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Question 1
ప్రశ్న 1
In the Eulerian description of a flow field, which condition correctly characterizes steady flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Steadiness is fundamentally a time-based classification at fixed spatial locations. In a steady flow, quantities such as velocity, pressure and density at a specified point do not change with time. They may nevertheless have different values at different locations in the flow field. A fluid particle can therefore accelerate while passing through a steady but spatially non-uniform flow. Hence Option B correctly distinguishes steadiness from uniformity and constant particle velocity.
వివరణ:
Question 2
ప్రశ్న 2
A one-dimensional velocity field is given by u = 3x m/s, where x is measured in metres, and the field contains no explicit time dependence. How should the velocity field be classified with respect to steadiness and uniformity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The velocity expression u = 3x contains no time variable, so the velocity at any fixed position remains unchanged with time. The flow is therefore steady. However, velocity changes as x changes, so different spatial locations have different velocities. This spatial variation makes the flow non-uniform. Consequently, Option B correctly classifies the field as steady and non-uniform.
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Question 3
ప్రశ్న 3
A velocity field throughout a region is V = (2 + 0.5t)i m/s, where t is in seconds and there is no dependence on position. Which classification is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The velocity changes explicitly with time because of the term 0.5t. The flow is therefore unsteady. At any given instant, however, the same velocity applies at every position because no spatial coordinate appears in the expression. The flow is consequently uniform in space at each instant. Option C correctly demonstrates that an unsteady flow can still be spatially uniform.
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Question 4
ప్రశ్న 4
Water flows at a constant discharge through a steadily operating converging nozzle. Neglecting boundary-layer details and considering section-average velocity, which description is most appropriate along the nozzle axis?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At a constant operating condition, the velocity at a specified section of the nozzle does not change with time, so the flow is steady. The cross-sectional area decreases along the nozzle and the mean velocity correspondingly changes with position for incompressible flow. The flow is therefore spatially non-uniform. A fluid particle experiences acceleration because it moves into regions having different velocities, and this is convective acceleration. Thus Option B correctly describes the engineering situation.
వివరణ:
Question 5
ప్రశ్న 5
Which statement correctly relates temporal and convective acceleration to steady and uniform flow classifications?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Material acceleration consists of local or temporal acceleration plus convective acceleration. In a steady flow, the partial time derivative of velocity at a fixed point is zero, so local acceleration vanishes. If velocity still varies with position, a moving particle may experience convective acceleration. An unsteady but spatially uniform flow can have local acceleration while its convective acceleration is zero. Therefore Option C is the only generally correct statement.
వివరణ:
Question 6
ప్రశ్న 6
What primarily determines whether an idealized flow field is called one-dimensional, two-dimensional or three-dimensional?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Dimensionality of a flow model refers primarily to the number of independent spatial coordinates needed to describe significant variations in the field. A one-dimensional model uses one spatial coordinate, a two-dimensional model uses two, and a three-dimensional model requires all three. This classification is not determined merely by counting the number of nonzero velocity components. Engineering models often neglect comparatively small variations in one or more directions to simplify analysis. Therefore Option B gives the correct criterion.
వివరణ:
Question 7
ప్రశ్న 7
Why is flow through a long pipe frequently treated as one-dimensional in engineering calculations even though the actual velocity varies across the pipe cross-section?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Real viscous pipe flow has a velocity distribution over the cross-section and is not literally one-dimensional at every point. For many engineering purposes, a cross-sectional mean velocity and other section-average quantities are used. Their principal changes are then represented as functions of distance along the pipe. This approximation can greatly simplify continuity, energy and momentum analyses while retaining useful engineering accuracy. Hence Option B correctly explains the basis of the one-dimensional model.
వివరణ:
Question 8
ప్రశ్న 8
A velocity field is described by u = ax, v = by and w = 0, where a and b are nonzero constants. With respect to spatial dimensionality, how should the field generally be classified?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The u component varies with x and the v component varies with y. Hence two independent spatial coordinates are required to describe the velocity field. The absence of a z-directed velocity component does not by itself define the dimensionality. Since no velocity variation with z is involved, a third spatial coordinate is unnecessary for this field. Therefore Option B correctly identifies the flow as two-dimensional.
వివరణ:
Question 9
ప్రశ్న 9
A velocity field has components u = ax, v = by and w = cz, where a, b and c are nonzero constants. Which spatial classification is appropriate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The u component varies with x, the v component varies with y, and the w component varies with z. All three spatial coordinates are therefore required to represent the complete velocity field. Such a field is classified as three-dimensional. It is also spatially non-uniform because its velocity changes with position, but that does not alter its dimensionality. Hence Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
Which statement correctly distinguishes rotational flow from irrotational flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Rotationality concerns the local rotation of an infinitesimal fluid element, not simply the geometric shape of its path. Vorticity is the curl of the velocity field and provides a measure of this local rotational motion. An irrotational region has zero vorticity even though the fluid may possess substantial translational velocity. Curved streamlines alone do not prove that a flow is rotational. Therefore Option C provides the correct fundamental distinction.
