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GATE Aerospace Engineering Aerodynamics Syllabus

The Aerodynamics syllabus for GATE Aerospace Engineering in full: 6 chapters, 19 topics and 5 sub-topics, every one listed below, plus 50 Aerodynamics flashcards with answers.

6Chapters
19Topics
5Sub-topics
50Flashcards

Aerodynamics syllabus: all 6 chapters

Expand any chapter to see its topics and sub-topics.

  1. Basic Fluid Mechanics

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

  2. Potential Flow Theory

     1 topic
    • Sources, sinks, doublets, line vortex and their superposition

  3. Elementary ideas of viscous flows including boundary layers

     overview

    No separate topics listed for this chapter.

  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. 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. Special Topics

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

GATE Aerospace Engineering Aerodynamics flashcards — 50 questions with 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): $$C_p = 1 - \left(\frac{V}{V_\infty}\right)^{2}$$

Show the other 30 Aerodynamics flashcards

  1. 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, $x_{ac}=c/4$.

  2. 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 $\Gamma$.

  3. 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.

  4. 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.

  5. State the fundamental result of thin airfoil theory for the lift-curve slope of a symmetric airfoil.

    The lift coefficient is $$c_l = 2\pi\alpha$$ giving a lift-curve slope of $\dfrac{dc_l}{d\alpha}=2\pi$ per radian. The zero-lift angle of attack is $\alpha_{L=0}=0$ for a symmetric airfoil.

  6. In thin airfoil theory, give the lift coefficient for a cambered airfoil in terms of the Fourier coefficients $A_0$ and $A_1$.

    $$c_l = \pi(2A_0 + A_1) = 2\pi\left(\alpha - \alpha_{L=0}\right)$$ The slope remains $2\pi$/rad; camber shifts the zero-lift angle $\alpha_{L=0}$.

  7. In thin airfoil theory, give the moment coefficient about the quarter chord for a cambered airfoil.

    $$c_{m,c/4} = \frac{\pi}{4}(A_2 - A_1)$$ It is independent of angle of attack, confirming the quarter chord as the aerodynamic center. For a symmetric airfoil $A_1=A_2=0$, so $c_{m,c/4}=0$.

  8. Write the fundamental equation of thin airfoil theory (the camber-line boundary condition integral).

    $$\frac{1}{2\pi}\int_0^{c}\frac{\gamma(\xi)\,d\xi}{x-\xi} = V_\infty\left(\alpha - \frac{dz}{dx}\right)$$ where $\gamma$ is the vortex sheet strength along the chord and $\dfrac{dz}{dx}$ is the camber-line slope.

  9. Why does a finite (3-D) wing experience induced drag while a 2-D airfoil does not?

    On a finite wing the pressure difference drives flow around the wingtips, creating trailing vortices that induce a downwash. The downwash tilts the local lift vector rearward, producing a streamwise force component called induced drag (drag due to lift).

  10. How does downwash $w$ change the effective angle of attack of a wing section?

    The downwash reduces the angle: $$\alpha_{eff} = \alpha - \alpha_i$$ where the induced angle is $\alpha_i = \tan^{-1}\!\left(\dfrac{w}{V_\infty}\right)\approx \dfrac{w}{V_\infty}$ for small angles.

  11. State the formula for the induced drag coefficient of a finite wing and define the span efficiency factor.

    $$C_{D,i} = \frac{C_L^{2}}{\pi e\, AR}$$ where $AR$ is the aspect ratio and $e$ ($\leq 1$) is the span (Oswald) efficiency factor. $e=1$ for an elliptical lift distribution (minimum induced drag).

  12. Define aspect ratio and state how increasing it affects induced drag.

    $$AR = \frac{b^{2}}{S}$$ ( $b$ = span, $S$ = planform area). Higher aspect ratio reduces induced drag since $C_{D,i}\propto 1/AR$.

  13. Write Prandtl's lifting-line (fundamental monoplane) equation.

    $$\alpha(y_0) = \frac{\Gamma(y_0)}{\pi V_\infty c(y_0)} + \alpha_{L=0}(y_0) + \frac{1}{4\pi V_\infty}\int_{-b/2}^{b/2}\frac{(d\Gamma/dy)\,dy}{y_0 - y}$$ It relates geometric angle of attack to the spanwise circulation distribution $\Gamma(y)$.

  14. What lift distribution minimizes induced drag for a given lift and span, and what is its planform consequence?

    An elliptical lift (circulation) distribution gives the minimum induced drag, with $e=1$ and constant downwash across the span. It is produced by an elliptical planform (untwisted).

  15. For an elliptical lift distribution, give the induced drag coefficient and constant downwash.

    Downwash is constant: $w = \dfrac{\Gamma_0}{2b}$, induced angle $\alpha_i = \dfrac{C_L}{\pi AR}$, and $$C_{D,i} = \frac{C_L^{2}}{\pi AR}$$ (i.e. $e=1$).

  16. Define the critical Mach number $M_{cr}$.

    $M_{cr}$ is the freestream Mach number at which the local flow speed first reaches sonic ($M=1$) somewhere on the body (typically the point of maximum surface velocity / minimum pressure). Below it the flow is everywhere subsonic.

  17. Define the drag-divergence Mach number and describe what happens there.

    The drag-divergence Mach number $M_{drag\text{-}divergence}$ (slightly above $M_{cr}$) is where the drag coefficient rises sharply due to the formation of shock waves and shock-induced flow separation (wave drag). It marks the onset of the transonic drag rise.

  18. State the Prandtl–Glauert compressibility correction for the pressure coefficient in subsonic flow.

    $$C_p = \frac{C_{p,0}}{\sqrt{1 - M_\infty^{2}}}$$ where $C_{p,0}$ is the incompressible value. Likewise $c_l = \dfrac{c_{l,0}}{\sqrt{1-M_\infty^2}}$. Valid for thin bodies at small angles in subsonic flow.

