GATE AE 2016 Question Paper & Solutions

Verbal Aptitude

With increase in airfoil thickness, the critical Mach number for an airfoil is likely to

Verbal Aptitude

Due to a body in potential flow, the velocity at a point A in the flow field is 20 m/s while the free stream velocity is only 10 m/s. The value of coefficient of pressure (C p) at the point A is _________.

Quantitative Aptitude

Which of the following airfoil will have location of the maximum camber at half chord length from the leading edge?

Analytical & Spatial Aptitude

For a laminar incompressible flow past a flat plate at zero angle of attack, the variation of skin friction drag coefficient  fC with Reynolds number based on the chord length  cRe can be expressed as

Analytical & Spatial Aptitude

Which of the following statement is NOT TRUE across an oblique shock wave?

Verbal Aptitude

For a completely subsonic isentropic flow through a convergent nozzle, which of the following statement is TRUE?

Quantitative Aptitude

Which of the following aircraft engines has the highest propulsive efficiency at a cruising Mach number of less than 0.5?

Quantitative Aptitude

Air, with a Prandtl number of 0.7, flows over a flat plate at a high Reynolds number. Which of the following statement is TRUE?

Verbal Aptitude

Shaquille O' Neal is a 60% career free throw shooter, meaning that he successfully makes 60 free throws out of 100 attempts on average. What is the probability that he will successfully make exactly 6 free throws in 10 attempts?

Analytical & Spatial Aptitude

If A and B are both non-singular n n matrices, then which of the following statement is NOT TRUE. Note: det represents the determinant of a matrix.

Linear Algebra

The total number of material constants that are necessary and sufficient to describe the three dimensional Hooke's law for an isotropic material is ____.

Linear Algebra

Determine the correctness or otherwise of the following statements, [a] and [r]: [a]: In a plane stress problem, the shear strains along the thickness direction of a body are zero but the normal strain along the thickness is not zero. [r]: In a plane stress problem, Poisson effect induces the normal strain along the thickness direction of the body.

Calculus

Consider four thin -walled beams of different open cross-sections, as shown in the cases (i-iv). A shear force of magnitude 'F' acts vertically downward at the location 'P' in all the beams. In which of the following case, does the shear force induce bending and twisting? Case (i) Case (ii) Case (iii) Case (iv)

Differential Equations

The effective stiffness of the spring-mass system as shown in the figure below is ____ N/mm.

Numerical Methods

A structural member supports loads, which produce at a particular point, a state of pure shear stress of 50 N/mm 2. At what angles are the principal planes oriented with respect to the plane of pure shear?

Basic Fluid Mechanics

Let x be a positive real number. The function   2 2 x 1x x f  has its minima at x=______.

Airfoil & Wing Theory

The vector u is defined as y xeˆx eˆy u   , where xeˆ and yeˆ are the unit vectors along x and y directions, respectively. If the vector  is defined as u    , then      u ______.

Compressible Flow & Shocks

The partial differential equation 2 2 x u t u     , where α is a positive constant, is

Compressible Flow & Shocks

Combustion in gas turbine engines is ideally represented as the following process:

Wind Tunnel Testing & Instrumentation

For a given chamber pressure, the thrust of a rocket engine is highest when

Atmospheric Flight Mechanics

The d amping ratio in phugoid motion for gliders is usually less compared to powered aircraft because

Atmospheric Flight Mechanics

During an aircraft cruising flight, the altitude above the ground is usually measured using

Static Stability & Control

Indicated airspeed is used by a pilot during

Dynamic Stability

The pitch angle and the angle of attack for a fixed wing aircraft are equal during

Space Dynamics & Orbital Mechanics

The load factor of an aircraft turnin g at a constant altitude is 2. The coefficient of lift required for turning flight as compared to level flight at the same speed will be

Thermodynamic Cycles of Gas Turbines

An un-mixed turbofan engine with a bypass ratio of 6.0, flies with a velocity of 200 m/s. The core and the bypass nozzles of the engine, that are both convergent nozzles, operate under choked condition and have exhaust static temperatures of 580 K and 295 K, respectively. The specific gas constant and the ratio of specific heats for both the streams are 287 J/kgK and 1.4, respectively. If the fuel-air ratio is negligible, the thrust per unit mass flow rate generated by the engine is _______Ns/kg.

Thermodynamic Cycles of Gas Turbines

A single-stage gas turbine operates with an axial absolute flow at the entry and exit from the stage. The absolute flow angle at the nozzle exit is 70 o. The turbine stage generates a specific work of 228 kJ/kg when operating with a mean blade speed of 440 m/s. The absolute velocity at the rotor entry is

Inlets, Combustors & Nozzles

An axial compressor operates such that it has an inlet and an exit total temperature of 300 K and 430 K, respectively. The isentropic efficiency of the compressor is 85 %. If the ratio of specific heats is 1.4, then the total pressure ratio across the compressor is ____________.

