Fluid Mechanics (XE-B) - GATE XE (Engineering Sciences) Subject-Wise PYQ Practice

Question 1

Fluid at a constant flow rate passes through a long, straight, cylindrical pipe that has an axisymmetric convergent section at the end. Which one of the following options correctly represents the velocity field in the converging section in cylindrical (𝑟, 𝜃, 𝑧) coordinates?

Accepted Answer

Two-dimensional function of 𝑟 and 𝑧

Answer

One-dimensional function of 𝑟

Answer

Two-dimensional function of 𝑟 and 𝜃

Answer

One-dimensional function of 𝑧

Question 2

A sharp flat plate of length L and infinite width is immersed parallel to a fluid stream having velocity 𝑢∞. At a point on the plate, far away from the leading edge and not near the trailing edge, the boundary layer thickness, the displacement thickness, and the momentum thickness are denoted as 𝛿, 𝛿∗, and 𝜃, respectively. Which one of the following options correctly represents the relation between these thicknesses?

Accepted Answer

𝛿> 𝛿∗> 𝜃

Answer

𝛿> 𝜃> 𝛿∗

Answer

𝛿∗> 𝛿> 𝜃

Answer

𝜃> 𝛿∗> 𝛿

Question 3

Consider the following Statements [1] and [2]. Statement [1]: The Eulerian study focusses attention on individual particle and its motion is observed as a function of time. Statement [2]: The Lagrangian study focusses attention on the motion of the particles passing through an identified point. Which one of the following options identifies the correctness of the given statements?

Accepted Answer

Both [1] and [2] are NOT correct.

Answer

Both [1] and [2] are correct.

Answer

[1] is correct, but [2] is NOT correct.

Answer

[1] is NOT correct, but [2] is correct.

Question 4

Statement of Reynolds Transport Theorem is given below with three blanks. The rate of change of ________ extensive property can be calculated by summing the rate of change of the amount of same property in the ________ and the rate at which the property is ________ the surface of the control volume. Which one of the following options correctly fills the blanks by using its comma-separated phrases in sequence?

Accepted Answer

system, control volume, exiting

Answer

control volume, system, exiting

Answer

system, control volume, entering

Answer

control volume, control volume, entering

Question 5

For a steady and incompressible flow, the velocity field (𝑉⃗ ) in Cartesian (𝑥, 𝑦, 𝑧) coordinate system is given as: 𝑉⃗ = 5𝑥𝑖−𝑃𝑦𝑗+ 3𝑘 Here, 𝑖, 𝑗, and 𝑘 are unit vectors along x, y, and z directions, respectively and 𝑃 is a constant. Which one of the following options is the correct value of 𝑃 that satisfies the conservation of mass for the given velocity field?

Accepted Answer

5

Answer

−5

Answer

8

Answer

2

Question 6

Conservation of mass for a steady axisymmetric flow field in the cylindrical (r, z) coordinates is: 1 𝑟 𝜕(𝑟𝑉𝑟) 𝜕𝑟 + 𝜕𝑉𝑧 𝜕𝑧= 0 Here, 𝑉𝑟 and 𝑉𝑧 are radial and axial components of velocity, respectively. Which one of the following options is correct if 𝜓 is the stream function?

Accepted Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= 1 𝑟 𝜕𝜓 𝜕𝑟

Answer

𝑉𝑟= 1 𝑟 𝜕𝜓 𝜕𝑧 and 𝑉𝑧= − 𝜕𝜓 𝜕𝑟

Question 7

Group-I indicates different properties of fluid and Group-II defines their basic dimensions in terms of Force (𝐹), Length (𝐿), and Time (𝑇). Group-I Group-II P Dynamic viscosity 1 𝐹𝐿−4𝑇2 Q Surface tension 2 𝐹𝐿−2𝑇 R Density 3 𝐹𝐿−1 Which one of the following options identifies the correct match between Group-I and Group-II?

