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Question 1
ప్రశ్న 1
In hydraulic-model analysis, which statement correctly distinguishes a model from a prototype?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A model is a representation of a physical system used to investigate its behaviour under controlled conditions. The prototype is the actual system or full-scale installation for which predictions are required. Hydraulic models are commonly smaller than their prototypes, although similitude principles are not restricted to reduced models. Measurements made on a model are converted to prototype quantities using appropriate scale relationships. Therefore Option B is correct.
వివరణ:
Question 2
ప్రశ్న 2
What is required for geometric similarity between a hydraulic model and its prototype?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Geometric similarity means that the model and prototype have the same shape. All homologous linear dimensions must be related by a constant length-scale ratio in an undistorted model. Corresponding areas consequently scale as the square of the length ratio. Corresponding volumes scale as the cube of the length ratio. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Throughout this test let Lr = Lp/Lm. A geometrically similar model is constructed to a model-to-prototype linear scale of 1:20. If the prototype area corresponding to a model surface is 200 m², what is the model area?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A model-to-prototype scale of 1:20 gives Lr = Lp/Lm = 20. For geometrically similar systems, the prototype-to-model area ratio is Lr². Thus Ap/Am = 20² = 400. The model area is therefore 200/400 = 0.50 m². Hence Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
A geometrically similar hydraulic model has Lr = Lp/Lm = 20. What is the prototype-to-model volume ratio?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For geometrically similar bodies, volume is proportional to the cube of a characteristic length. The prototype-to-model volume ratio is therefore Lr³. With Lr = 20, the ratio is 20³. This evaluates to 8000. Therefore Option C is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which statement best defines kinematic similarity between a model and prototype?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Kinematic similarity concerns similarity of motion. Velocity vectors at homologous points must have corresponding directions and scaled magnitudes. The streamline patterns are consequently similar. Time and acceleration scales must also be compatible with the selected length and velocity scales. Therefore Option A is correct.
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Question 6
ప్రశ్న 6
If Lr = Lp/Lm and Vr = Vp/Vm, what is the prototype-to-model time-scale ratio Tr = Tp/Tm required by kinematic similarity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A characteristic time is proportional to characteristic length divided by characteristic velocity. Therefore Tp/Tm = (Lp/Lm)/(Vp/Vm). Using the defined scale ratios gives Tr = Lr/Vr. This is a kinematic relation and does not itself specify which dynamic model law determines Vr. Therefore Option C is correct.
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Question 7
ప్రశ్న 7
What is meant by dynamic similarity between a model and prototype?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Dynamic similarity concerns the forces responsible for fluid motion. Corresponding forces of the same type must occur in consistent ratios between model and prototype. In practice this requirement is expressed by matching the important nondimensional force ratios. The particular dimensionless numbers that must be matched depend on the forces dominant in the phenomenon. Therefore Option A is correct.
వివరణ:
Question 8
ప్రశ్న 8
Which similarity criterion is generally the primary model law for spillways, weirs and other gravity-dominated free-surface flows when viscous and surface-tension scale effects are secondary?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Free-surface hydraulic flows are strongly governed by the interaction of inertia and gravity. The Froude number represents this inertia-to-gravity relationship. Hydraulic models of spillways, stilling basins, weirs and channels therefore commonly use equality of model and prototype Froude numbers. Reynolds and Weber effects should still be checked to ensure that undesirable scale effects are sufficiently small. Therefore Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
For model and prototype operating under the same gravitational acceleration and satisfying Froude similarity, which velocity-scale relation follows when Lr = Lp/Lm and Vr = Vp/Vm?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Froude similarity requires Vp/sqrt(gLp) = Vm/sqrt(gLm). When gravitational acceleration is the same for model and prototype, g cancels. The resulting relation is Vp/Vm = sqrt(Lp/Lm). Hence Vr = sqrt(Lr). Therefore Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
A Froude-scaled hydraulic model has a model-to-prototype length scale of 1:25 and operates under the same gravitational acceleration as the prototype. If the model velocity is 1.20 m/s, what is the corresponding prototype velocity?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The scale gives Lr = Lp/Lm = 25. Under Froude similarity, Vr = sqrt(Lr) = 5. Thus the prototype velocity is five times the model velocity. Therefore Vp = 5 × 1.20 = 6.00 m/s. Hence Option C is correct.
