GATE AE 2009 Question Paper & Solutions

Verbal Aptitude

For two-dimensional irrotational and incompressible flows

Verbal Aptitude

A trailing edge plain flap deflected downward increases the lift coefficient of an airfoil by

Quantitative Aptitude

Symmetric airfoils only. (C) Any airfoil shape. (B) Cambered airfoils only. (D) Joukowski airfoils only. Q.5 The ordinary differential equation ds? + ky = 0 where k is real and positive

Analytical & Spatial Aptitude

is non-linear (B) has a characteristic equation with one real and one complex root (C) has a characteristic equation with two real roots (D) has a complementary function that is simple harmonic Q.6 A non-trivial solution to the (nXn) system of equations [A]{x} = {0}, where {0} is the null vector

Analytical & Spatial Aptitude

The propulsive efficiency of a turbo-jet engine moving at velocity Uo and having exhaust velocity Ue with respect to the engine is given by

Verbal Aptitude

An aircraft is flying at M = 2 where the ambient temperature around the aircraft is 250 K. If the specific heat ratio for air y = 1.4, the stagnation temperature on the surface of the aircraft is

Quantitative Aptitude

The division of feed air to an aircraft gas-turbine combustor into primary and secondary streams serves which of the following purposes ? P. a flammable mixture can be formed Q. cooling of combustor liner and flame tube can be accomplished R. specific fuel consumption can be reduced

Quantitative Aptitude

(C) P and Q (D) P, Q and R Q.11 Classify the following propellants as: cryogenic (C) , semi-cryogenic (SC), compressed gas (CG) and earth storable (ES) N,0,-UDMH (nitrogen tetra oxide and unsymmetrical di-methyl hydrazine) LOX-RP1 (liquid oxygen and kerosene) LOX-LH2 (liquid oxygen and liquid hydrogen) N2 (nitrogen gas)

Verbal Aptitude

2009 AE Q.14 An unswept fixed-winged aircraft has a large roll stability if the wing is placed

Analytical & Spatial Aptitude

low on the fuselage and has negative dihedral angle (B) low on the fuselage and has positive dihedral angle (C) high on the fuselage and has negative dihedral angle (D) high on the fuselage and has positive dihedral angle Q.15 Thrust available from a turbojet engine

Linear Algebra

increases as altitude increases (B) increases up to the tropopause and then decreases (C) remains constant at all altitudes (D) decreases as altitude increases Q.16 If Cmca is the pitching moment coefficient about the center of gravity of an aircraft, and A is the angle of attack, then dC mcG is da

Linear Algebra

a stability derivative which represents stiffness in pitch (B) a stability derivative which represents damping in pitch (C) a control derivative in pitch (D) positive for an aircraft that is stable in pitch Q.17 The life of a geo-stationary communications satellite is limited by

Calculus

For a critically damped single degree of freedom spring - mass - damper system with a damping constant c of 4 Ns/m and spring constant k of 16 N/m, the system mass m is

Differential Equations

An ideal axial compressor is driven by an ideal turbine across which the total temperature ratio is 0.667. If the total temperature at turbine inlet is To = 1500 K and specific heat of gas c, = 1 kJ/kg/K, the power drawn by the compressor per unit mass flow rate of air is approximately

Numerical Methods

The performance of a solid rocket motor is improved by replacing the old propellant with a new one. The new propellant gives a combustion temperature 40% higher than the previous propellant without appreciable change in molecular weight of combustion products and other operating parameters. By approximately what percentage is the specific impulse of the new motor higher than the old one ?

Basic Fluid Mechanics

18% (B) 96% (C) 42% (D) 112% Q.24 A solid rocket motor has an end burning grain of cross-sectional area Acs = 0.4 m? . The density of propellant is pp = 1500 kg / m and has linear regression rate i = 5 mm/s. If the specific impulse of the propulsion system is Isp = 200 seconds, the thrust produced by the motor is approximately

Airfoil & Wing Theory

(C) 500 N-s/kg (D) 4000 N-s/kg A combat aircraft engine is equipped with an afterburner followed by a variable area convergent nozzle (operating with the nozzle choked). The exhaust gas temperature is 750 K when afterburner is off and 3000 K when it is on. When the afterburner is turned on, (assuming the total pressure remains the same, the mass of fuel added in the afterburner is negligible i.e., the mass flow rate remains the same, and the specific heat ratio (Y) remains constant), approximately by what factor must the nozzle area be changed ?