Accepted Answer

P−2, Q−3, R−1

Answer

P−1, Q−3, R−2

Answer

P−2, Q−1, R−3

Answer

P−3, Q−2, R−1

Question 8

Consider the steady, incompressible, and fully developed laminar flow of a fluid through a circular pipe. Here, ∆𝑃 is the pressure drop in the direction of the flow and 𝑉 is the average axial velocity of the fluid at any cross-section. The relation between ∆𝑃 and 𝑉 is: ∆𝑃= 𝐾 𝑉𝑛 Here, 𝐾 and 𝑛 are constants. Which one of the following options is the correct value of 𝑛?

Accepted Answer

1

Answer

2

Answer

1.75

Answer

0.5

Question 9

A doublet is the resulting flow pattern when a sink and a source of equal strength are brought together. Which one of the following options correctly represents the nature of the product of the strength and the distance between them during approach?

Accepted Answer

Remains always constant

Answer

Continuously decreases

Answer

Continuously increases

Answer

First increases and then continuously decreases after reaching a maximum

Question 10

Figure shows two parallel plates (upper plate at 𝑥= 𝑏 and lower one at 𝑥= −𝑏) of length L (aligned in 𝑧 direction) and infinite width (in 𝑦 direction, normal to the plane of the figure). Two immiscible, incompressible liquids are flowing steadily in the 𝑧 direction through the thin passage between the plates under the influence of horizontal pressure gradient (𝑃0 −𝑃𝐿) L ⁄ . During the flow, the passage is always half-filled with denser fluid I (viscosity 𝜇𝐼) at the bottom and rest is occupied by lighter fluid II (viscosity 𝜇𝐼𝐼; 𝜇𝐼𝐼< 𝜇𝐼). Considering exactly planar interface between the fluids and no instabilities in the flow, the shear stress, 𝜏𝑥𝑧 is expressed as: 𝜏𝑥𝑧= (𝑃0 −𝑃𝐿)𝑏 L [(𝑥 𝑏) −1 2 (𝜇𝐼−𝜇𝐼𝐼 𝜇𝐼+ 𝜇𝐼𝐼)] Which one of the following options correctly identifies the location of the point having maximum velocity of the flow?

Accepted Answer

Above the interface

Answer

Below the interface

Answer

At the interface

Answer

At the top plate

Question 11

Group-I shows different two-dimensional bodies and Group-II mentions their total drag coefficient (𝐶𝐷) based on frontal area while facing parallel flow of fluid having Reynolds number 𝑅𝑒≥104 along the direction of arrow. The bodies are placed symmetrically with respect to the flow direction. Group-I Group-II P 1 1.2 Q 2 1.6 R 3 2.1 S 4 2.3 Which one of the following options identifies the correct match between Group-I and Group-II, as per the concept of degree of streamlining?

Accepted Answer

P−3, Q−2, R−1, S−4

Answer

P−3, Q−2, R−4, S−1

Answer

P−2, Q−3, R−1, S−4

Answer

P−3, Q−1, R−2, S−4

Question 12

A solid body of uniform specific gravity floats in a deep liquid pool. Take 𝐵, 𝐺, and 𝑀 as the centre of buoyancy, centre of gravity, and metacentre of the body, respectively. Which one of the following options is correct for the stable floatation of the body in the pool when the body is given a small tilt angle?

Accepted Answer

𝑀𝐺̅̅̅̅̅ is the metacentric height and 𝐺 should lie below 𝑀

Answer

𝑀𝐺̅̅̅̅̅ is the metacentric height and 𝐵 should lie above 𝑀

Answer

𝑀𝐵̅̅̅̅̅ is the metacentric height and 𝐵 should lie below 𝑀

Answer

𝑀𝐵̅̅̅̅̅ is the metacentric height and 𝐺 should lie above 𝑀

Question 13

Figure shows the steady and incompressible flow of a fluid in the direction of arrow from section A to section D. Three pipe connectors are to be placed between sections at A and D having Total Energy Line (TEL) and Hydraulic Grade Line (HGL) as depicted in the figure. Consider, g, P, Q, V, γ, and Z denote gravitational acceleration, pressure, volume flow rate, velocity, specific weight, and elevation of centerline of the pipe connectors from the datum, respectively. Which one of the following options, in sequence, indicates the correct nature of connectors between sections A and B, B and C, and C and D in the direction of flow?