Compressors and Turbines

The maximum value of coefficient of lift ( lC ) for a 2D circular cylinder, provided at least one stagnation point lies on the cylinder surface, is predicted by the potential flow theory to be

Rocket Propulsion

In an aerospace engineering analysis of Rocket Propulsion (Tsiolkovsky Rocket Equation & Specific Impulse), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Strength of Materials & Elasticity

The rate of change of moment coefficient with respect to the angle of attack, d dC m , at half chord point of a thin airfoil, as per approximations from the thin airfoil theory is

Strength of Materials & Elasticity

An untwisted wing of elliptic planform and aspect ratio 6 consists of thin symmetric airfoil sections. The coefficient of lift (C L) at o10 angle of attack assuming inviscid incompressible flow is

Thin-Walled Structures

A gaseous mixture of air and fuel enters a constant area combustion chamber at a velocity of 100 m/s and at a static temperature of 300 K. The heat release due to combustion is 1000 kJ/kg. The specific heat at constant pressure of the calorically perfect gas is 1000 J/kgK. The total temperature of air-fuel mixture after combustion is ______ K.

Structural Dynamics & Aeroelasticity

Consider 1 -D, steady, in viscid, compressible flow through a convergent nozzle . The total temperature and total pressure are oT , oP respectively. The flow through the nozzle is choked with a mass flow rate of om . If the total temperature is increased to oT 4, with total pressure remaining unchanged, then the mass flow rate through the nozzle

Aerospace Materials & Fatigue

Consider a second order linear ordinary differential equation 0 y 4dx dy4 dx y d 2 2   , with the boundary conditions 1dx dy; 1 ) 0 ( y 0 x   . The value of y at x =1 is

Linear Algebra

Consider the following system of linear equations: 2x - y + z = 1 3x - 3y + 4z = 6 x - 2y + 3z = 4 This system of linear equations has

Calculus

A bar made of linear elastic isotropic material is fixed at one end and subjected to an axial force of 1 kN at the other end. The cross-sectional area of the bar is 100 mm 2, length is 100 mm and the Young's Modulus is 1105 N/mm2. The strain energy stored in the bar is ____ Nmm.

Differential Equations

A cantilever beam -spring system is shown in the figure. The beam is made with a material of Young's modulus 1105 N/mm 2 and geometry such that its moment of inertia is 100 mm 4 and length l = 100 mm. It is supported by a spring of stiffness K = 30 N/mm and subjected to a load of P = 100 N at the point 'B'. The deflection at the point 'B' due to the load P is ____mm.

Numerical Methods

Determine the correctness or otherwise of the following statements, [a] and [r], [a]: Ribs, used in airplane wings, increase the column buckling strength of the longitudinal stiffeners. [r]: Ribs distribute concentrated loads into the structure and redistribute stresses around discontinuities.

Airfoil & Wing Theory

An aerospace system operating under standard sea level conditions is governed by Airfoil & Wing Theory (Thin Airfoil Theory & Camber Effects). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Basic Fluid Mechanics

The governing differential equation of motion of a damped system is given by 0 kxdt dxcdt x dm 2 2   . If m = 1 kg, c = 2 Ns/m and k = 2 N/m then the frequency of the damped oscillation of this system is ____ rad/s.

Compressible Flow & Shocks

The two dimensional state of stress in a body is described by the Airy's stress function: 12 yE6 xy72 y x36 y x 12 x5 432 23 4      . The Airy's stress function will satisfy the equilibrium and the compatibility requirements if and only if the value of the coefficient E is ____.

Airfoil & Wing Theory

The value of definite integral    0 dx x sin x is _______.

Compressible Flow & Shocks

Use Newton-Raphson method to solve the equation: 1 e xx  . Begin with the initial guess 5 . 0 x0  . The solution after one step is x _________.

Basic Fluid Mechanics

A wall of thickness 5 mm is heated by a hot gas flowing along the wall. The gas is at a temperature of 3000 K, and the convective heat transfer coefficient is 160 W/m 2K. The wall thermal conductivity is 40 W/mK. If the colder side of the wall is held at 500 K, the temperature of the side exposed to the hot gas is _______ K.

Airfoil & Wing Theory

A launch vehicle has a main rocket engine with two identical strap-on motors, all of which fire simultaneously during the operation. The main engine delivers a thrust of 6300 kN with a specific impulse of 428 s. Each strap-on motor delivers a thrust of 12000 kN with specific impulse of 292 s. The acceleration due to gravity is 9.81 m/s 2. The effective (combined) specific impulse of the vehicle is _______ s.