Compressible Flow & Shocks

0.5 (B) 4 (C) 1 (D) 2 An airplane flying at 100 m/s is pitching at the rate of 0.2 deg/s. Due to this pitching, the horizontal tail surface located 4 metres behind the centre-of-mass of the airplane will experience a change in angle of attack, which is

Compressible Flow & Shocks

0.01 deg (B) 0.008 deg (C) 0.04 deg (D) 0.004 deg The contribution of the horizontal tail to the pitching moment coefficient about the center of gravity (Cmcg) of an aircraft is given by Cmail = 0.2-0.0215 a, where a is the angle of attack of the aircraft. The contribution of the tail to the aircraft longitudinal stability

Wind Tunnel Testing & Instrumentation

The linearized dynamics of an aircraft (which has no large rotating components) in straight and level flight is governed by the equations dx dt [[a] [в]]. [[c] [D] where x=[u w q 0 v pr ], [I represents the transpose of a matrix, [A], [B], [C] and [D] are 4x4 matrices and [O] is the 4x4 null matrix. Which of the following is true ?

Atmospheric Flight Mechanics

2009 AE Q.30 The velocity vector of an aircraft along its body-fixed axis is given by V = If V is the magnitude W of V, a is the angle of attack and B is the angle of sideslip, which of the following set of relations is correct ?

Atmospheric Flight Mechanics

An aircraft of mass 2500 kg in straight and level flight at a constant speed of 100 m/s has available excess power of 1.0 x 10° W. The steady rate of climb it can attain at that speed is

Static Stability & Control

100 m/s (B) 60 m/s (C) 40 m/s (D) 20 m/s Q.32 The acceleration due to gravity on the surface of Mars is 0.385 times that on earth, and the diameter of Mars is 0.532 times that of earth. The ratio of the escape velocity from the surface of Mars to the escape velocity from the surface of earth is approximately

Dynamic Stability

(C) 0.851 (D) 0.724 Q.33 Which of the following statements are true for flow across a stationary normal shock ? P. Stagnation temperature stays constant. Q. Stagnation pressure decreases. R. Entropy increases. S. Stagnation pressure increases. T. Stagnation temperature increases.

Space Dynamics & Orbital Mechanics

A model airfoil in a wind tunnel that is operating at 50 m/s develops a minimum pressure co-efficient of - 6.29 at some point on its upper surface. The local airspeed at that point is

Thermodynamic Cycles of Gas Turbines

A symmetrical airfoil section produces a lift coefficient of 0.53 at an angle of attack of 5 degrees measured from its chord line. An untwisted wing of elliptical planform and aspect ratio 6 is made of this airfoil. At an angle of attack of 5 degrees relative to its chordal plane, this wing would produce a lift coefficient of

Thermodynamic Cycles of Gas Turbines

d Which of the following statements is true ?

Inlets, Combustors & Nozzles

2nd? (D) Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution and angular speed nd? The laminar boundary layer over a large flat plate held parallel to the flow is 7.2 mm thick at a point 0.33 m downstream of the leading edge. If the free stream speed is increased by 50%, then the new boundary layer thickness at this location will be approximately

Compressors and Turbines

The buckling load for a simply supported column of rectangular cross section of dimensions 1 cmx1.5 cm and length 0.5 m made of steel (E = 210x10% N/m') is approximately

Rocket Propulsion

0.025 m 0.025 m chord line 1 cm? 1 cm' 0.5 m The wing root bending moment in steady level flight is M, = 10 N-m. If the airplane flies at a load factor n = 3.5, the maximum bending stress at the root is

Strength of Materials & Elasticity

(D) underdamped with natural frequency C, = 2 rad/s A 2-celled tube with wall thickness 0.5 mm is subjected to a torque of 10 N-m. The resulting shear flows in the two cells are q, and q2 as shown below. 50 mm 50 mm 42 50 mm The torque balance equation (Bredt-Batho formula) for this section leads to

Strength of Materials & Elasticity

2009 AE The value of the integral 1+ x + sin x - evaluated using the trapezoidal rule with two equal intervals is approximately

Thin-Walled Structures

In an aerospace engineering analysis of Thin-Walled Structures (Shear Flow in Open and Closed Thin-Walled Beams), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Structural Dynamics & Aeroelasticity

2009 AE Common Data Questions Common Data for Questions 51 and 52: The roots of the characteristic equation for the longitudinal dynamics of a certain aircraft are: 4=-0.02 + 0.21; 22 = -0.02 - 0.2; 23 = -2.5 + 2.61; 24 = -2.5 - 2.6i, where i = V-1. Q.51 The pair of eigenvalues that represent the phugoid mode is

Aerospace Materials & Fatigue

My and 23 (B) 22 and 24 (C) 23 and 24 (D) 2 and 22 Q.52 The short period damped frequency is