Accepted Answer

Converging, Constant area, Diverging

Answer

Diverging, Constant area, Converging

Answer

Constant area, Constant area, Constant area

Answer

Constant area, Converging, Diverging

Question 14

A liquid flows under steady and incompressible flow conditions from station 1 to station 4 through pipe sections P, Q, R, and S as shown in figure. Consider, 𝑑, 𝑉, and ℎ represent the diameter, velocity, and head loss, respectively, in each pipe section with subscripts ‘P’, ‘Q’, ‘R’, and ‘S’. ∆ℎ represents the head difference between the inlet (station 1) and outlet (station 4). All the pipe sections are placed on the same horizontal plane for which the figure shows the top view. Which one of the following options is correct for the given flow loop?

Accepted Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅+ ℎ𝑆 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 = 𝑉𝑆𝑑𝑆 2

Answer

∆ℎ= ℎ𝑃+ ℎ𝑄+ ℎ𝑅+ ℎ𝑆 and 𝑉𝑃𝑑𝑃 2 = 𝑉𝑄𝑑𝑄 2 = 𝑉𝑅𝑑𝑅 2 + 𝑉𝑆𝑑𝑆 2

Question 15

Consider, 𝑖 and 𝑗 are unit vectors along x and y directions of a Cartesian (𝑥, 𝑦) coordinate system, respectively and 𝑡 is time. Temperature (𝑇) and fluid velocity (𝑉⃗ ) are given for a flow field as: 𝑇= 𝑥2 + 𝑦𝑡+ 35 𝑉⃗ = (4𝑥𝑦)𝑖+ (𝑥𝑡−2𝑦2)𝑗 The total rate of change of temperature in the flow field (in integer) for time 𝑡= 2 at a point (2, 3) is ________

Accepted Answer

71

Question 16

Driven by a pressure gradient of 100 kPa/m, a fluid of dynamic viscosity 0.1 Pa.s flows between two fixed infinitely 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 ________

Accepted Answer

4.80 to 5.00

Question 17

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 both the plates in the flow field such that one of its sides is parallel to the plates. The magnitude of circulation in mm2/s (in integer) along the edges of the square fluid element is ________

Accepted Answer

1

Question 18

Consider, a kite weighing 100 grams as essentially a rigid flat plate making an angle 8° with the horizontal and having a planform area of 0.045 m2 when exposed to horizontal parallel wind of 60 km/h. The thread string of the kite makes an angle 45° with the horizontal. A tension of 450 grams in the thread is necessary to float the kite steadily. Take air density as 1.2 kg/m3 and gravitational acceleration as 9.81 m/s2. The lift coefficient (𝐶𝐿) associated with the air flow around steadily floating kite (rounded off to 2 decimal places) is ________

Accepted Answer

0.50 to 0.60

Question 19

A fixed control volume has four one-dimensional boundary sections (1, 2, 3, and 4). For a steady flow inside the control volume, the flow properties at each section are tabulated below: Boundary Section Type Density (kg/m3) Surface Normal Velocity (m/s) Cross-sectional Area (m2) Specific Energy (J/kg) 1 Inlet 1000 10 0.5 200 2 Inlet 1000 2 3.0 50 3 Outlet 1000 5 1.0 100 4 Outlet 1000 4 1.5 80 The rate of change of energy of the system which occupies the control volume at this instant is 𝐸× 106 J/s. The value of 𝐸 (rounded off to 2 decimal places) is ________

