Aerodynamics - I 2025

(a) The point on an airfoil where the pitching moment coefficient is independent of the angle of attack is known as:

1. Center of Pressure
2. Aerodynamic Center
3. Stagnation Point
4. Trailing Edge

(b) In a NACA 2412 airfoil, the maximum camber is:

1. 2% of chord
2. 4% of chord
3. 12% of chord
4. 20% of chord

(c) D'Alembert's Paradox states that for an inviscid, incompressible flow over a closed body:

1. Lift is non-zero, Drag is zero
2. Lift is zero, Drag is non-zero
3. Both Lift and Drag are zero
4. Both Lift and Drag are non-zero

(d) Which elementary flow combination simulates the flow over a non-lifting circular cylinder?

1. Uniform flow + Source
2. Uniform flow + Doublet
3. Uniform flow + Vortex
4. Source + Sink

(e) The condition required for the flow to leave the trailing edge of an airfoil smoothly is called:

1. Kutta Condition
2. Rankine Condition
3. Kelvin's Condition
4. Blasius Condition

(f) For an elliptic wing planform, the induced drag coefficient ($C_{Di}$) is proportional to:

1. $C_L$
2. $(C_L)^2$
3. $1/C_L$
4. $1/(C_L)^2$

(g) The transformation used to map a circle into an airfoil shape is known as:

1. Laplace Transformation
2. Fourier Transformation
3. Joukowski Transformation
4. Legendre Transformation

(h) The ratio of the forward speed of the aircraft to the rotational tip speed of the propeller is related to:

1. Aspect Ratio
2. Advance Ratio
3. Solidity
4. Pitch Ratio

(i) In a boundary layer, the shape factor is defined as the ratio of:

1. Momentum thickness to Displacement thickness
2. Displacement thickness to Momentum thickness
3. Energy thickness to Momentum thickness
4. Displacement thickness to Boundary layer thickness

(j) Flow separation occurs when the pressure gradient is:

1. Zero ($dp/dx = 0$)
2. Favorable ($dp/dx < 0$)
3. Adverse ($dp/dx > 0$)
4. Constant

(a) Derive the momentum equation in integral form for a control volume and explain the physical significance of each term.

(b) Explain the NACA 4-digit and 5-digit series nomenclature with suitable examples. Describe the geometric parameters of a wing.

(a) Consider the superposition of a Uniform Flow and a Doublet. Derive the stream function for this combination and show that it represents flow over a circular cylinder.

(b) State and prove the Kutta-Joukowski theorem for lift on a cylinder with circulation.

(a) Discuss Thin Airfoil Theory. State the assumptions made and write the expressions for the lift coefficient ($C_l$) and moment coefficient ($C_{m,c/4}$) for a symmetric airfoil.

(b) Describe the working principle of a closed-circuit wind tunnel with a neat sketch. List the major components and their functions.

(a) Define Circulation and Vorticity. Explain Kelvin's Circulation Theorem and the concept of the Starting Vortex.

(b) Explain the source and sink flow method to generate a Rankine Oval. Derive the equation for the length and width of the oval.

(a) Using the Joukowski transformation $z = \zeta + (c^2 / \zeta)$, show how a circle in the $\zeta$-plane transforms into a flat plate or an ellipse in the $z$-plane.

(b) State the Cauchy-Riemann equations. If the velocity potential $\phi = x^2 - y^2$, determine the stream function and the complex potential $W(z)$.

(a) State the Biot-Savart law. Derive the expression for the induced velocity at a point due to a straight infinite vortex filament.

(b) Explain Prandtl's Lifting Line Theory. Discuss the concepts of bound vortex, trailing vortex, and downwash.

(a) Explain the Blade Element Theory for propellers. Derive the expression for thrust and torque of a propeller blade element.

(b) Define the following propeller coefficients: Thrust Coefficient, Torque Coefficient, and Power Coefficient. Discuss how propeller efficiency varies with the Advance Ratio.

(a) Define Boundary Layer. Derive the expression for Displacement Thickness and Momentum Thickness.

(b) Explain the phenomenon of boundary layer separation. Discuss the effect of an adverse pressure gradient on the velocity profile and skin friction.