Reynolds Transport Theorem and Conservation Laws - Integral Analysis for a Control Volume - Engineering Sciences Previous Year Questions

1

2007 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2007

The power utilized for propelling the boat is

A

130 kW

B

100 kW

C

80 kW

D

30 kW

Open complete paper

2

2007 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2007

Water enters a pipe of cross-sectional area \(A_1\) that branches out into sections of equal areas \(A_2\) and \(A_3\), as shown in the figure below. At one instant, the flow velocities are \(V_1 = 2\) m/s, \(V_2 = 3\) m/s and \(V_3 = 5\) m/s. At another instant, \(V_1 = 3\) m/s and \(V_2 = 4\) m/s. What is the value of \(V_3\) at this instant?

A

5 m/s

B

6 m/s

C

7 m/s

D

8 m/s

Open complete paper

3

2008 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2008

A two-dimensional water jet hits a splitter plate as shown. The velocities at sections ①, ② and ③ may be taken as uniform and equal to V. The weight of the water and the friction along the plate may be neglected. For the data shown what is θ?

A

0

B

tan⁻¹(0.5)

C

cos⁻¹(0.5)

D

sin⁻¹(0.5)

Open complete paper

4

2008 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2008

A single engine jet aircraft is in a steady level flight at speed \(V_a\) with respect to ground. Assume that the engine intake area (\(A_{in}\)) is much larger than the engine exhaust area (\(A_e\)). If the density of the exhaust gas is \(\rho_e\) and the exhaust velocity relative to the aircraft is \(V_e\), the thrust generated by the engine is

A

\(\rho_e V_e^2 A_e\)

B

\(\rho_e (V_a + V_e)^2 A_e\)

C

\(\rho_e (V_a - V_e)^2 A_e\)

D

\(\rho_e (V_a + V_e) V_e A_e\)

Open complete paper

5

2011 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2011

After splitting, the velocity of the upward half-jet along the plate is

A

5 m/s

B

7.5 m/s

C

2.5 m/s

D

10 m/s

Open complete paper

6

2012 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2012

The total kinetic energy imparted to the water per second (in kW) by the pump is

A

10

B

25

C

28

D

81

Open complete paper

7

2012 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2012

Water is supplied to a tank at the rate of \(0.02\text{ m}^3/\text{s}\), as shown in the figure below. The cross-sectional area of the tank is \(1\text{ m}^2\) and the inner diameter of the outlet pipe is \(60\text{ mm}\). At a time when the water level in the tank is increasing at the rate of \(5\text{ mm/s}\), the average velocity (in m/s) of water in the outlet pipe is approximately

A

0.005

B

0.06

C

5.3

D

20

Open complete paper

8

2013 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2013

The magnitude of the force, in kN, required to hold the pipe in place, is

A

2.7

B

5.4

C

19

D

27

Open complete paper

9

2013 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2013

An incompressible fluid at a pressure of 150 kPa (absolute) flows steadily through a two-dimensional channel with a velocity of 5 m/s as shown in the Figure. The channel has a 90° bend. The fluid leaves the channel with a pressure of 100 kPa (absolute) and linearly-varying velocity profile. \(v_{max}\) is four times \(v_{min}\). The density of the fluid is 914.3 kg/m³. The velocity \(v_{min}\), in m/s, is

A

25

B

2.5

C

2.0

D

0.2

Open complete paper

10

2014 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2014

A reducing elbow is used to deflect water upward by \(30^{\circ}\) as shown in the figure. The mass flow rate at the inlet is 14 kg/s. Water is entering at a gauge pressure of 200 kPa and exits to the atmosphere. The cross-sectional area is \(113 \text{ cm}^2\) at the inlet and \(7 \text{ cm}^2\) at the exit. Density of water and acceleration due to gravity are 1000 kg/m³ and 10 m/s², respectively. Magnitude of \(x\)-component of the water force on the elbow is ____ N.