Accepted Answer

-0.32

Question 20

A ship is to be operated in a fluid medium with kinematic viscosity 0.032 × 10−3 m2/s. A one-tenth scale model of the ship is built for testing. Consider, inertia, viscous and gravity forces are dominant for the ship and its model during the operation. The required kinematic viscosity of the liquid for testing the model is 𝑃× 10−6 m2/s. The value of 𝑃 (rounded off to 2 decimal places) is ________

Accepted Answer

0.95 to 1.05

Question 21

Water flows through a pipe of diameter 20 cm at a flow rate of 0.025 m3/s. A pitot- static tube is placed at the centre of the pipe and indicates the pressure difference of 5 cm of water column. Theoretical velocity measured through pitot-static tube when multiplied with velocity coefficient 𝐶𝑉 gives the actual velocity of the flow. If the mean velocity in the pipe is 90% of the actual velocity at the centre of the pipe and the gravitational acceleration is 10 m/s2, the value of 𝐶𝑉 (rounded off to 2 decimal places) is ________

Accepted Answer

0.85 to 0.90

Question 22

An oil of density 870 kg/m3 and viscosity 0.036 Pa.s flows through a straight pipe of 10 cm diameter and 1.5 km length at the flow rate of 250 liters per minute under the steady and incompressible flow conditions. To control the flow rate of oil, a valve is fixed at the middle of the pipe causing no change in the total length of the pipe. The total head loss measured across the two ends of the pipe is 11.60 m. Using gravitational acceleration as 10 m/s2, the minor head loss contributed by the presence of the valve in m (rounded off to 2 decimal places) is ________

Accepted Answer

0.85 to 1.28

Question 23

Which one of the following figures shows the CORRECT dependence of apparent viscosity (η) on rate of shear strain (𝑑𝑢/𝑑𝑦) for pseudoplastic fluids?

Accepted Answer

Question 24

The locus of temporary locations of all particles that have passed through a fixed point in the flow field at a particular instant is known as

Accepted Answer

streakline.

Answer

streamline.

Answer

pathline.

Answer

timeline.

Question 25

Consider the velocities 𝑢, 𝑣, and 𝑤 in x-, y-, and z-directions, respectively. The vorticity expression in the y-z plane is

Accepted Answer

𝜕𝑤 𝜕𝑦−𝜕𝑣 𝜕𝑧

Answer

𝜕𝑣 𝜕𝑥−𝜕𝑢 𝜕𝑦

Answer

𝜕𝑣 𝜕𝑦−𝜕𝑤 𝜕𝑧

Answer

𝜕𝑢 𝜕𝑧−𝜕𝑤 𝜕𝑥

Question 26

For the laminar, incompressible flow over a flat plate with uniform free stream velocity, the axial pressure gradient within the boundary layer is

Accepted Answer

equal to zero.

Answer

greater than zero.

Answer

less than zero.

Answer

equal to the axial velocity gradient.

Question 27

Let 𝑟 , 𝑉⃗ , and 𝑚 be position vector, velocity vector, and mass, respectively in a control mass system. Which one of the following properties is considered as conserved extensive property in Reynolds Transport Theorem to obtain the angular momentum equation?

Accepted Answer

𝑟 × 𝑚𝑉⃗

Answer

𝑟 × 𝑉⃗

Answer

𝑚𝑉⃗

Answer

𝑚

Question 28

The hydraulic diameter for a circular pipe of radius 𝑅 is

Accepted Answer

2R

Answer

0.5R

Answer

R

Answer

4R

Question 29

For incompressible, laminar, fully-developed flow through a circular pipe, Darcy friction factor and Fanning friction factor are represented as 𝑓 and 𝐶𝑓, respectively. Which one of the following options is correct?

Accepted Answer

𝑓= 4𝐶𝑓

Answer

𝑓= 0.25𝐶𝑓

Answer

𝑓= 0.5𝐶𝑓

Answer

𝑓= 2𝐶𝑓

Question 30

For an immersed neutrally buoyant body to be in stable equilibrium, the center of gravity of the body is directly

Accepted Answer

below the center of buoyancy.