వివరణ:
Question 11
ప్రశ్న 11
A Froude model has Lr = Lp/Lm = 36. If an event takes 12 s in the model, what corresponding prototype time is predicted?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For equal-gravity Froude similarity, Vr = sqrt(Lr). Since Tr = Lr/Vr, the time-scale ratio is also sqrt(Lr). For Lr = 36, Tr = 6. The prototype time is therefore 6 × 12 = 72 s. Hence Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
A geometrically similar Froude model has Lr = 16 and carries a model discharge of 0.020 m³/s. What prototype discharge corresponds to this condition?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Discharge is the product of flow area and representative velocity. Geometric similarity gives an area scale of Lr². Froude similarity gives a velocity scale of Lr^(1/2). Hence Qp/Qm = Lr^(5/2). For Lr = 16, the discharge ratio is 1024, giving Qp = 0.020 × 1024 = 20.48 m³/s, so Option D is correct.
వివరణ:
Question 13
ప్రశ్న 13
For a same-fluid Froude model in the same gravitational field, what is the prototype-to-model scale ratio of corresponding inertia or gravity forces?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A representative inertia force scales as rho V²L². Under same-fluid Froude similarity, the density ratio is one and V² scales as Lr. Multiplying by the area scale Lr² gives a force ratio of Lr³. Gravity force also scales as rho gL³ under equal gravity, giving the same result. Therefore Option C is correct.
వివరణ:
Question 14
ప్రశ్న 14
Which dynamic-similarity criterion is principally associated with flows in which inertial and viscous forces are the dominant competing effects?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Reynolds number characterizes the relative importance of inertial and viscous effects. If these are the principal competing forces, model and prototype Reynolds numbers should be equal for dynamic similarity. This requirement is important in many pipe flows and viscous external-flow problems. Froude similarity instead emphasizes the relationship between inertia and gravity. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
A model has a model-to-prototype length scale of 1:10 and uses the same fluid as its prototype. If Reynolds similarity alone is required and the prototype velocity is 2.0 m/s, what model velocity is required?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Reynolds similarity requires VpLp/nu_p = VmLm/nu_m. Because model and prototype use the same fluid, their kinematic viscosities are equal. Hence Vm/Vp = Lp/Lm = 10. With Vp = 2.0 m/s, the required model velocity is 20.0 m/s. Therefore Option D is correct.
వివరణ:
Question 16
ప్రశ్న 16
A free-surface model has Lr = 16 and is required theoretically to satisfy both Froude and Reynolds similarity under the same gravitational acceleration. What kinematic-viscosity ratio nu_m/nu_p would be required?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Froude similarity gives Vp/Vm = sqrt(Lr) = 4. Reynolds similarity requires VpLp/nu_p = VmLm/nu_m. Substituting Vm/Vp = 1/4 and Lm/Lp = 1/16 gives nu_m/nu_p = 1/(4 × 16). Therefore nu_m/nu_p = 1/64. This illustrates why simultaneously matching Froude and Reynolds numbers in a substantially reduced model is often impractical, so Option C is correct.
వివరణ:
Question 17
ప్రశ్న 17
Which dimensionless quantity represents pressure effects relative to inertia and is commonly written as Eu = Delta p/(rho V²)?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Euler number is a pressure-to-inertia similarity parameter. One common form is Eu = Delta p/(rho V²). Some texts use dynamic pressure with a factor of one-half, which changes only the numerical convention. Matching the same Euler-number definition allows corresponding pressure differences to be related through density and velocity scales. Therefore Option A is correct.
వివరణ:
Question 18
ప్రశ్న 18
A same-fluid Froude model has Lr = 25. If a corresponding pressure difference in the model is 400 Pa and Euler similarity is used to scale the pressure difference, what prototype pressure difference is predicted?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Equality of Euler number gives Delta p proportional to rho V² at corresponding points. The density ratio is one because the same fluid is used. Under Froude similarity, Vp²/Vm² equals Lr, which is 25. Therefore Delta p_p = 25 × 400 = 10000 Pa. Hence Option C is correct.
వివరణ:
Question 19
ప్రశ్న 19
Which similarity criterion is most directly associated with flows in which surface-tension effects are dynamically important, such as sufficiently small liquid jets or droplets?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Weber number compares inertial effects with surface-tension effects. A common expression is We = rho V²L/sigma. When surface tension is dynamically important, corresponding Weber numbers should be matched between model and prototype. This commonly matters for small-scale jets, droplets and free-surface phenomena in which capillary effects are significant. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
A prototype and model use the same liquid and must satisfy Weber similarity. If Lr = Lp/Lm = 9 and the prototype velocity is 2.0 m/s, what model velocity is required?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Weber similarity requires rho_p Vp²Lp/sigma_p = rho_m Vm²Lm/sigma_m. Using the same liquid makes the density and surface-tension ratios unity. Hence Vp²Lp = Vm²Lm. Since Lp/Lm = 9, Vm/Vp = sqrt(9) = 3. Thus Vm = 3 × 2.0 = 6.0 m/s and Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
Which similarity parameter is fundamental when compressibility effects and pressure-wave propagation are important in high-speed gas flows?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number is the ratio of flow velocity to the local speed of sound. It measures the significance of compressibility and pressure-wave propagation. When these effects materially influence a gas flow, appropriate Mach-number similarity is required. Other parameters such as Reynolds number and thermodynamic-property ratios may also need consideration for complete similitude. Therefore Option A is correct.