వివరణ:
Question 11
ప్రశ్న 11
For a two-dimensional velocity field V = u(x,y)i + v(x,y)j, which expression gives the z-component of vorticity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Vorticity is defined as the curl of the velocity vector. For a two-dimensional x-y flow, the relevant component is normal to the x-y plane. Its value is ζz = ∂v/∂x - ∂u/∂y. If this quantity is zero throughout a region, the two-dimensional flow is irrotational there. Thus Option B gives the correct expression.
వివరణ:
Question 12
ప్రశ్న 12
A two-dimensional velocity field is u = 2y m/s and v = 3x m/s, with x and y in metres. What is the z-component of vorticity and how is the flow classified with respect to rotation?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For two-dimensional flow, ζz = ∂v/∂x - ∂u/∂y. Here ∂v/∂x = 3 s^-1 and ∂u/∂y = 2 s^-1. Therefore ζz = 3 - 2 = 1 s^-1. Since the vorticity is nonzero, the flow is rotational. Option B gives both the correct value and the correct classification.
వివరణ:
Question 13
ప్రశ్న 13
For the steady two-dimensional velocity field u = 2x and v = -2y, which statement correctly describes its divergence and rotationality?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The divergence of the field is ∂u/∂x + ∂v/∂y. Here ∂u/∂x = 2 and ∂v/∂y = -2, so the divergence is zero. The z-component of vorticity is ∂v/∂x - ∂u/∂y, and both of these derivatives are zero. The field is therefore irrotational and is also divergence-free, making it compatible with the incompressible-flow continuity condition. Consequently, Option C is correct.
వివరణ:
Question 14
ప్రశ్న 14
A two-dimensional rigid-body rotation has velocity components u = -Ωy and v = Ωx, where Ω is constant. If Ω = 4 s^-1, what is the z-component of vorticity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The z-component of vorticity is ζz = ∂v/∂x - ∂u/∂y. For the given field, ∂v/∂x = Ω and ∂u/∂y = -Ω. Hence ζz = Ω - (-Ω) = 2Ω. With Ω = 4 s^-1, the vorticity is 8 s^-1. Therefore Option C is correct and the field is rotational.
వివరణ:
Question 15
ప్రశ్న 15
A fluid particle follows a curved streamline around a centre. Which conclusion about rotationality is valid solely from this information?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A curved trajectory of a fluid particle is not the same as local rotation of the fluid element about its own centre. Rotationality is determined by the vorticity of the velocity field. Certain vortex-type motions can have curved streamlines while being irrotational over regions away from a singular core. Conversely, rotational motion cannot be established merely from the appearance of one streamline. Therefore Option C is the technically defensible conclusion.
వివరణ:
Question 16
ప్రశ్న 16
Which statement best defines incompressible flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In incompressible flow, a material fluid element experiences no change, or a negligible change for the engineering model, in density as it moves. This condition is expressed by Dρ/Dt = 0. It does not require pressure to be constant because substantial pressure variations can exist in an incompressible-flow model. Gases can also be treated approximately as incompressible when their density variations are sufficiently small for the problem under consideration. Hence Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
For a constant-density three-dimensional incompressible flow with velocity components u, v and w, which differential condition must the velocity field satisfy?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Conservation of mass gives the continuity equation for a fluid flow. When density is constant, the continuity equation reduces to zero divergence of the velocity field. In Cartesian coordinates this is ∂u/∂x + ∂v/∂y + ∂w/∂z = 0. Zero vorticity is not required because an incompressible flow may be either rotational or irrotational. Therefore Option A gives the correct condition.
వివరణ:
Question 18
ప్రశ్న 18
Which engineering interpretation of gas flow is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Compressible versus incompressible flow is determined by the significance of density changes during the motion, not solely by whether the substance is a gas or liquid. Gas density can change appreciably when pressure, temperature or velocity changes are sufficiently large. In many low-speed engineering applications, however, the resulting density variation may be small enough to neglect. The flow may then be analysed using an incompressible approximation within the required accuracy. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
Which statement about liquids and the incompressible-flow approximation is most accurate?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Real liquids possess a finite bulk modulus and therefore are not perfectly incompressible in an absolute physical sense. Their density changes under ordinary pressure variations are often very small compared with those of gases. For many hydraulic calculations, treating density as constant is therefore an excellent engineering approximation. Situations involving rapid pressure transients, acoustic effects or very high pressures may require liquid compressibility to be considered. Hence Option B is the most technically accurate statement.
వివరణ:
Question 20
ప్రశ్న 20
Which statement correctly describes the physical distinction between laminar and turbulent flow at an introductory engineering level?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Laminar flow is characterized by comparatively smooth and orderly motion with limited transverse mixing between adjacent fluid layers. Turbulent flow contains irregular velocity fluctuations superimposed on the mean motion and generally exhibits stronger mixing. The tendency toward one regime or the other is related to the relative importance of inertial and viscous effects. Reynolds number is a principal dimensionless parameter used for this classification in many flow situations, with the relevant limiting values depending on the particular geometry and conditions. Therefore Option A correctly states the fundamental distinction.