Answer

above the metacenter.

Answer

below the metacenter.

Answer

above the center of buoyancy.

Question 31

The absolute pressure in a chamber is measured as 400 mm Hg at a location where the atmospheric pressure is 700 mm Hg. A vacuum gauge connected to the chamber reads ________ mm Hg (answer in integer).

Accepted Answer

300

Question 32

A thin film of an incompressible, Newtonian liquid (density 𝜌,⁡viscosity 𝜇) with an uniform thickness (h) is flowing down on a vertical plate. The flow is driven by gravity (𝑔) alone. Assume zero shear stress condition at the free surface. The maximum velocity is given by

Accepted Answer

1 2𝜇𝜌𝑔ℎ2

Answer

1 4𝜇𝜌𝑔ℎ2

Answer

1 𝜇𝜌𝑔ℎ2

Answer

1 8𝜇𝜌𝑔ℎ2

Question 33

A one-eighth scale model of a car is to be tested in a wind tunnel. If the air velocity over the car is 16 m/s, what should be the air velocity (in m/s) in the wind tunnel in order to achieve similarity between the model and the prototype?

Accepted Answer

128

Answer

2

Answer

16

Answer

64

Question 34

A set of basic dimensions, mass, length, and time are represented by M, L, and T, respectively. What will be the dimensions of pressure in M-L-T system?

Accepted Answer

ML−1T −2

Answer

MLT −2

Answer

MLT −1

Answer

ML−1T −1

Question 35

Consider a fluid flow around an airfoil as shown in figure. The directions of drag force and lift force, respectively are along

Accepted Answer

OB and OD.

Answer

OA and OC.

Answer

OA and OD.

Answer

OB and OC.

Question 36

A vessel which contains a volatile liquid and its vapour is connected with a mercury manometer as shown in figure. Both the liquid and vapour phases are at equilibrium. The vapour pressure and density of the volatile liquid are 107.6 kPa and 700 kg/m3, respectively. The density of the mercury is 13600 kg/m3. Acceleration due to gravity (g) is 10 m/s2 and atmospheric pressure is 101 kPa. Hydrostatic pressure created by the weight of the vapour is neglected. The height, h (in m, rounded off to two decimal places) of the mercury column in figure is _________.

Accepted Answer

0.09 to 0.11

Question 37

The velocity in a one-dimensional flow is given by 𝑢(𝑥) = 𝑎 (𝑏−𝑥)2 m/s, where 𝑎= 8 m3/s and 𝑏= 4 m. The acceleration (in m/s2, answer in integer) at 𝑥= 2 m is _____.

Accepted Answer

4

Question 38

Consider two parallel plates separated by a distance of 1 cm filled with a Newtonian fluid of viscosity 10-3 Pa.s. The top plate is moving with a velocity of 1 m/s whereas the bottom plate is stationary. The shear stress (in Pa, rounded off to one decimal place) on the top plate is _____ .

Accepted Answer

0.1

Question 39

A circular water jet of diameter 50 mm impinges with a velocity of 18 m/s normal to a plate. The density of water is 1000 kg/m3 and gravity force is neglected. The magnitude of net force (in N, rounded off to two decimal places) imparted by the jet on the stationary plate is _______________.

Accepted Answer

635.00 to 637.00

Question 40

Consider the steady, incompressible flow of water in a horizontal pipe of constant diameter 1 m with an inlet velocity of 12 m/s. As shown in figure, water is lost through a circular hole of diameter 0.6 m at the rate of 4.53 m3/s. The outlet velocity (in m/s, rounded off to two decimal places) of water in the pipe is ______.