  19. What is the definition of the speed of sound and its formula for a calorically perfect gas?

    $$a = \sqrt{\left(\frac{\partial p}{\partial \rho}\right)_s} = \sqrt{\gamma R T}$$ It is the speed at which small pressure disturbances propagate through the gas; for air $\gamma=1.4$, $R=287\ \text{J/(kg·K)}$.

  20. When is a flow generally treated as incompressible versus compressible, in terms of Mach number?

    Flow is usually treated as incompressible for $M < 0.3$ (density changes < ~5%). For $M \geq 0.3$ compressibility effects must be included. Regimes: subsonic, transonic ($M\approx 0.8\text{–}1.2$), supersonic ($M>1$), hypersonic ($M>5$).

  21. Write the energy equation for adiabatic 1-D flow relating temperature to the stagnation temperature.

    $$c_p T + \frac{V^{2}}{2} = c_p T_0 = \text{const}$$ Equivalently $$\frac{T_0}{T} = 1 + \frac{\gamma-1}{2}M^{2}$$

  22. Give the isentropic relations linking stagnation to static pressure and density in terms of Mach number.

    $$\frac{p_0}{p} = \left(1 + \frac{\gamma-1}{2}M^{2}\right)^{\frac{\gamma}{\gamma-1}}, \qquad \frac{\rho_0}{\rho} = \left(1 + \frac{\gamma-1}{2}M^{2}\right)^{\frac{1}{\gamma-1}}$$

  23. State the isentropic process relations among $p$, $\rho$, and $T$.

    $$\frac{p_2}{p_1} = \left(\frac{\rho_2}{\rho_1}\right)^{\gamma} = \left(\frac{T_2}{T_1}\right)^{\frac{\gamma}{\gamma-1}}$$ i.e. $p/\rho^{\gamma} = \text{const}$ for an isentropic (adiabatic, reversible) process.

  24. What are the stagnation-to-critical (sonic) property ratios for air ($\gamma=1.4$) at $M=1$?

    At $M=1$: $$\frac{T^{*}}{T_0}=\frac{2}{\gamma+1}=0.833,\quad \frac{p^{*}}{p_0}=\left(\frac{2}{\gamma+1}\right)^{\frac{\gamma}{\gamma-1}}=0.528,\quad \frac{\rho^{*}}{\rho_0}=\left(\frac{2}{\gamma+1}\right)^{\frac{1}{\gamma-1}}=0.634$$

  25. Write the area–Mach number relation (area ratio) for isentropic 1-D flow in a variable-area duct.

    $$\left(\frac{A}{A^{*}}\right)^{2} = \frac{1}{M^{2}}\left[\frac{2}{\gamma+1}\left(1+\frac{\gamma-1}{2}M^{2}\right)\right]^{\frac{\gamma+1}{\gamma-1}}$$ where $A^*$ is the sonic throat area.

  26. In a converging–diverging (Laval) nozzle, how must area change to accelerate the flow in subsonic vs supersonic regimes?

    From $\dfrac{dA}{A} = (M^{2}-1)\dfrac{dV}{V}$: subsonic ($M<1$) needs a converging area to accelerate; supersonic ($M>1$) needs a diverging area to accelerate. Sonic flow ($M=1$) can only occur at the throat (minimum area).

  27. Define Fanno flow and state its key assumptions.

    Fanno flow is steady, 1-D, adiabatic flow with friction in a constant-area duct, no work and no heat transfer. Key feature: stagnation temperature $T_0$ is constant; entropy increases due to friction.

  28. In Fanno flow, in which direction does friction drive the Mach number for subsonic and supersonic inlets?

    Friction drives the flow toward $M=1$ (Fanno limit): subsonic flow accelerates ($M\uparrow$ toward 1), supersonic flow decelerates ($M\downarrow$ toward 1). $M=1$ cannot be crossed; choking occurs at the duct exit.

  29. What happens to entropy and stagnation pressure along a Fanno line, and at what point is entropy maximum?

    Entropy increases in the flow direction (friction is irreversible) and stagnation pressure $p_0$ decreases. Entropy is maximum at the sonic point $M=1$, which is the tip of the Fanno curve on the T–s diagram.

  30. Write the Fanno-flow friction-length relation $\dfrac{4\bar{f}L^{*}}{D}$ in terms of Mach number.

    $$\frac{4\bar f L^{*}}{D} = \frac{1-M^{2}}{\gamma M^{2}} + \frac{\gamma+1}{2\gamma}\ln\!\left[\frac{(\gamma+1)M^{2}}{2\left(1+\frac{\gamma-1}{2}M^{2}\right)}\right]$$ where $L^{*}$ is the duct length needed to reach $M=1$.

GATE Aerospace Engineering Aerodynamics FAQ

What is in the GATE Aerospace Engineering Aerodynamics syllabus?

GATE Aerospace Engineering Aerodynamics is split into 6 chapters: Basic Fluid Mechanics, Potential Flow Theory, Elementary ideas of viscous flows including boundary layers, Airfoils and Wings, Compressible Flows and Special Topics. Together they contain 19 topics and 5 sub-topics.

How many chapters are in GATE Aerospace Engineering Aerodynamics?

6 chapters, containing 19 topics and 5 sub-topics. The largest chapter is Compressible Flows, with 8 topics.

Are there flashcards for GATE Aerospace Engineering Aerodynamics?

Yes — a 50-card Aerodynamics deck, printed in full in the flashcards section of this page and available in the Examius app with spaced repetition. The free plan covers one exam of your choice, including its flashcards; Examius Pro, a one-time purchase, unlocks every other exam and deck.