circulation, derive Kelvin’s circulation theorem. (b) State and explain Kutta condition.

[8+8]

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4. Describe the supersonic airfoils and supersonic wings, using neat sketches. Explain why these would not be good subsonic airfoils or wings. [16] 5. Explain about the velocity induced at a point S by an infinitesimal segment of the lifting surface assume the velocity is perpendicular to the paper, obtain expression for the normal velocity at point S. [16]

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6. A constant strength vortex panel of strength 60 units is located on the X-axis from X1=2.5 to X2=4.65. Determine the influence of this vortex panel at a point P(5.5,5.5) to evaluate V(u,w). Develop the expressions used for determining (a) Velocity Potential

(b) Velocity Components.

[8+8]

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7. How does a source panel method differ from a vortex panel method and what conditions? Hence describe the formulation of a source panel method for a nonlifting flow over a circular cylinder. [16] 8. Assuming that an airfoil can be replaced by a vortex sheet, prove that the lift coefficient is proportional to angle of attack for a cambered airfoil. [16] ?????

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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.TECH SEM SUPPLEMENTARY EXAMINATIONS FEBRUARY - 2010 II II B.Tech II II Semester Semester Supplimentary Examinations,February 2010 AERODYNAMICS - I Aeronautical Engineering Time: 3 hours Max Marks: 80 Answer any FIVE Questions All Questions carry equal marks ????? 1. Write briefly about the following

(b) Horseshoe vortex (c) Downwash and induced velocity (d) Lifting line.

[16]

(b) elementary flows.

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2. Explain, with the aid of neat sketches, (a) boundary conditions

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(a) Bound vortex

[8+8]

3. Sketch a swept back wing showing sweep, taper and dihedral. Explain the utility of these features. Draw neat sketches. [16]

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4. (a) Apply the transformation formula ξ = z 2 to a uniform flow. (b) Explain Kutta condition. Draw neat sketches.

[10+6]

5. (a) Derive the moment coefficient about the leading edge for a cambered airfoil. (b) Derive the expression for the distance of the centre of pressure from the leading edge of a cambered airfoil. [12+4] 6. Explain with neat sketch various types of source panel methods.

[16]

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7. Consider a planar wing of aspect ratio 5, taper ratio unity, and swept aft by 45o in the plane of symmetry. Develop the Vortex Lattice Method to calculate lift coefficient for this wing. Take the uniform chord of the wing as c = 1.0 unit. Divide the wing into 4 panels. [16]

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8. (a) A constant strength vortex panel located from [(x/c)1=0.234,(y/c)1=0.072 to (x/c)2=0.245,(y/c)=0.0742] is part of an airfoil under study for its lifting Characteristics, where the airfoil is divided in to 40 vortex panels and 20 panels on the wake. Setup the influence coefficient and the matrix for applying the appropriate boundary conditions. (b) Explain the procedure to obtain lift coefficient from the above formulation. [8+8] ?????

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