GATE Aerospace Engineering Aerodynamics Syllabus

Aerodynamics syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Aerodynamics in GATE Aerospace Engineering, not a summary of it.

1. 1

   Basic Fluid Mechanics

   2 topics

   • Conservation laws
     • Mass, momentum and energy (Integral and differential form)
   • Dimensional analysis and dynamic similarity
2. 2

   Potential Flow Theory

   1 topic

   • Sources, sinks, doublets, line vortex and their superposition
3. 3

   Elementary ideas of viscous flows including boundary layers

   overview

   Examined as a single unit within Aerodynamics — no further topic split in the official outline.

4. 4

   Airfoils and Wings

   6 topics

   • Airfoil nomenclature
   • Aerodynamic coefficients: lift, drag and moment
   • Kutta-Joukoswki theorem
   • Thin airfoil theory
     • Kutta condition
     • Starting vortex
   • Finite wing theory
     • Induced drag
     • Prandtl lifting line theory
   • Critical and drag divergence Mach number
5. 5

   Compressible Flows

   8 topics

   • Basic concepts of compressibility
   • One-dimensional compressible flows
   • Isentropic flows
   • Fanno flow
   • Rayleigh flow
   • Normal and oblique shocks
   • Prandtl-Meyer flow
   • Flow through nozzles and diffusers
6. 6

   Special Topics

   2 topics

   • Wind Tunnel Testing: Measurement and visualization techniques
   • Shock - boundary layer interaction

Aerodynamics flashcards for GATE Aerospace Engineering

24 of 50 cards from the Aerodynamics deck — real questions with worked answers.

1. State the integral form of the continuity (conservation of mass) equation for a control volume.

   $$\frac{\partial}{\partial t}\iiint_V \rho\, dV + \oiint_S \rho\,\vec{V}\cdot d\vec{S} = 0$$ The rate of mass accumulation inside the control volume plus the net mass flux out through its surface equals zero.

2. Write the differential (conservation) form of the continuity equation.

   $$\frac{\partial \rho}{\partial t} + \nabla\cdot(\rho\vec{V}) = 0$$ For steady flow it reduces to $\nabla\cdot(\rho\vec{V})=0$, and for incompressible flow to $\nabla\cdot\vec{V}=0$.

3. Write the momentum (Navier–Stokes) equation in differential conservation-free (substantial-derivative) form for a viscous fluid.

   $$\rho\frac{D\vec{V}}{Dt} = -\nabla p + \rho\vec{g} + \mu\nabla^{2}\vec{V}$$ where $\frac{D}{Dt}=\frac{\partial}{\partial t}+\vec{V}\cdot\nabla$ is the material derivative.

4. State the integral form of the momentum equation for a control volume (steady, neglecting body forces).

   $$\sum \vec{F} = \oiint_S (\rho\,\vec{V}\cdot d\vec{S})\,\vec{V}$$ The net external force equals the net rate of momentum flux out of the control surface.

5. Write the energy equation in differential form for an inviscid, adiabatic flow (in terms of total enthalpy).

   For steady adiabatic inviscid flow the total enthalpy is constant along a streamline: $$h_0 = h + \frac{V^{2}}{2} = \text{const}$$ Differentially, $\rho\frac{D}{Dt}\!\left(e+\frac{V^2}{2}\right) = -\nabla\cdot(p\vec{V}) + \rho\vec{g}\cdot\vec{V} + \text{(heat \& viscous terms)}$.

6. State the Buckingham Pi theorem.

   If a physical problem involves $n$ variables expressible in $k$ fundamental dimensions, the relationship can be reduced to $n-k$ independent dimensionless groups (Pi terms): $f(\Pi_1,\Pi_2,\dots,\Pi_{n-k})=0$.

7. Define the Reynolds number and state its physical meaning.

   $$Re = \frac{\rho V L}{\mu} = \frac{V L}{\nu}$$ It is the ratio of inertial forces to viscous forces and governs dynamic similarity in viscous flows.

8. Define the Mach number and state what it physically represents.

   $$M = \frac{V}{a}$$ where $a$ is the local speed of sound. It is the ratio of flow speed to sound speed and represents the importance of compressibility effects.

9. State the conditions required for complete dynamic similarity between a model and a prototype.

   Geometric similarity (same shape/scaled dimensions), kinematic similarity (similar velocity fields), and dynamic similarity (equal relevant dimensionless groups, e.g. matching $Re$ and $M$ for the dominant forces).

10. Give the velocity potential and stream function for a 2-D source of strength $\Lambda$.

    $$\phi = \frac{\Lambda}{2\pi}\ln r, \qquad \psi = \frac{\Lambda}{2\pi}\theta$$ Radial velocity $v_r = \dfrac{\Lambda}{2\pi r}$, tangential velocity $v_\theta = 0$. A sink has $-\Lambda$.

