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Question 1
ప్రశ్న 1
In pipe-system analysis, what is meant by a local or minor head loss?
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Explanation:
Local or minor losses occur in regions where the flow is disturbed by changes in geometry or fittings. Typical examples include entrances, exits, bends, valves, contractions and expansions. These losses arise from separation, mixing and other irreversible flow processes. Distributed wall-friction loss along a substantial pipe length is conventionally classified as major loss. The term minor does not imply that such a loss must always be smaller than the major loss, so Option B is correct.
వివరణ:
Question 2
ప్రశ్న 2
A local loss coefficient K is specified using a reference mean velocity V. Which expression gives the corresponding head loss?
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Explanation:
A local loss coefficient is commonly defined by hL = KV²/(2g). The velocity V must be the particular reference velocity associated with the stated coefficient. The quantity V²/(2g) is a velocity head and has dimensions of length. Because K is dimensionless, the product also has dimensions of head. Therefore Option A is correct.
వివరణ:
Question 3
ప్రశ్న 3
Several fittings in a constant-diameter pipe have loss coefficients K1, K2 and K3, all defined using the same pipe mean velocity V. What is their combined local head loss?
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Explanation:
Individual irreversible head losses occurring successively in a pipe system are additive. Because all three coefficients are referenced to the same mean velocity, their losses can be added directly. Thus hL,total = K1V²/(2g) + K2V²/(2g) + K3V²/(2g). Factoring out the common velocity head gives (K1 + K2 + K3)V²/(2g). Therefore Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
A particular sharp-edged pipe entrance is specified to have an entrance-loss coefficient Ke = 0.50 based on the velocity in the downstream pipe. What head loss should be used?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The problem explicitly specifies the entrance-loss coefficient as 0.50. A local loss is calculated from hL = KV²/(2g) using the velocity on which K is based. Therefore the entrance loss is 0.50V²/(2g). The numerical value of an entrance coefficient depends on entrance geometry, so it should not be treated as universal without qualification. Hence Option A is correct.
వివరణ:
Question 5
ప్రశ్న 5
Water enters a pipe at a fitting whose entrance-loss coefficient is Ke = 0.50 based on a pipe velocity of 3.0 m/s. What is the entrance head loss? Take g = 9.81 m/s².
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Explanation:
The entrance loss is hL = KeV²/(2g). Substituting Ke = 0.50 and V = 3.0 m/s gives hL = 0.50 × 9/(2 × 9.81). This evaluates to approximately 0.2294 m. The calculation uses the downstream pipe velocity because that is the stated reference velocity for Ke. Therefore Option B is correct.
వివరణ:
Question 6
ప్రశ్న 6
A pipe discharges directly into a very large reservoir. If V is the mean velocity in the pipe immediately before the discharge, what exit head loss is conventionally used?
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Explanation:
Fluid leaving the pipe enters the large reservoir as a jet and ultimately slows to essentially zero mean velocity. Its pipe velocity head is dissipated by mixing in the reservoir. The conventional exit loss is therefore hL = V²/(2g). This corresponds to an exit-loss coefficient K = 1 when based on the pipe velocity. Hence Option C is correct.
వివరణ:
Question 7
ప్రశ్న 7
Water leaves a pipe at 4.0 m/s and discharges into a large reservoir. What is the exit head loss? Take g = 9.81 m/s².
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Explanation:
For discharge from a pipe into a large reservoir, the conventional exit-loss coefficient is unity. Hence hL = V²/(2g). Substituting V = 4.0 m/s gives 16/(2 × 9.81). The resulting head loss is approximately 0.8155 m. Therefore Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
A bend has a specified loss coefficient K = 0.40 based on the pipe mean velocity. If water flows through the bend at 3.0 m/s, what is the local head loss? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The bend loss is calculated from hL = KV²/(2g). The velocity head at 3.0 m/s is 9/(19.62), or approximately 0.4587 m. Multiplying by K = 0.40 gives approximately 0.1835 m. The value of K itself depends on the bend geometry and is supplied explicitly in the question. Therefore Option B is correct.
వివరణ:
Question 9
ప్రశ్న 9
A valve has a specified loss coefficient K = 2.0 based on the pipe velocity. If the mean velocity through the pipe is 2.5 m/s, what head loss occurs across the valve? Take g = 9.81 m/s².
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Explanation:
The local valve loss is hL = KV²/(2g). For V = 2.5 m/s, the velocity head is 6.25/(19.62), or approximately 0.3186 m. Multiplication by K = 2.0 gives approximately 0.6371 m. The supplied loss coefficient already represents the resistance of the specified valve condition. Therefore Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
For an incompressible flow through a sudden expansion from mean velocity V1 in the smaller pipe to V2 in the larger pipe, which expression gives the idealized Borda-Carnot head loss?