Accepted Answer

6.00 to 6.50

Question 41

The axial velocity profile of a laminar, incompressible and fully-developed flow in a circular pipe of radius (R) is given as 𝑢𝑧= − 1 4𝜇 𝜕𝑝 𝜕𝑧𝑅2 (1 − 𝑟2 𝑅2), where r, 𝑧, 𝜇, and 𝑝 are radial direction, axial direction, fluid viscosity, and pressure, respectively. If the average velocity of the flow is given by 𝑢𝑧,𝑎𝑣𝑔= 1 𝐾(− 𝑅2 𝜇 𝜕𝑝 𝜕𝑧), then the value of K (answer in integer) is ______.

Accepted Answer

8

Question 42

The velocity potential function in a two-dimensional flow field is given by 𝜙(𝑥, 𝑦) = −(𝑎𝑥𝑦+ 𝑏𝑥2 −𝑏𝑦2) m2/s where a = 2 per second and b = 0.5 per second. The magnitude of the velocity (in m/s, answer in integer) at 𝑥= 2 m, 𝑦= 1 m is _____.

Accepted Answer

5

Question 43

Consider the incompressible, steady and irrotational flow through a concentric reducer in a horizontal pipeline. The pipe diameter reduces from d1 = 12 cm to d2 = 4 cm as shown in figure. The pressure at position 1 and position 2 of the reducer is p1 = 55 kPa and p2 = 27 kPa, respectively. The specific weight of fluid is 7 kN/m3. Acceleration due to gravity is 10 m/s2. Neglecting frictional effects, the mass flow rate (in kg/s, rounded off to two decimal places) of the fluid through the reducer is _____.

Accepted Answer

7.85 to 8.11

Question 44

Consider the incompressible fluid flow over a flat plate with a free stream velocity, 𝑈∞= 1 m/s. The fluid kinematic viscosity is 10−6 m2/s and density is 1 kg/m3. The velocity profile within the boundary layer at any location 𝑥 is given by 𝑢(𝑦) = 𝑈∞( 3 2 𝑦 𝛿− 1 2 𝑦2 𝛿2), where boundary layer thickness, 𝛿= 4.64𝑥 √𝑅𝑒𝑥. The local wall shear stress at 𝑥= 1 m from the leading edge is _____ × 10 -3 N/m2 (rounded off to two decimal places).

Accepted Answer

0.30 to 0.35

Question 45

Match the following measuring instruments with the appropriate figures. I – Pitot probe II – Pitot-static probe III – Piezometer

Accepted Answer

I – R; II – Q; III – P

Answer

I – P; II – Q; III – R

Answer

I – R; II – P; III – Q

Answer

I – Q; II – P; III – R

Question 46

Among the following non-dimensional numbers, which one characterizes periodicity present in a transient flow?

Accepted Answer

Strouhal number

Answer

Froude number

Answer

Peclet number

Answer

Lewis number

Question 47

For an incompressible boundary layer flow over a flat plate shown in the figure, the momentum thickness is expressed as

Accepted Answer

∫ 𝑢 𝑈∞ (1 −𝑢 𝑈∞ ) 𝑑𝑦 ∞ 0

Answer

∫ 𝑢 𝑈∞ 𝑑𝑦 ∞ 0

Answer

∫ (1 −𝑢 𝑈∞ ) 𝑑𝑦 ∞ 0

Answer

∫ (1 −𝑢2 𝑈∞2 ) 𝑑𝑦 ∞ 0

Question 48

Among the shear stress versus shear strain rate curves shown in the figure, which one corresponds to a shear thinning fluid?

Accepted Answer

R

Answer

P

Answer

Q

Answer

S

Question 49

Consider steady incompressible flow over a flat plate, where the dashed line represents the edge of the boundary layer, as shown in the figure. Which one among the following statements is true?

Accepted Answer

Bernoulli’s equation cannot be applied in Region I.

Answer

Bernoulli’s equation can be applied in Region I between any two arbitrary points.

Answer

Bernoulli’s equation can be applied in Region I only along a streamline.

Answer

Bernoulli’s equation cannot be applied in Region II.