వివరణ:
Question 22
ప్రశ్న 22
What is meant by a distorted hydraulic model?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Complete similitude may be impossible when several independent similarity criteria must be satisfied simultaneously. A model for which one or more required similarity conditions are not reproduced exactly is commonly described as distorted or incompletely similar. In river modeling, a familiar form of distortion uses different horizontal and vertical geometric scales. Such a model can still provide useful results when the dominant effects and the consequences of distortion are properly understood. Therefore Option A is correct.
వివరణ:
Question 23
ప్రశ్న 23
A river model has a horizontal scale Lp/Lm = 100 and a vertical depth scale Dp/Dm = 20. By what factor are the model's vertical dimensions exaggerated relative to an undistorted model having Lp/Lm = Dp/Dm = 100?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
An undistorted 1:100 model would have a vertical prototype-to-model depth ratio of 100. The distorted model instead has Dp/Dm = 20, so each model vertical dimension is five times as large as it would be under the 1:100 scale. The vertical exaggeration factor is therefore 100/20. This equals 5. Hence Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
Which set correctly matches the dominant physical effect with the usual similarity criterion?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Froude number represents inertia relative to gravity and is therefore central to gravity-dominated free-surface models. Reynolds number compares inertial and viscous effects. Weber number compares inertia with surface tension, while Mach number describes compressibility through the ratio of flow speed to sound speed. Euler number expresses pressure effects relative to inertia. Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about similitude: I. Complete physical similarity requires appropriate geometric, kinematic and dynamic similarity. II. A same-gravity Froude model has Vp/Vm = (Lp/Lm)^(1/2). III. Matching both Reynolds and Froude numbers with the same liquid in a substantially reduced model is generally impossible without accepting a scale-effect compromise. IV. Distorted geometric models may deliberately use different horizontal and vertical scales. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I correctly identifies geometric, kinematic and dynamic similarity as the classical components of complete similitude. Statement II follows directly from Froude-number equality under the same gravitational acceleration. Statement III reflects the conflicting velocity and viscosity requirements imposed by simultaneous Reynolds and Froude matching in a reduced same-fluid model. Statement IV correctly identifies a common form of deliberate geometric distortion in hydraulic river models. Therefore all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. The model is a physical representation used for study, while the prototype is the actual system whose behaviour is to be predicted సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: A. All corresponding linear dimensions must have the same constant scale ratio సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. 0.50 m² సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: C. 8000 సమాధానం: C.
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Question 5 ప్రశ్న 5Answer: A. Corresponding velocity vectors have similar directions and their magnitudes are related by a constant scale ratio సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: C. Tr = Lr/Vr సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: A. All relevant corresponding force ratios are maintained in the same proportion at homologous points సమాధానం: A.
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Question 8 ప్రశ్న 8Answer: B. Froude similarity సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. Vr = sqrt(Lr) సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: C. 6.00 m/s సమాధానం: C.
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Question 11 ప్రశ్న 11Answer: C. 72 s సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: D. 20.48 m³/s సమాధానం: D.
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Question 13 ప్రశ్న 13Answer: C. Lr³ సమాధానం: C.
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Question 14 ప్రశ్న 14Answer: B. Reynolds law సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: D. 20.0 m/s సమాధానం: D.
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Question 16 ప్రశ్న 16Answer: C. 1/64 సమాధానం: C.
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Question 17 ప్రశ్న 17Answer: A. Euler number సమాధానం: A.
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Question 18 ప్రశ్న 18Answer: C. 10000 Pa సమాధానం: C.
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Question 19 ప్రశ్న 19Answer: B. Weber similarity సమాధానం: B.
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Question 20 ప్రశ్న 20Answer: C. 6.0 m/s సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: A. Mach number, Ma = V/a సమాధానం: A.
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Question 22 ప్రశ్న 22Answer: A. A model in which one or more similarity requirements are not reproduced exactly; a common geometric example uses different horizontal and vertical scales సమాధానం: A.
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Question 23 ప్రశ్న 23Answer: B. 5 సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: A. Gravity-dominated free-surface flow—Froude; viscous effects—Reynolds; surface tension—Weber; compressibility—Mach; pressure-to-inertia effects—Euler సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.