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Explanation:
A sudden expansion causes flow separation and strong mixing as the high-speed stream enters the larger pipe. The resulting irreversible head loss is described by the Borda-Carnot relation. For the usual incompressible sudden-expansion model, hL = (V1 - V2)²/(2g). It is the square of the velocity difference, not simply the difference of the velocity heads. Therefore Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
Water at Q = 0.030 m³/s flows through a sudden expansion from a 100 mm diameter pipe to a 200 mm diameter pipe. What is the sudden-expansion head loss? Take g = 9.81 m/s².
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Explanation:
The upstream area is π(0.10)²/4, giving V1 approximately equal to 3.820 m/s. The downstream area is four times larger, so V2 is approximately 0.955 m/s. The sudden-expansion loss is (V1 - V2)²/(2g). Substitution gives approximately 0.4183 m. Therefore Option C is correct.
వివరణ:
Question 12
ప్రశ్న 12
For a sudden expansion from area A1 to area A2, the loss coefficient is to be based on the upstream velocity V1. Which expression follows from the Borda-Carnot equation?
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Explanation:
Continuity gives V2/V1 = A1/A2 for incompressible flow. The Borda-Carnot relation is hL = (V1 - V2)²/(2g). Factoring V1 from the velocity difference gives hL = [1 - A1/A2]²V1²/(2g). Therefore the coefficient based on upstream velocity is K = (1 - A1/A2)². Hence Option A is correct.
వివరణ:
Question 13
ప్రశ్న 13
Water flows horizontally through a sudden expansion with no pump or turbine. Which statement correctly describes the energy and pressure behavior through the expansion?
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Explanation:
A sudden expansion irreversibly dissipates part of the mechanical energy, so the energy grade line must decrease in the direction of flow. At the same time, the larger area produces a lower mean velocity. Part of the upstream velocity head is therefore recovered as static pressure. The pressure recovery is less than it would be in an ideal lossless diffuser because some head is dissipated. Consequently Option A is correct.
వివరణ:
Question 14
ప్రశ్న 14
Which flow feature is characteristically associated with a sudden contraction from a large pipe to a smaller pipe?
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Explanation:
At a sudden contraction, streamlines cannot turn sharply enough to follow the solid boundary exactly. The stream therefore contracts to an area smaller than the downstream pipe area. This minimum stream-tube section is called the vena contracta. The jet then expands from the vena contracta to fill the smaller pipe, producing separation and mixing losses. Therefore Option A is correct.
వివరణ:
Question 15
ప్రశ్న 15
For an idealized sudden-contraction model, let Cc be the coefficient of contraction and let V2 be the mean velocity in the smaller downstream pipe. Which loss coefficient Kc based on V2 follows from treating the main loss as the expansion from the vena contracta to the smaller pipe?
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Explanation:
At the vena contracta, Ac = CcA2. Continuity therefore gives Vc = V2/Cc. Treating the principal contraction loss as the subsequent expansion from the vena contracta to the smaller pipe gives hL = (Vc - V2)²/(2g). Factoring V2 produces hL = (1/Cc - 1)²V2²/(2g). Hence Option A gives the corresponding coefficient.
వివరణ:
Question 16
ప్రశ్న 16
For an idealized sudden contraction, the coefficient of contraction is Cc = 0.62 and the mean velocity in the smaller downstream pipe is 4.0 m/s. Using Kc = (1/Cc - 1)², what is the contraction head loss? Take g = 9.81 m/s².
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Explanation:
The loss coefficient is Kc = (1/0.62 - 1)². This gives Kc approximately equal to 0.37565. The downstream velocity head is 4²/(2 × 9.81), or approximately 0.8155 m. Multiplying the coefficient by this velocity head gives approximately 0.3063 m. Therefore Option B is correct.
వివరణ:
Question 17
ప్రశ్న 17
A constant-diameter pipe contains an entrance with K = 0.50, one valve with K = 2.0 and two bends each having K = 0.30. If all coefficients use the same pipe velocity of 2.0 m/s, what is the total local head loss? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The total loss coefficient is 0.50 + 2.0 + 0.30 + 0.30 = 3.10. Because the pipe diameter is constant, all coefficients use the same specified velocity. The velocity head is 2²/(2 × 9.81), or approximately 0.2039 m. Thus the combined loss is 3.10 × 0.2039 = approximately 0.6320 m. Therefore Option B is correct.
వివరణ:
Question 18
ప్రశ్న 18
A fitting having local loss coefficient K is to be represented by an equivalent length Le of the same constant-diameter pipe. If f is the Darcy friction factor, which relation is correct?
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Explanation:
The local loss is hL = KV²/(2g). The Darcy-Weisbach loss through an equivalent pipe length is hf = f(Le/D)V²/(2g). Equating these two heads gives K = fLe/D. Solving for equivalent length gives Le = KD/f. Therefore Option A is correct.
వివరణ:
Question 19
ప్రశ్న 19
A valve has a loss coefficient K = 3.0 in a 100 mm diameter pipe. If the Darcy friction factor for equivalent-length purposes is f = 0.020, what is the valve's equivalent pipe length?
