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Question 1
ప్రశ్న 1
Which statement best describes compressible flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Compressible-flow analysis accounts for significant changes in fluid density. Such density variations commonly become important in gas flows involving appreciable pressure, temperature or velocity changes. The term does not imply that viscosity is zero or that pressure is constant. Liquids also possess finite compressibility, although many ordinary liquid-flow problems can be treated approximately as incompressible. Therefore Option A is correct.
వివరణ:
Question 2
ప్రశ్న 2
Which expression correctly defines the bulk modulus K of a fluid for a specified compression process?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Bulk modulus measures the resistance of a fluid to volumetric compression. During compression, an increase in pressure normally produces a decrease in volume. The negative sign in K = -V(dp/dV) makes the bulk modulus positive for ordinary stable fluids. A large bulk modulus indicates that a comparatively large pressure change is needed to produce a given fractional volume change. Therefore Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
If K is the bulk modulus of a fluid, which expression gives its coefficient of compressibility β?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The coefficient of compressibility measures fractional volume change per unit pressure change. It is the reciprocal of the bulk modulus. Hence β = 1/K. A highly compressible material has a relatively large β and a relatively small bulk modulus. Therefore Option C is correct.
వివరణ:
Question 4
ప్రశ్న 4
A liquid has bulk modulus K = 2.0 GPa. If its pressure is increased by 10 MPa and K may be treated as constant, what is the approximate fractional increase in density?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a small compression, the fractional density increase is approximately Δρ/ρ = Δp/K. Here Δp/K = 10 × 10^6 divided by 2.0 × 10^9. This equals 0.005. Expressed as a percentage, 0.005 is 0.50%. Therefore Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
Which general thermodynamic relation defines the speed of a small sound disturbance in a fluid?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A sound wave consists of very small and rapid pressure and density disturbances. These small disturbances are conventionally treated as nearly reversible and adiabatic, and therefore approximately isentropic. The acoustic relation is a² = (∂p/∂ρ)s. This relation applies more generally than the perfect-gas sound-speed formula. Therefore Option A is correct.
వివరణ:
Question 6
ప్రశ్న 6
A liquid has isentropic bulk modulus Ks = 2.2 × 10^9 Pa and density 1000 kg/m³. What is its approximate speed of sound?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a liquid represented by its isentropic bulk modulus, a = √(Ks/ρ). Substituting the data gives a = √[(2.2 × 10^9)/1000]. This is √(2.2 × 10^6). The result is approximately 1483 m/s. Therefore Option C is correct.
వివరణ:
Question 7
ప్రశ్న 7
For a calorically perfect ideal gas, which expression gives the local speed of sound?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a calorically perfect ideal gas, the isentropic relation gives a² = γp/ρ. Using the ideal-gas equation p = ρRT converts this to a² = γRT. Therefore a = √(γRT). The temperature in this equation must be an absolute temperature. Hence Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
For the same calorically perfect ideal gas with constant γ and R, the absolute temperature increases from 300 K to 432 K. What is the ratio of the new speed of sound to the original speed of sound?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For a calorically perfect ideal gas, speed of sound is proportional to the square root of absolute temperature. Therefore a2/a1 = √(T2/T1). The temperature ratio is 432/300 = 1.44. Its square root is 1.20. Therefore Option D is correct.
వివరణ:
Question 9
ప్రశ్న 9
For air, take γ = 1.4, R = 287 J/(kg·K) and static temperature T = 300 K. What is the speed of sound approximately?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For the stated ideal-gas model, a = √(γRT). Substitution gives a = √(1.4 × 287 × 300). The quantity inside the square root is 120540 m²/s². Its square root is approximately 347.2 m/s. Therefore Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
Which expression defines the local Mach number M of a flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number compares the local flow speed with the local speed of sound. It is defined as M = V/a. Both V and a have dimensions of velocity, so Mach number is dimensionless. Because both quantities can vary through a compressible flow field, Mach number can also vary spatially. Therefore Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
A gas flows at 250 m/s where the local speed of sound is 340 m/s. What is the local Mach number and basic regime classification?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number is M = V/a. Thus M = 250/340 = approximately 0.735. Because this value is less than one, the flow is subsonic according to the basic Mach-number classification. It is not sonic because the flow speed is below the local acoustic speed. Therefore Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
A gas flows at 680 m/s where its local speed of sound is 340 m/s. How should the flow be classified using the basic Mach-number definition?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The Mach number is 680/340 = 2.0. A Mach number greater than one means the flow velocity exceeds the local speed of sound. Such a flow is classified as supersonic under the basic classification. This statement does not require the more detailed aerodynamic subdivision into transonic or hypersonic ranges. Therefore Option D is correct.