Linear Algebra

2.6 rad/s (B) 0.2 rad/s (C) 2.5 rad/s (D) 0.02 rad/s Common Data for Questions 53 and 54: Consider the vector field à = (y3 + z3)Î+(x +z)f+(x+y')k defined over the unit sphere x? + y2+2₴ =1. Q.53 The surface integral (taken over the unit sphere) of the component of A normal to the surface is

Calculus

Statement for Linked Answer Questions 57 and 58: Air enters the combustor of a gas-turbine engine at a total temperature To of 500 K. The air stream is split into two parts: primary and secondary streams. The primary stream reacts with fuel supplied at a fuel-air ratio of 0.05. The resulting combustion products are then mixed with the secondary air stream to obtain gas with total temperature of 1550 K at the turbine inlet. The fuel has a heating value of 42 MJ/kg. The specific heats of air and combustion products are taken as Cp = 1 kJ/kg/K. Q.57 If the sensible enthalpy of fuel is neglected, the temperature of combustion products from the reaction of primary air stream with fuel is approximately

Differential Equations

2100 K (B) 3200 K (C) 2600 K (D) 1800 K Q.58 The approximate ratio of mass flow rates of the primary air stream to the secondary air stream required to achieve the turbine inlet total temperature of 1550 K is

Numerical Methods

(D) 1:1 Statement for Linked Answer Questions 59 and 60: A piston compresses 1 kg of air inside a cylinder as shown Air AE The rate at which the piston does work on the air is 3000 W. At the same time, heat is being lost through the walls of the cylinder at a rate of 847.5 W. Q.59 After 10 seconds, the change in specific internal energy of the air is

Airfoil & Wing Theory

21,525 J/kg (B) - 21,525 J/kg (C) 30,000 J/kg (D) - 8,475 J/kg Q.60 Given that the specific heats of air at constant pressure and volume are Cp = 1004.5 J/kg-K and C, = 717.5 J/kg-K respectively, the corresponding change in the temperature of the air is

Basic Fluid Mechanics

In an aerospace engineering analysis of Basic Fluid Mechanics (Viscous Flow & Boundary Layer Equations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (Normal & Oblique Shock Waves), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Airfoil & Wing Theory

In an aerospace engineering analysis of Airfoil & Wing Theory (Finite Wing Theory & Induced Drag), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressible Flow & Shocks

In an aerospace engineering analysis of Compressible Flow & Shocks (Rayleigh & Fanno Flow), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Basic Fluid Mechanics

In an aerospace engineering analysis of Basic Fluid Mechanics (Incompressible Potential Flow & Stream Functions), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Airfoil & Wing Theory

In an aerospace engineering analysis of Airfoil & Wing Theory (High-Lift Devices & Flaps), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Drag Polar & Aircraft Performance Equations), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Atmospheric Flight Mechanics

In an aerospace engineering analysis of Atmospheric Flight Mechanics (Range and Endurance of Jet & Propeller Aircraft), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Static Stability & Control

In an aerospace engineering analysis of Static Stability & Control (Static Margin & Stick-Fixed/Free Stability), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Dynamic Stability

In an aerospace engineering analysis of Dynamic Stability (Dutch Roll, Spiral & Roll Subsidence Modes), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

In an aerospace engineering analysis of Space Dynamics & Orbital Mechanics (Hohmann Transfer & Orbital Maneuvers), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Space Dynamics & Orbital Mechanics

In an aerospace engineering analysis of Space Dynamics & Orbital Mechanics (Rocket Trajectory & Staging), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thermodynamic Cycles of Gas Turbines

In an aerospace engineering analysis of Thermodynamic Cycles of Gas Turbines (Brayton Cycle with Real Component Efficiencies), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Thermodynamic Cycles of Gas Turbines

In an aerospace engineering analysis of Thermodynamic Cycles of Gas Turbines (Thrust Equations & Specific Fuel Consumption), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Inlets, Combustors & Nozzles

In an aerospace engineering analysis of Inlets, Combustors & Nozzles (Convergent & Convergent-Divergent (C-D) Nozzles), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressors and Turbines

In an aerospace engineering analysis of Compressors and Turbines (Centrifugal Compressors), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

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

In an aerospace engineering analysis of Rocket Propulsion (Solid, Liquid & Hybrid Rocket Engines), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Compressors and Turbines

In an aerospace engineering analysis of Compressors and Turbines (Axial Flow Gas Turbines & Blade Cooling), which one of the following statements is CORRECT regarding the governing aerodynamic and structural behavior?

Strength of Materials & Elasticity

In an aerospace engineering analysis of Strength of Materials & Elasticity (Euler Buckling of Columns & Energy Methods), 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 (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

In an aerospace engineering analysis of Structural Dynamics & Aeroelasticity (Free & Forced Vibrations of Continuous Beams), 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 (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?