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Aerospace Engineering Gate 2009 Questions with Answer

1 2 3 4 5

Ques 27 GATE 2009

The contribution of the horizontal tail to the pitching moment coefficient about the center of gravity
(C_{m_CG}) of an aircraft is given by C_{m_talt}=0.2-0.0215 α where α is the angle of attack of the
aircraft. The contribution of the tail to the aircraft longitudinal stability

is stabilizing

is destabilizing

is nil

cannot be determined from the given information

(a) is the correct answer.

Ques 28 GATE 2009

The roots of the characteristic equation for the longitudinal dynamics of a certain aircraft are:

λ₁ = -0.02 + 0.2i
λ₂ = -0.02 - 0.2i
λ₃ = -2.5 + 2.6i
λ₄ = -2.5 - 2.6i

where i = √-1. .The pair of eigenvalues that represent the phugoid mode is

λ₁ and λ₃

λ₂ and λ₄

λ₃ and λ₄

λ₁ and λ₂

(d) is the correct answer.

Ques 29 GATE 2009

The roots of the characteristic equation for the longitudinal dynamics of a certain aircraft are:

λ₁ = -0.02 + 0.2i
λ₂ = -0.02 - 0.2i
λ₃ = -2.5 + 2.6i
λ₄ = -2.5 - 2.6i

where i = √-1. The short period damped frequency is

2.6 rad/s

0.2 rad/s

2.5 rad/s

0.02 rad/s

(a) is the correct answer.

Ques 30 GATE 2009

Consider an ideal flow of density ρ through a variable area duct as shown in the figure below:

Let the cross-sectional areas at sections (1) and (2) be A₁ and A₂ respectively. The velocity measured
at section (1) using a Pitot static probe is V₁. Then the static pressure drop p₂-p₁ is

-¹₂ρ(1-^A₁²_A₂²)V₁²

¹₂ρ(1-^A₁²_A₂²)V₁²

¹₂ρ(1+^A₁²_A₂²)V₁²

-¹₂ρ(1+^A₁²_A₂²)V₁²

(a) is the correct answer.

Ques 31 GATE 2009

Two vortices of the same strength and sign are placed a distance d apart as shown below. Assume that the vortices are free to move and the fluid is ideal.

Which of the following statements is true ?

Vortices 1 and 2 spiral inwards with an initial angular speed ^Γ_{2π d²} to finally merge and form one vortex of twice the strength.

Vortices 1 and 2 spiral inwards with an initial angular speed to finally merge and form one vortex of twice the strength.

Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution ^d₂ and angular speed ^Γ_{π d²}

Vortices 1 and 2 perpetually revolve about the midpoint P with radius of revolution ^d₂ and angular speed ^Γ_{2π d²}

(d) is the correct answer.

Ques 32 GATE 2009

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

10.8 mm

8.8 mm

5.9 mm

4.8 mm

Ques 33 GATE 2009

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

²_{U_∞/U_e+1}

1-^U_∞_{U_e}

^2U_∞U_e_{U_e²+U_∞²}

^2U_∞_{U_e+U_∞}

(d) is the correct answer.

Ques 34 GATE 2009

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

P and R

Q and R

P and Q

P, Q and R

Ques 35 GATE 2009

Thrust available from a turbojet engine

increases as altitude increases

increases up to the tropopause and then decreases

remains constant at all altitudes

decreases as altitude increases

(d) is the correct answer.

Ques 36 GATE 2009

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 T₀=1500 K and specific heat of gas c_p=1 kJ/kg/K, the
power drawn by the compressor per unit mass flow rate of air is approximately

300 kW/kg/s

1000 kW/kg/s

600 kW/kg/s

500 kW/kg/s

(d) is the correct answer.

Ques 37 GATE 2009

An ideal ramjet is flying at an altitude of 10 km with a velocity of 1 km/s. The ambient pressure is
0.25 bar and temperature is 225 K. The exhaust gases from the engine are optimally expanded and
leave the nozzle at 900 K. If the specific heat ratio (γ) remains constant, the specific thrust developed
by the engine is approximately

1000 N-s/kg

2000 N-s/kg

500 N-s/kg

4000 N-s/kg

(a) is the correct answer.

Ques 38 GATE 2009

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 ( ) remains constant), approximately by what factor must the nozzle area be
changed ?

0.5

(d) is the correct answer.

Ques 39 GATE 2009

Air enters the combustor of a gas-turbine engine at a total temperature T₀ 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 c_p = 1 kJ/kg/K.
If the sensible enthalpy of fuel is neglected, the temperature of combustion products from the reaction
of primary air stream with fuel is approximately

2100 K

3200 K

2600 K

1800 K

1 2 3 4 5

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