GATE XE Differential Analysis PYQs & Answers — Page 3

Questions 21–30 of 53. Imported answers require independent review unless marked reviewed.

For an inviscid fluid with density 1 kg/m

, the Cartesian velocity field is given as:

Neglecting the body forces, find the magnitude of pressure gradient (in Pa/m) at

. (Round off to two decimal places)

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The horizontal belt of negligible weight shown in the figure moves with a steady velocity (

) of 2.5 m/s and skims over the top surface of an oil-film of depth

= 3 cm. The length (

) and width (

) of the belt are, respectively, 2 m and 60 cm. Find the viscosity of the oil (in Pa-s), given that the minimum power required to move the belt is 100 W. Neglect the end effects. (Round off to two decimal places)

Diagram for Engineering Sciences question 43

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and

are the average pressures at inlet and outlet respectively for a fully-developed flow inside a channel having a height of

, then the absolute value of average shear stress (in Pa) acting on the walls of the channel of length

Your answerChoose one option.

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Which one of the following statements is TRUE about the continuity equation

(where

are the velocity components along the

and

coordinates respectively):

Your answerChoose one option.

The equation is valid only for steady incompressible flows.

The equation is valid for both steady and unsteady incompressible flows.

The equation is valid only for steady compressible flows.

The equation is valid only for unsteady compressible flows.

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In a Cartesian coordinate system, a steady, incompressible velocity field of a Newtonian fluid is given by

Here, V is the velocity vector in m/s, i is the unit vector in the x-direction,

is a positive, real constant (in m/s), and

is a positive, real constant (in m

). The viscosity of the fluid is

(in Pa-s). The absolute value of the pressure gradient (in Pa/m) is

Your answerChoose one option.

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The two-dimensional velocity field

of a flow in a Cartesian coordinate system is given in dimensionless form by

. Here,

and

are the unit vectors along the x and y directions respectively,

and

are independent of

and time. If the flow is incompressible, then the value of

, up to one decimal place, is ________.

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Figures given below show the velocity and shear stress profiles for the flow in a duct. In each option, ‘1’ represents velocity profile and ‘2’ represents shear stress profile.

Choose the correct option that closely represents the turbulent flow condition.

Your answerChoose one option.

Diagram for Engineering Sciences question 1

Diagram for Engineering Sciences question 1 (figure 2)

Diagram for Engineering Sciences question 1 (figure 3)

Diagram for Engineering Sciences question 1 (figure 4)

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The volume flow between any two points not lying on the same stream in a flow field is equal to

Your answerChoose one option.

Change in strain rate between the points

Change in vorticity between the points

Change in potential function between the points

Change in stream function between the points

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The velocity field for a flow is

, where

is time. Choose the correct option representing the total acceleration at

Your answerChoose one option.

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An incompressible viscous fluid is placed between two infinite horizontal parallel plates as shown in Figure. The plates move in opposite direction with constant velocities

and

. The pressure gradient in the x-direction is zero and the only body force is due to the fluid weight. The flow is steady, laminar and two-dimensional. Assume velocity component in ‘y’ direction to be zero.

Diagram for Engineering Sciences question 12

The correct expression for the velocity distribution between the plates is:

Your answerChoose one option.

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GATE XE Differential Analysis PYQs

Question 38

Question 43

Question 3

Question 6

Question 12

Question 14

Question 1

Question 7

Question 11

Question 12