Check answer

Open complete paper

11

2019 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2019

An incompressible fluid flows past a flat plate as shown in the figure below with a uniform inlet velocity profile u = U and a parabolic exit velocity profile u = U(2η - η²), where u is the component of velocity parallel to the wall, y is the normal distance from the plate and η = y/δ. If the volume flow rate across the top surface of the control volume (CV) is Q = pUδ per unit width (perpendicular to the x-y plane) of the plate, the value of p (rounded off to 2 decimal places) is ______

Check answer

Open complete paper

12

2019 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2019

A jet engine is to be tested on a thrust stand as shown in the figure below. The conditions prevailing in a typical test are as follows: Axial intake air velocity = 100 m/s; axial exhaust gas velocity = 250 m/s; intake cross-sectional area = 1 m\(^2\); intake static pressure = –22 kPa (gauge); exhaust static pressure = 0 kPa (gauge); mass flow rate through the engine = 100 kg/s. The anchoring force (in kN) in axial direction on the thrust stand is ______

Check answer

Open complete paper

13

2020 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2020

A liquid flow through a horizontal smooth pipe of diameter 5 cm and discharges into a collection tank of dimension 50 cm x 50 cm x 50 cm. Time taken for a 10 cm rise of liquid level in the collection tank is 40 s.

The flow velocity in the pipe is -------- m/s (rounded off to two decimal places).

Check answer

Open complete paper

14

2021 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2021

A spherical ball is steadily supported against gravity by an upward air jet as shown in the figure. Take acceleration due to gravity to be \( g = 10\, \text{m/s}^2 \). The mass flow rate of air, reaching the ball, is 0.01 kg/s and the air reaches the ball at an upward velocity of 3 m/s. Neglecting the buoyancy force, and using the principle of integral momentum balance, the mass (in grams, up to one decimal place) of the ball is ____.

Check answer

Open complete paper

15

2021 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2021

Water (density = 10^3 kg/m^3) enters steadily into a horizontal pipe bend, which is part of a larger piping system, as shown in the figure. The volumetric flow rate of water is 0.1 m^3/s. The gage pressure at the inlet is 500 kPa, while the exit is open to atmosphere. The x-component of the force on the support is F. The absolute value of F (in kN, up to one decimal place) is ____.

Check answer

Open complete paper

16

2021 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2021

Air (of density 0.5 kg/m^3) enters horizontally into a jet engine at a steady speed of 200 m/s through an inlet area of 1.0 m^2. Upon entering the engine, the air passes through the combustion chamber and the exhaust gas exits the jet engine horizontally at a constant speed of 700 m/s. The fuel mass flow rate added in the combustion chamber is negligible compared to the air mass flow rate. Also neglect the pressure difference between the inlet air and the exhaust gas. The absolute value of the horizontal force (in kN, up to one decimal place) on the jet engine is ____.

Check answer

Open complete paper

17

2022 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2022

A 10 kg mass placed on an infinitely long horizontal massless flat platform is to be supported by a steady vertical water jet as shown in the figure. The diameter of the jet is 5 cm. What minimum average velocity is required to hold the mass in place?
Assume \(\rho_{water} = 1000 \text{ kg/m}^3\), \(g = 10 \frac{\text{m}}{\text{s}^2}\) and \(\pi = 3.14\). Neglect friction.

(Round off to two decimal places)

Check answer

Open complete paper

18

2022 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2022

Consider a lawn sprinkler with horizontal arms of radius, \(a = 10 \text{ cm}\) which has water introduced vertically through the centre, as shown in the figure. The exit area of the jet is \(25 \text{ cm}^2\) and the jet velocity is \(1 \text{ m/s}\). The water is ejected orthogonal to the sprinkler arm and the jet makes an angle of \(60^\circ\) with the horizontal plane. Find the torque (in N-m) required to hold the sprinkler stationary.
Consider water density \(1000 \text{ kg/m}^3\). Neglect the effects of friction and gravity.

(Round off to two decimal places)

Check answer

Open complete paper

19

2024 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2024

Let \( \vec{r}, \vec{V}, \) 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?

A

\(\vec{r} \times m\vec{V} \)

B

\(\vec{r} \times \vec{V} \)

C

\(m\vec{V} \)

D

\(m \)

Open complete paper

20

2024 · Engineering Sciences · Integral Analysis for a Control Volume · Reynolds Transport Theorem and Conservation Laws

Engineering Sciences (XE) 2024

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 ______.

Check answer

Open complete paper