Question 50

An inviscid steady incompressible flow is formed by combining a uniform flow with velocity 𝑈∞ and a clockwise vortex of strength 𝐾 at the origin, as shown in the figure. Velocity potential (𝜙) for the combined flow in polar coordinate (𝑟, 𝜃) is

Accepted Answer

𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 cos 𝜃

Answer

𝜙= 𝐾𝜃 2 𝜋−𝑈∞𝑟 sin 𝜃

Answer

𝜙= 𝐾ln 𝑟+ 𝑈∞𝑟 cos 𝜃

Answer

𝜙= −𝐾ln 𝑟+ 𝑈∞𝑟 sin 𝜃

Question 51

Which of the following statements are true? (i) Conservation of mass for an unsteady incompressible flow can be represented as ∇⋅𝑉⃗⃗= 0, where 𝑉⃗⃗ denotes velocity vector. (ii) Circulation is defined as the line integral of vorticity about a closed curve. (iii) For some fluids, shear stress can be a nonlinear function of the shear strain rate. (iv) Integration of the Bernoulli’s equation along a streamline under steady-state leads to the Euler’s equation.

Accepted Answer

(i) and (iii) only

Answer

(i), (ii) and (iv) only

Answer

(i), (ii) and (iii) only

Answer

(ii) and (iv) only

Question 52

For a two-dimensional flow field given as 𝑉⃗⃗= −𝑥𝑖̂ + 𝑦𝑗̂, a streamline passes through points (2, 1) and (5, p). The value of p is

Accepted Answer

2/5

Answer

5

Answer

5/2

Answer

2

Question 53

A stationary object is fully submerged in a static fluid, as shown in the figure. Here, CG and CB stand for center of gravity and center of buoyancy, respectively. Which one(s) among the following statements is/are true?

Accepted Answer

The object is in stable equilibrium if 𝑦𝐶𝐺> 𝑦𝐶𝐵.

Accepted Answer

The object is in neutral equilibrium if 𝑦𝐶𝐺= 𝑦𝐶𝐵.

Answer

The object is in stable equilibrium if 𝑦𝐶𝐺< 𝑦𝐶𝐵.

Answer

The object is in unstable equilibrium if 𝑦𝐶𝐺= 𝑦𝐶𝐵.

Question 54

Consider steady fully-developed incompressible flow of a Newtonian fluid between two infinite parallel flat plates. The plates move in the opposite directions, as shown in the figure. In the absence of body force and pressure gradient, the ratio of shear stress at the top surface (𝑦= 𝐻) to that at the bottom surface (𝑦= 0) is

Accepted Answer

1

Answer

𝑈1 𝑈2

Answer

𝑈1 −𝑈2 𝑈2

Answer

𝑈1 + 𝑈2 𝑈2

Question 55

A two-dimensional incompressible flow field is defined as, 𝑉⃗⃗(𝑥, 𝑦) = (𝐴𝑥𝑦) 𝑖̂ + (𝐵𝑦2) 𝑗̂ where, 𝐴 and 𝐵 are constants. The dynamic viscosity of the Newtonian fluid is 𝜇. In the absence of body force, which among the following expressions represents the pressure gradient at the location (5, 0) in the concerned flow field?

Accepted Answer

𝜇𝐴(−𝑗̂)

Answer

𝜇𝐴(5 𝑖̂ + 𝑗̂)

Answer

𝜇(−5𝐵 𝑖̂ + 𝐴 𝑗̂)

Answer

𝜇𝐴(5 𝑖̂)

Question 56

For a potential flow, the fluid velocity is given by 𝑉⃗⃗(𝑥, 𝑦) = 𝑢𝑖̂ + 𝑣𝑗̂ . The slope of the potential line at (𝑥, 𝑦) is

Accepted Answer

−𝑢 𝑣

Answer

𝑢 𝑣

Answer

𝑣 𝑢

Answer

−𝑣 𝑢

Question 57

Consider steady incompressible flow of a Newtonian fluid over a horizontal flat plate, as shown in the figure. The boundary layer thickness is proportional to