వివరణ:
Question 21
ప్రశ్న 21
What does the Reynolds number primarily represent in classifying viscous fluid flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Reynolds number compares the relative importance of inertial and viscous effects in a flow. For internal flow in a circular pipe it is commonly written as Re = ρVD/μ or equivalently VD/ν. Low Reynolds numbers indicate stronger relative viscous influence and tend to favour laminar motion. High Reynolds numbers indicate stronger relative inertial influence and tend to favour turbulence. Hence Option B correctly expresses the physical meaning of Reynolds number.
వివరణ:
Question 22
ప్రశ్న 22
Water flows through a 20 mm diameter circular pipe at a mean velocity of 0.50 m/s. If its kinematic viscosity is 1.0 × 10^-5 m²/s, what is the Reynolds number and the corresponding regime using the stated criterion Re < 2000 for laminar pipe flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For circular-pipe flow, Reynolds number may be calculated from Re = VD/ν. The diameter is 20 mm = 0.020 m. Substitution gives Re = 0.50 × 0.020/(1.0 × 10^-5) = 1000. This value is below the explicitly stated laminar limit of 2000. Therefore the flow is classified as laminar and Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
Oil flows in a circular pipe of diameter 25 mm at a mean velocity of 1.20 m/s and has kinematic viscosity 1.0 × 10^-5 m²/s. Using the stated classification Re < 2000 as laminar, Re from 2000 to 4000 as transitional, and Re > 4000 as turbulent, how should the flow be classified?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Reynolds number is Re = VD/ν for the stated circular-pipe problem. Converting diameter gives D = 0.025 m, so Re = 1.20 × 0.025/(1.0 × 10^-5). This gives Re = 3000. Under the classification explicitly supplied in the question, a Reynolds number between 2000 and 4000 lies in the transition range. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
Consider the following statements about flow classification: I. Steadiness concerns variation with time at a fixed point. II. Uniformity concerns spatial variation at an instant. III. Incompressible flow may be either laminar or turbulent. IV. Rotational flow may be either steady or unsteady. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is correct because steady versus unsteady classification concerns time dependence at fixed spatial locations. Statement II is correct because uniform versus non-uniform classification concerns spatial variation of the flow field. Statement III is correct because incompressibility and laminar-turbulent behaviour describe different characteristics and are not mutually exclusive classifications. Statement IV is also correct because rotationality concerns vorticity and does not by itself determine whether the field changes with time. Hence all four statements are valid and Option D is correct.
వివరణ:
Question 25
ప్రశ్న 25
A velocity field is given by u = ax, v = -ay + bt and w = 0, where a and b are nonzero constants. Which description of the velocity field is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The component v contains the explicit time term bt, so the velocity field is unsteady. The velocity also depends on x and y, making the field spatially non-uniform and two-dimensional. Its divergence is ∂u/∂x + ∂v/∂y = a - a = 0, so the field is divergence-free and satisfies the usual incompressible-flow continuity condition. Its z-component of vorticity is ∂v/∂x - ∂u/∂y = 0 - 0 = 0, making the field irrotational. Therefore Option B gives the complete correct description.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. The flow properties at each fixed point do not change with time, although they may vary from one location to another సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: B. Steady and non-uniform సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: C. Unsteady and uniform సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. Steady and non-uniform, with possible convective acceleration సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: C. Steady flow has zero local acceleration, while spatially non-uniform steady flow may have convective acceleration సమాధానం: C.
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Question 6 ప్రశ్న 6Answer: B. The number of spatial coordinates required to describe significant variation of the flow variables సమాధానం: B.
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Question 7 ప్రశ్న 7Answer: B. Because cross-sectional average properties can be used and their principal variation may be represented along the pipe coordinate సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: B. Two-dimensional because the field depends on x and y but not on z సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. Three-dimensional సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: C. Rotational flow has nonzero local angular rotation or vorticity of fluid elements, whereas irrotational flow has zero vorticity సమాధానం: C.
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Question 11 ప్రశ్న 11Answer: B. ∂v/∂x - ∂u/∂y సమాధానం: B.
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Question 12 ప్రశ్న 12Answer: B. 1 s^-1; rotational సమాధానం: B.
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Question 13 ప్రశ్న 13Answer: C. The divergence is zero and the flow is irrotational సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: C. 8 s^-1 సమాధానం: C.
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Question 15 ప్రశ్న 15Answer: C. No conclusion can be drawn solely from streamline curvature; local vorticity must be examined సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: B. A flow in which the density of each moving fluid element remains effectively constant సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: A. ∂u/∂x + ∂v/∂y + ∂w/∂z = 0 సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: B. A gas flow may be approximated as incompressible when density changes are negligible for the required engineering accuracy సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: B. Liquids are often treated as incompressible because their density changes are small in many engineering flows, although real liquids possess finite compressibility సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: A. Laminar flow is characterized by relatively orderly motion, whereas turbulent flow contains irregular velocity fluctuations and enhanced mixing సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: B. The ratio of inertial effects to viscous effects సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: B. Re = 1000; laminar సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: C. Re = 3000; transitional సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: D. I, II, III and IV సమాధానం: D.
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Question 25 ప్రశ్న 25Answer: B. Unsteady, non-uniform, divergence-free and irrotational సమాధానం: B.