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GATE Aeronautical Engineering
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GATE Aeronautical Engineering
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The propellant in a single stage sounding rocket occupies 60% of its initialmass.
If all of it is expended instantaneously at an equivalent exhaust velocity of 3000 m/s, what would be the altitude attained by the payload when launched vertically? [Neglect drag and assume acceleration due to gravity to be constant at 9.81 m/s2.]
A rocket is to be launched from the bottom of a very deep crater on Mars for earthreturn.
The specific impulse of the rocket, measured in seconds, is to be normalized by the acceleration due to gravity at
Mars standard “sea level”.
the bottom of the crater on Mars.
earth’s standard sea level.
the same depth of the crater on earth.
Consider two engines P and Q. In P, the high pressure turbine blades are cooled with a bleed of 5% from the compressor after the compression process and in Q the turbine blades are notcooled.
Comparing engine P with engine Q, which one of the following is NOT TRUE
Compressor work is the same for both P and Q
Turbine inlet temperature is higher for engine P
Specific thrust is higher for engine P
Fuel flow rate is lower for engine P
At x = 0 , the function y = |x| is
continuous and differentiable
continuous but not differentiable
not continuous and not differentiable
not continuous but differentiable
The constraint A2 = A on any square matrix A is satisfied for
the null matrix only.
no square matrix A.
both the identity matrix and the null matrix.
the identity matrix only.
A thin long circular pipe of 10 mm diameter has porous walls and spins at 60 rpm about its ownaxis.
Fluid is pumped out of the pipe such that it emerges radially relative to the pipe surface at a velocity of 1 m/s. [Neglect the effect ofgravity.
] What is the radial component of the fluid’s velocity at a radial location 0.5 m from the pipe axis
The volume of a solid generated by rotating the region between semi-circle y = 1 − √1− x2 and straight line y = 1, about x axis, is
∏2 - 4/3 ∏
3/4 ∏2 - ∏
∏2 - 3/4 ∏
4∏2 - 1/3 ∏
All professors are researchers Some scientists are professors Which of the given conclusions is logically valid and is inferred from the above arguments
All scientists are researchers
Some researchers are scientists
All professors are scientists
No conclusion follows
Which one of the following is TRUE with respect to Phugoid mode of an aircraft
Frequency is directly proportional to the square root of flight speed
Frequency is inversely proportional to the square root of flight speed
Frequency is directly proportional to flight speed
Frequency is inversely proportional to flight speed
Consider one-dimensional isentropic flow at a Mach number of 0.5. If the area of cross-section of a streamtube increases by 3% somewhere along the flow, the corresponding percentage change in density is ________
Choose the most appropriate alternative from the options given below to complete the following sentence: The administrators went on to implement yet another unreasonable measure, arguing that the measures were already ___ and one more would hardly make a difference
Three identical eagles of wing span s are flying side by side in a straight line with no gap between their wingtips.
Assume a single horse shoe vortex model (of equal strength Γ) for eachbird.
The net downwash experienced by the middle bird is
The ideal static pressure coefficient of a diffuser with an area ratio of 2.0 is
Select the pair that best expresses a relationship similar to that expressed in the pair: water: pipe
Values of a, b and c, which render the matrix orthonormal are, respectively
-1/√6, 2/√6, -1/√6
1/√6, -2/√6, 1/√6
-1/√3, -1/√3, 1/√3
1/√2, 1/√2, 0
A solid propellant of density 1800 kg/m3 has a burning rate law r = 6.65 x 10-3p0.
45 mm/s, where p is pressure inPascals.
It is used in a rocket motor with a tubular grain with an initial burning area of 0.314 m2. The characteristic velocity is 1450 m/s. What should be the nozzle throat diameter to achieve an equilibrium chamber pressure of 50 bar at the end of the ignition transient
A wing and tail are geometrically similar, while tail area is one-third of the wing area and distance between two aerodynamic centres is equal to wing semi-span
(b/2). In addition, following data is applicable: ∈α = 0.3, CL = 1.0, CLα 0.08/deg.