వివరణ:
Question 13
ప్రశ్న 13
Which set correctly gives the basic Mach-number classification of a flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number directly compares flow speed with sound speed. If M is less than one, the flow speed is below the local acoustic speed and the flow is subsonic. At M = 1, flow speed equals the local speed of sound and the condition is sonic. When M exceeds one, the flow is supersonic in the basic classification. Therefore Option A is correct.
వివరణ:
Question 14
ప్రశ్న 14
Which statement most accurately describes the commonly used M < 0.3 incompressible approximation for gas flow?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The value M ≈ 0.3 is widely used as a practical low-Mach guideline. Below this level, flow-induced density changes are often small enough to neglect for many engineering calculations. It is an approximation rather than a mathematical statement that density can never vary. Heating, large imposed pressure changes or other effects can still alter gas density even at low velocity. Therefore Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
At a location where the speed of sound is 343 m/s, what flow speed corresponds to Mach 0.30?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number is M = V/a. Therefore V = Ma. Substitution gives V = 0.30 × 343 m/s. The result is 102.9 m/s. This value represents the flow speed corresponding exactly to the stated Mach number at that local acoustic speed. Therefore Option C is correct.
వివరణ:
Question 16
ప్రశ్న 16
For a calorically perfect ideal gas with fixed γ, R and static temperature, which statement about the local speed of sound is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For the stated ideal-gas assumptions, a = √(γRT). If γ, R and T are fixed, changing static pressure alone does not explicitly change the computed sound speed. The density must change consistently with p = ρRT when pressure changes at fixed temperature. In a real flow, pressure changes can also be accompanied by temperature changes, which can then change the sound speed. Therefore Option A is correct.
వివరణ:
Question 17
ప్రశ్న 17
Which statement correctly relates bulk modulus, compressibility and speed of sound in a liquid of fixed density?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Bulk modulus measures resistance to compression, so a larger bulk modulus means the fluid is less compressible. The coefficient of compressibility is the reciprocal of bulk modulus. For a liquid represented by a = √(Ks/ρ), increasing Ks at fixed density increases acoustic speed. Thus stiffer fluids transmit small pressure disturbances more rapidly. Therefore Option D is correct.
వివరణ:
Question 18
ప్రశ్న 18
A liquid has density 900 kg/m³ and measured sound speed 1400 m/s. Assuming a² = Ks/ρ, what is its isentropic bulk modulus Ks?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The acoustic relation gives Ks = ρa². Substitution gives Ks = 900 × 1400² Pa. Since 1400² = 1.96 × 10^6, the product is 1.764 × 10^9 Pa. This equals 1.764 GPa. Therefore Option B is correct.
వివరణ:
Question 19
ప్రశ్న 19
For an isentropic process of a calorically perfect ideal gas with constant γ, which pressure-density relation is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A calorically perfect ideal gas undergoing an isentropic change satisfies p/ρ^γ = constant. This relation is used in deriving the ideal-gas speed-of-sound expression. It shows directly that pressure and density changes are coupled during compressible isentropic motion. The simpler relation p/ρ = constant would correspond to constant temperature for an ideal gas rather than a general isentropic change. Therefore Option A is correct.
వివరణ:
Question 20
ప్రశ్న 20
A calorically perfect ideal gas undergoes an isentropic compression in which its absolute pressure doubles. If γ = 1.4, what is the density ratio ρ2/ρ1?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For an isentropic ideal-gas change, p/ρ^γ remains constant. Therefore ρ2/ρ1 = (p2/p1)^(1/γ). With p2/p1 = 2 and γ = 1.4, the ratio is 2^(1/1.4). This evaluates to approximately 1.641. Therefore Option C is correct.
వివరణ:
Question 21
ప్రశ్న 21
Air is treated as an ideal gas with R = 287 J/(kg·K). What is its density at an absolute pressure of 100 kPa and temperature of 300 K?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The ideal-gas equation is p = ρRT. Rearranging gives ρ = p/(RT). Substitution gives ρ = 100000/(287 × 300). The result is approximately 1.161 kg/m³. Therefore Option B is correct.
