GATE AE year:2019 PYQs & Answers — Page 5

Questions 41–50 of 65. Imported answers require independent review unless marked reviewed.

Topic practice 65 questionsPage 5 of 7

For real

, the number of points of intersection between the curves

and

is ______.

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One of the eigenvalues of the following matrix is 1.

The other eigenvalue is ______.

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The curve

is such that its slope is equal to

for all real

. If the curve passes through

, the value of

is ______ (round off to 1 decimal place).

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The inviscid, incompressible flow field resulting from a uniform flow past a circular cylinder of radius

centered at the origin is given by:

Diagram for Aerospace Engineering question 34

where

and

are the radial and azimuthal velocity components in polar coordinates,

, as shown in the figure.

is the free stream speed. Ignore the effects of gravity. The azimuthal location (in the first quadrant) on the cylinder at which the pressure coefficient is zero is ______ degrees (round off to the nearest integer).

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A cylindrical container of radius

cm is filled with water up to a height

. Upon rotating the cylinder about its central axis at a constant angular speed, the free surface takes a parabolic shape (see figure), and is displaced upwards by

cm at

. The magnitude of the downward displacement

of the free surface at

is ______ cm (round off to the nearest integer).

Diagram for Aerospace Engineering question 35

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A two-dimensional, incompressible fluid flow is described by the stream function

/s on the Cartesian

plane. If the density and dynamic viscosity of the fluid are 1 kg/m

and 0.1 kg/m-s, respectively, the magnitude of the pressure gradient in the

direction at

m and

m is ______ N/m

(round off to 1 decimal place).

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The static pressure ratio across a stationary normal shock is given by

where

is the upstream Mach number. For a stationary normal shock in air (

J/kg-K) with upstream flow conditions given by: speed 800 m/s, static temperature 300 K and static pressure 1 atm., the static pressure downstream of the shock is ______ atm. (round off to 2 decimal places).

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For a symmetric airfoil at an angle of attack of 10°, assuming thin airfoil theory, the magnitude of the pitching moment coefficient about the leading edge is ______ (round off to 2 decimal places).

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The span-wise distribution of circulation over a finite wing of span

m is

/s and the free stream density and speed are 1.2 kg/m

and 100 m/s, respectively, the total lift is ______ kN (round off to 2 decimal places).

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The airplane shown in figure starts executing a symmetric pull-up maneuver from steady level altitude with a constant nose-up pitch acceleration of 20 deg/s

. The vertical load factor measured at this instant at the centre of gravity (CG) is 2. Given that the acceleration due to gravity is 9.81 m/s

, the vertical load factor measured at point P on the nose of the airplane, which is 2 m ahead of the CG, is ______ (round off to 2 decimal places).

Diagram for Aerospace Engineering question 40

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GATE AE year:2019 PYQs

Question 31

Question 32

Question 33

Question 34

Question 35

Question 36

Question 37

Question 38

Question 39

Question 40