, c = 2.5 , b = 30m , CMac = 0, ηt = 1. The symbols have their usual aerodynamicinterpretation.
The maximum distance that the centre of gravity can be behind aerodynamic centre without destabilizing the wing-tail combination is
The integration computed using trapezoidal rule with n = 4 intervals is ____
0.32 to 0.33
0.22 to 0.23
0.26 to 0.27
0.25 to 0.26
If 3 ≤ X ≤ 5 and 8 ≤ Y ≤ 11 then which of the following options is TRUE
3/5 ≤ X/Y ≤ 8/5
3/11 ≤ X/Y ≤ 5/8
3/11 ≤ X/Y ≤ 8/5
3/5 ≤ X/Y ≤ 8/11
Which one of the following criteria leads to maximum turn rate and minimum radius in a level turn flight
Lowest possible load factor and highest possible velocity
Lowest possible load factor and lowest possible velocity
Highest possible load factor and lowest possible velocity
Highest possible load factor and highest possible velocity
An airfoil generates a lift of 80 N when operating in a freestream flow of 60 m/s. If the ambient pressure and temperature are 100 kPa and 290 K respectively (specific gas constant is 287 J/kg-K), the circulation on the airfoil in m2/s is ____
0.5 to 0.7
1.2 to 1.3
1.1 to 1.2
2.1 to 2.2
If a prime number on division by 4 gives a remainder of 1, then that number can be expressed as
sum of square roots of two natural numbers
sum of cube roots of two natural numbers
sum of cubes of two natural numbers
sum of squares of two natural numbers
The boundary condition of a rod under longitudinal vibration is changed from fixed-fixed tofixedfree.
The fundamental natural frequency of the rod is now k times the original frequency, where k is
The mass flow rate of air through an aircraft engine is 10 kg/s. The compressor outlet temperature is 400 K and the turbine inlet temperature is 1800 K. The heating value of the fuel is 42 MJ/kg and the specific heat at constant pressure is 1 kJ/kg-K. The mass flow rate of the fuel in kg/s is approximately ___________
0.3 to 0.35
0.7 to 0.75
0.2 to 0.25
0.5 to 0.55
Data for an airplane are given as follows: weight W = 30kN, thrust available at sea-level T0 = 4000 N, wing planform area S = 30 m2, maximum lift coefficient CL max = 1.4, and drag coefficient CD = 0.015 + 0.024C2L.
Assume air density at sea-level P∞ = 1.22 kg/ m3. Stall speed of the airplane in m/s is
A cantilever beam of negligible mass is 0.6 mlong.
It has a rectangular cross-section of width 8 mm and thickness 6 mm and carries a tip mass of 1.4 kg. If the natural frequency of this system is 10 rad/s, Young’s modulus of the material of the beam in GPa is ________
Which one of the following statements is NOT TRUE for a supersonic flow
Over a gradual expansion, entropy remains constant
Over a gradual compression, entropy can remain constant
Over a sharp compression corner, entropy increases
Over a sharp expansion corner, entropy can increase
The channel section of uniform thickness 2mm shown in the figure is subjected to a torque of 10 Nm. If it is made of a material with shear modulus of 25 GPa, the twist per unit length in radians/m is _________
0.13 to 0.14
0.12 to 0.13
0.14 to 0.15
0.15 to 0.16
A gas turbine engine is mounted on an aircraft which can attain a maximum altitude of 11 km from sealevel.
The combustor volume of this engine is decided based on conditions at
11 km altitude
5.5 km altitude
8 km altitude
The thin rectangular plate has dimensions L×b×t. It develops a stress field corresponding to an applied bending moment M as shown in thefigure.
A valid Airy’s stress function is
2M/tb3 (x3 + y3)
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