వివరణ:
Question 22
ప్రశ్న 22
An ideal gas is maintained at constant absolute pressure while its temperature rises from 300 K to 360 K. What is the ratio of final density to initial density?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For an ideal gas, ρ = p/(RT). At constant pressure and for the same gas, density is inversely proportional to absolute temperature. Therefore ρ2/ρ1 = T1/T2 = 300/360. This ratio is approximately 0.8333. Hence Option C is correct.
వివరణ:
Question 23
ప్రశ్న 23
Air at 300 K is modeled as a calorically perfect ideal gas with γ = 1.4 and R = 287 J/(kg·K). If its velocity is 300 m/s, what is the Mach number and basic regime?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At 300 K, the sound speed from a = √(γRT) is approximately 347.2 m/s. Mach number is therefore 300/347.2. This gives M approximately equal to 0.864. Since this value is less than one, the basic classification is subsonic. Therefore Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
A gas stream initially has Mach number 0.90. Its flow velocity remains unchanged, but its local absolute temperature increases so that the local speed of sound becomes 1.20 times its original value. What is the new Mach number?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mach number is the ratio of flow velocity to local sound speed. The velocity is unchanged while the sound speed increases by a factor of 1.20. Therefore the new Mach number is 0.90/1.20. This gives 0.75. Therefore Option C is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about fundamental compressible flow: I. Mach number is the ratio of local flow speed to local sound speed. II. Small acoustic disturbances are associated with an approximately isentropic pressure-density response. III. For a calorically perfect ideal gas, sound speed varies as the square root of absolute temperature. IV. The commonly used M < 0.3 incompressible criterion is an engineering approximation rather than a universal statement that density can never vary. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is the definition of Mach number. Statement II is correct because acoustic disturbances are sufficiently small and rapid to be treated as approximately isentropic in the classical derivation. Statement III follows from a = √(γRT) for a calorically perfect ideal gas. Statement IV correctly recognizes the limited and approximate nature of the usual low-Mach incompressible guideline. 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: A. A flow in which density variations can be significant and must be considered in the analysis సమాధానం: A.
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Question 2 ప్రశ్న 2Answer: B. K = -V(dp/dV) సమాధానం: B.
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Question 3 ప్రశ్న 3Answer: C. β = 1/K సమాధానం: C.
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Question 4 ప్రశ్న 4Answer: B. 0.50% సమాధానం: B.
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Question 5 ప్రశ్న 5Answer: A. a² = (∂p/∂ρ)s సమాధానం: A.
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Question 6 ప్రశ్న 6Answer: C. 1483 m/s సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: B. a = √(γRT) సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: D. 1.200 సమాధానం: D.
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Question 9 ప్రశ్న 9Answer: C. 347 m/s సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: B. M = V/a సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: C. M = 0.735; subsonic సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: D. Supersonic because M = 2 సమాధానం: D.
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Question 13 ప్రశ్న 13Answer: A. Subsonic: M < 1; sonic: M = 1; supersonic: M > 1 సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: B. For many engineering flows at sufficiently low Mach number, density changes caused by flow acceleration are small enough that an incompressible approximation is often acceptable సమాధానం: B.
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Question 15 ప్రశ్న 15Answer: C. 102.9 m/s సమాధానం: C.
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Question 16 ప్రశ్న 16Answer: A. It is independent of static pressure directly because a = √(γRT) సమాధానం: A.
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Question 17 ప్రశ్న 17Answer: D. A larger bulk modulus means lower compressibility and generally higher sound speed సమాధానం: D.
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Question 18 ప్రశ్న 18Answer: B. 1.764 GPa సమాధానం: B.
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Question 19 ప్రశ్న 19Answer: A. p/ρ^γ = constant సమాధానం: A.
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Question 20 ప్రశ్న 20Answer: C. 1.641 సమాధానం: C.
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Question 21 ప్రశ్న 21Answer: B. 1.161 kg/m³ సమాధానం: B.
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Question 22 ప్రశ్న 22Answer: C. 0.833 సమాధానం: C.
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Question 23 ప్రశ్న 23Answer: B. M = 0.864; subsonic సమాధానం: B.
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Question 24 ప్రశ్న 24Answer: C. 0.750 సమాధానం: C.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.