GATE XE Differential Analysis PYQs & Answers

Questions 1–10 of 53. Imported answers require independent review unless marked reviewed.

The velocity components in

- and

-directions of a two-dimensional, incompressible flow field are

and

, respectively. Here,

is a polynomial function and

is a polynomial function of

only. Which one of the following options for

is correct?

Your answerChoose one option.

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A steady, laminar, and incompressible flow between a pair of infinite parallel plates is driven by a constant pressure gradient

. The plates are separated by a distance

, as shown in the figure. The fully-developed velocity profile of the flow is

where

is the dynamic viscosity.

The values of

, for which the local flow velocity is equal to the average flow velocity, are

Diagram for Engineering Sciences question 31

Your answerChoose one option.

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An incompressible fluid flows between a pair of infinite plates separated by a distance

. The top plate is moving with a constant velocity

, whereas the bottom plate is stationary, as shown in the figure. The difference of the stream functions (

) at the two plates for a laminar and fully-developed flow is equal to

Diagram for Engineering Sciences question 32

Your answerChoose one option.

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The axial velocity profile of a laminar, incompressible, and fully-developed flow in a circular pipe of radius

is given as

, where

, and

are dynamic viscosity, pressure, axial coordinate, and radial coordinate, respectively. If the magnitude of shear stress at the pipe wall is given as

, then the value of

is __________. (answer in integer)

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For a steady and incompressible flow, the velocity field (

) in Cartesian

coordinate system is given as:

Here,

, and

are unit vectors along

, and

directions, respectively and

is a constant. Which one of the following options is the correct value of

that satisfies the conservation of mass for the given velocity field?

Your answerChoose one option.

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Conservation of mass for a steady axisymmetric flow field in the cylindrical

coordinates is:

Here,

and

are radial and axial components of velocity, respectively. Which one of the following options is correct if

is the stream function?

Your answerChoose one option.

and

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Figure shows two parallel plates (upper plate at

and lower one at

) of length L (aligned in

direction) and infinite width (in

direction, normal to the plane of the figure). Two immiscible, incompressible liquids are flowing steadily in the

direction through the thin passage between the plates under the influence of horizontal pressure gradient

. During the flow, the passage is always half-filled with denser fluid I (viscosity

) at the bottom and rest is occupied by lighter fluid II (viscosity

;

). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress,

is expressed as:

Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Your answerChoose one option.

Above the interface

Below the interface

At the interface

At the top plate

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Consider,

and

are unit vectors along x and y directions of a Cartesian

coordinate system, respectively and

is time. Temperature (

) and fluid velocity (

) are given for a flow field as:

The total rate of change of temperature in the flow field (in integer) for time

at a point

is ________

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Driven by a pressure gradient of 100 kPa/m, a fluid of dynamic viscosity 0.1 Pa.s flows between two fixed infinite large parallel plates under steady, incompressible, and fully developed laminar conditions. The average velocity of the flow is 2 m/s. The gap between the parallel plates in mm (rounded off to 2 decimal places) is ________

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An incompressible fluid is flowing between two infinitely large parallel plates separated by 5 mm distance. The bottom plate is stationary and the top plate is moving at a constant velocity of 5 mm/s in the direction parallel to the bottom plate. The flow of the fluid between the plates is steady, two-dimensional, laminar, and the variation of fluid velocity is linear between the plates. A square fluid element of 1 mm side is considered at equal distance from the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in mm

/s (in integer) along the edges of the square fluid element is ________

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GATE XE Differential Analysis PYQs

How to practice Differential Analysis

Question 28

Question 31

Question 32

Question 42

Question 26

Question 27

Question 31

Question 36

Question 37

Question 38