11. Give the stream function and velocity potential for a 2-D doublet of strength $\kappa$.

    $$\psi = -\frac{\kappa}{2\pi}\frac{\sin\theta}{r}, \qquad \phi = \frac{\kappa}{2\pi}\frac{\cos\theta}{r}$$ A doublet is the limit of a source–sink pair as their spacing $\to 0$ while the product of strength and distance stays constant.

12. Give the velocity potential and stream function for a 2-D line (point) vortex of strength $\Gamma$.

    $$\phi = -\frac{\Gamma}{2\pi}\theta, \qquad \psi = \frac{\Gamma}{2\pi}\ln r$$ Tangential velocity $v_\theta = \dfrac{\Gamma}{2\pi r}$ and $v_r = 0$. The flow is irrotational everywhere except at the origin.

13. What combination of elementary flows produces non-lifting flow over a circular cylinder, and what is the cylinder radius?

    Uniform flow + doublet. The radius is $$R = \sqrt{\frac{\kappa}{2\pi V_\infty}}$$ where $\kappa$ is the doublet strength and $V_\infty$ the freestream speed.

14. What superposition gives lifting flow over a circular cylinder, and what is the resulting lift per unit span?

    Uniform flow + doublet + vortex. Lift per unit span follows the Kutta–Joukowski result: $$L' = \rho_\infty V_\infty \Gamma$$

15. State the Kutta–Joukowski theorem.

    For an inviscid, incompressible 2-D flow, the lift per unit span on a body equals $$L' = \rho_\infty V_\infty \Gamma$$ where $\Gamma$ is the circulation around the body. Lift is directly proportional to circulation.

16. Define chord, camber line (mean camber line), and thickness in airfoil nomenclature.

    Chord: straight line from leading edge to trailing edge. Mean camber line: locus of points midway between upper and lower surfaces. Camber: max distance between mean camber line and chord. Thickness: distance between upper and lower surfaces measured perpendicular to the chord.

17. In a 4-digit NACA airfoil designation (e.g. NACA 2412), what does each digit represent?

    First digit: maximum camber as % of chord (2%). Second digit: position of max camber in tenths of chord (0.4c). Last two digits: maximum thickness as % of chord (12%).

18. Define the lift coefficient $C_L$.

    $$C_L = \frac{L}{\tfrac{1}{2}\rho_\infty V_\infty^{2} S}$$ where $S$ is the reference (planform) area and $q_\infty=\tfrac{1}{2}\rho_\infty V_\infty^2$ is dynamic pressure. (Use $c$ instead of $S$ for 2-D section coefficient $c_l$.)

19. Define the drag coefficient $C_D$ and moment coefficient $C_M$.

    $$C_D = \frac{D}{\tfrac{1}{2}\rho_\infty V_\infty^{2} S}, \qquad C_M = \frac{M}{\tfrac{1}{2}\rho_\infty V_\infty^{2} S c}$$ where $c$ is a reference length (chord) for the moment.

20. Define the pressure coefficient $C_p$ and give its incompressible expression in terms of local velocity.

    $$C_p = \frac{p - p_\infty}{\tfrac{1}{2}\rho_\infty V_\infty^{2}}$$ For incompressible flow (Bernoulli): $$C_p = 1 - \left(\frac{V}{V_\infty}\right)^{2}$$

21. What is the aerodynamic center of an airfoil, and what is its theoretical chordwise location for a thin airfoil?

    The aerodynamic center is the point about which the pitching moment coefficient is independent of angle of attack. For a thin airfoil (incompressible) it lies at the quarter chord, $x_{ac}=c/4$.

22. State the Kutta condition for flow over an airfoil.

    The flow leaves the sharp trailing edge smoothly, so the velocity there is finite. For a finite-angle trailing edge the velocities on the upper and lower surfaces are equal (stagnation at TE); for a cusped TE they are equal in magnitude and direction. It uniquely fixes the circulation $\Gamma$.

23. What is the starting vortex and which physical principle explains its formation?

    When an airfoil starts moving, a vortex of opposite sign to the bound circulation is shed from the trailing edge and left behind in the fluid. It arises from Kelvin's circulation theorem ($D\Gamma/Dt=0$): the total circulation in the fluid must remain zero, so the bound circulation is balanced by the equal-and-opposite starting vortex.

24. State Kelvin's circulation theorem.

    $$\frac{D\Gamma}{Dt} = 0$$ For an inviscid, barotropic flow with conservative body forces, the circulation around a closed material curve remains constant with time.

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