Accepted Answer

𝑥1/2

Answer

𝑥1/4

Answer

𝑥−1/2

Answer

𝑥2

Question 58

In a steady two-dimensional compressible flow, 𝑢 and 𝑣 are the 𝑥- and 𝑦- components of flow velocity, respectively and 𝜌 is the fluid density. Among the following pairs of relations, which one(s) perfectly satisfies/satisfy the definition of stream function, 𝜓, for this flow?

Accepted Answer

𝜌𝑢= 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= − 𝜕𝜓 𝜕𝑥

Accepted Answer

𝜌𝑢= − 𝜕𝜓 𝜕𝑦 and 𝜌𝑣= 𝜕𝜓 𝜕𝑥

Answer

𝑢= 𝜕𝜓 𝜕𝑦 and 𝑣= − 𝜕𝜓 𝜕𝑥

Answer

𝑢= − 𝜕𝜓 𝜕𝑥 and 𝑣= − 𝜕𝜓 𝜕𝑦

Question 59

A water jet (density = 1000 kg/m3) is approaching a vertical plate, having an orifice at the center, as shown in the figure. While a part of the jet passes through the orifice, remainder flows along the plate. Neglect friction and assume both the inlet and exit jets to have circular cross-sections. If V = 5 m/s, 𝐷 = 100 mm and 𝑑 = 25 mm, magnitude of the horizontal force (in N, rounded off to one decimal place) required to hold the plate in its position is ___________.

Accepted Answer

183.0 to 185.0

Question 60

Water (density = 1000 kg/m3) and alcohol (specific gravity = 0.7) enter a Y-shaped channel at flow rates of 0.2 m3/s and 0.3 m3/s, respectively. Their mixture leaves through the other end of the channel, as shown in the figure. The average density (in kg/m3) of the mixture is _______.

Accepted Answer

820

Question 61

The velocity and acceleration of a fluid particle are given as 𝑉⃗⃗= (−𝑖̂ + 2𝑗̂) m/s and 𝑎⃗= (−2𝑖̂ −4𝑗̂) m/s2, respectively. The magnitude of the component of acceleration (in m/s2, rounded off to two decimal places) of the fluid particle along the streamline is _______.

Accepted Answer

2.60 to 2.75

Question 62

A hydraulic turbine with rotor diameter of 100 mm produces 200 W of power while rotating at 300 rpm. Another dynamically-similar turbine rotates at a speed of 1500 rpm. Consider both turbines to operate with the same fluid (identical density and viscosity), and neglect any gravitational effect. Then the power (in W, rounded off to nearest integer) produced by the second turbine is _______________.

Accepted Answer

430 to 460

Question 63

Water (density = 1000 kg/m3) flows steadily with a flow rate of 0.05 m3/s through a venturimeter having throat diameter of 100 mm. If the pipe diameter is 200 mm and losses are negligible, the pressure drop (in kPa, rounded off to one decimal place) between an upstream location in the pipe and the throat (both at the same elevation) is _______.

Accepted Answer

18.5 to 19.5

Question 64

Water flows around a thin flat plate (0.25 m long, 2 m wide) with a free stream velocity (𝑈∞) of 1 m/s, as shown in the figure. Consider linear velocity profile ( 𝑢 𝑈∞= 𝑦 𝛿) for which the laminar boundary layer thickness is expressed as 𝛿= 3.5𝑥 √𝑅𝑒𝑥 . For water, density = 1000 kg/m3 and dynamic viscosity = 0.001 kg/m.s. Net drag force (in N, rounded off to two decimal places) acting on the plate, neglecting the end effects, is ________.

Accepted Answer

1.10 to 1.20

Fluid Mechanics (XE-B) - GATE XE (Engineering Sciences) Subject-Wise PYQ Practice

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