Atmospheric Flight Mechanics

A substance experiences an entropy change of 0 s in a quasi-steady process. The rise in temperature (corresponding to the entropy change s ) is highest for the following process:

Atmospheric Flight Mechanics

In a particular rocket engine, helium propellant is heated to 6000 K and 95% of its total enthalpy is recovered as kinetic energy of the nozzle exhaust. Consider helium to be a calorically perfect gas with specific heat at constant pressure of 5200 J/kgK. The exhaust velocity for such a rocket for an optimum expansion is _____ m/s.

Static Stability & Control

An aircraft is flying level in the North direction at a velocity of 55 m/s under cross wind from East to West of 5 m/s. For the given aircraft C nβ = 0.012/deg and C nδr = - 0.0072/deg, where δr is the rudder deflection and β is the side slip angle . The rudder deflection exerted by pilot is __________ degrees.

Dynamic Stability

An aircraft weighing 10000 N is flying level at 100 m/s and it is powered by a jet engine. The thrust required for level flight is 1000 N. The maximum possible thrust produced by the jet engine is 5000 N. The minimum time required to climb 1000 m, when flight speed is 100 m/s, is ________s.

Space Dynamics & Orbital Mechanics

The aircraft velocity (m/s) components in body axes are given as [ u, v, w] = [100, 10, 10]. The air velocity (m/s), angle of attack (deg) and sideslip angle (deg) in that order are

Space Dynamics & Orbital Mechanics

The Dutch roll motion of the aircraft is described by following relationship                       r 76 . 0 49 . 4 1 26 . 0 r  The undamped natural frequency (rad/s) and damping ratio for the Dutch roll motion in that order are:

Thermodynamic Cycles of Gas Turbines

A glider weighing 3300 N is flying at 1000 m above sea level. The wing area is 14.1 m2 and the air density is 1.23 kg/m3. Under zero wind conditions, the velocity for maximum range is __________ m/s. α (deg) C L CD C L/CD 11 1.46 0.0865 16.9 9 1.36 0.0675 20.1 7 1.23 0.0535 22.9 5 1.08 0.0440 24.5 3 0.90 0.0350 25.7 1 0.70 0.0275 25.4 -1 0.49 0.0220 22.2 -3 0.25 0.0180 13.8

Thermodynamic Cycles of Gas Turbines

A rocket, with a total lift-off mass of 10000 kg, moves vertically upward from rest under a constant gravitational acceleration of 9.81 m/s 2. The propellant mass of 8400 kg burns at a constant rate of 1200 kg/s. If the specific impulse of the rocket engine is 240 s, neglecting drag, the burnout velocity in m/s is

Inlets, Combustors & Nozzles

A satellite is injected at an altitude of 350 km above the Earth's surface, with a velocity of 8.0 km/s parallel to the local horizon. (Earth radius=6378 km, µE (GM=Gravitational constant × Earth mass) = 3.986×1014 m3s-2). The satellite

Compressors and Turbines

An aerospace system operating under standard sea level conditions is governed by Compressors and Turbines (Centrifugal Compressors). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Inlets, Combustors & Nozzles

In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Combustor Design & Flame Stabilization), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Rocket Propulsion

An aerospace system operating under standard sea level conditions is governed by Rocket Propulsion (Solid, Liquid & Hybrid Rocket Engines). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Compressors and Turbines

An aerospace system operating under standard sea level conditions is governed by Compressors and Turbines (Axial Flow Gas Turbines & Blade Cooling). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Strength of Materials & Elasticity

An aerospace system operating under standard sea level conditions is governed by Strength of Materials & Elasticity (Euler Buckling of Columns & Energy Methods). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Thin-Walled Structures

In an aerospace engineering analysis of Thin-Walled Structures (Torsion of Multi-Cell Thin-Walled Tubes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thin-Walled Structures

In an aerospace engineering analysis of Thin-Walled Structures (Tension Field Beams & Wagner Beams), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Structural Dynamics & Aeroelasticity

An aerospace system operating under standard sea level conditions is governed by Structural Dynamics & Aeroelasticity (Free & Forced Vibrations of Continuous Beams). Compute the required parameter in standard SI units (rounded off to the acceptable range).

Aerospace Materials & Fatigue

In an aerospace engineering analysis of Aerospace Materials & Fatigue (Aluminum, Titanium & Aerospace Alloys), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Aerospace Materials & Fatigue

In an aerospace engineering analysis of Aerospace Materials & Fatigue (Damage Tolerance & Non-Destructive Testing), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?