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Explanation:
The equivalent length is Le = KD/f when the Darcy friction factor is used. Substitution gives Le = 3.0 × 0.10/0.020. This evaluates to 15 m. The result means that the valve produces the same specified head loss as approximately 15 m of that pipe under the assumptions used. Therefore Option C is correct.
వివరణ:
Question 20
ప్రశ్న 20
Let H = z + p/γ + V²/(2g). Which extended energy equation correctly includes a pump head hp, turbine head ht, major pipe losses and local losses between sections 1 and 2?
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Explanation:
A pump adds mechanical head to the flowing fluid and therefore appears as a positive input. A turbine extracts mechanical head and therefore appears on the expenditure side of the balance. Major and minor losses also represent irreversible reductions in mechanical head. The extended energy equation can consequently be written as H1 + hp = H2 + ht + Σhmajor + Σhminor. Therefore Option A is correct.
వివరణ:
Question 21
ప్రశ్న 21
Two large reservoirs have a free-surface elevation difference of 10 m and are connected by a 100 m long, 200 mm diameter pipe. The Darcy friction factor is 0.020, the entrance coefficient is 0.50 and the exit coefficient is 1.0. Neglect all other losses. What steady discharge results? Take g = 9.81 m/s².
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Explanation:
Between the two large reservoir surfaces, the pressure heads are both atmospheric and their mean velocities are negligible. The available 10 m head is therefore consumed by pipe friction, entrance loss and exit loss. The total coefficient multiplying V²/(2g) is fL/D + Ke + Kexit = 0.020(100/0.20) + 0.50 + 1.0 = 11.5. Solving 10 = 11.5V²/(2g) gives V approximately 4.130 m/s, and multiplying by the 200 mm pipe area gives Q approximately 0.1298 m³/s. Therefore Option C is correct.
వివరణ:
Question 22
ప్రశ్న 22
A local device with K = 2.5 is installed in a 100 mm diameter pipe. If the allowable head loss across the device is 1.50 m, what discharge corresponds to this loss? Take g = 9.81 m/s².
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Explanation:
From hL = KV²/(2g), the required velocity is V = sqrt(2ghL/K). Substitution gives V = sqrt[2(9.81)(1.50)/2.5], which is approximately 3.431 m/s. The area of a 100 mm diameter pipe is π(0.10)²/4 = approximately 0.007854 m². Thus Q = AV = approximately 0.02695 m³/s. Therefore Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
Under the usual one-dimensional energy-head convention, what is the separation between the energy grade line and hydraulic grade line at a pipe section?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The energy grade line represents z + p/γ + V²/(2g). The hydraulic grade line represents z + p/γ. Their vertical separation is therefore V²/(2g). In a constant-diameter pipe carrying steady incompressible flow, this separation remains constant if the mean velocity remains constant. Therefore Option C is correct.
వివరణ:
Question 24
ప్రశ్న 24
A local valve or fitting lies between two nearby sections of the same horizontal constant-diameter pipe. The mean velocity is the same immediately upstream and downstream, and no pump or turbine is present. How do the EGL and HGL change across the fitting?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
A fitting dissipates mechanical energy and therefore causes the energy grade line to fall by the local head loss. Because the pipe diameter is unchanged, the mean velocity and velocity head are the same on the two sides under the stated steady-flow condition. The EGL-to-HGL separation therefore remains unchanged. The HGL consequently falls by the same head amount as the EGL across the idealized localized fitting. Hence Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about local losses and energy lines: I. A pipe discharging into a large reservoir has an exit loss equal to one pipe velocity head under the conventional model. II. Across a sudden expansion, static pressure can recover even though the EGL falls. III. Loss coefficients referenced to different velocities should not be added directly without first expressing the losses on a common basis. IV. In a short pipe system containing many restrictive fittings, total minor losses can exceed the distributed pipe-friction loss. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I is correct because the conventional exit-loss coefficient is unity when based on the pipe velocity. Statement II is correct because the reduction in velocity through an expansion can produce pressure recovery while irreversible mixing still lowers total head. Statement III is correct because K values are meaningful only with their specified reference velocities, so unlike-based coefficients cannot simply be summed. Statement IV is correct because the labels major and minor do not prescribe their relative magnitudes in a particular system. Therefore all four statements are valid and Option D is correct.
వివరణ:
Answer Key సమాధానాల పట్టిక
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Question 1 ప్రశ్న 1Answer: B. A localized mechanical-energy loss associated with a fitting, entrance, exit or change in flow geometry సమాధానం: B.
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Question 2 ప్రశ్న 2Answer: A. hL = KV²/(2g) సమాధానం: A.
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Question 3 ప్రశ్న 3Answer: A. (K1 + K2 + K3)V²/(2g) సమాధానం: A.
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Question 4 ప్రశ్న 4Answer: A. 0.50V²/(2g) సమాధానం: A.
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Question 5 ప్రశ్న 5Answer: B. 0.229 m సమాధానం: B.
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Question 6 ప్రశ్న 6Answer: C. V²/(2g) సమాధానం: C.
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Question 7 ప్రశ్న 7Answer: B. 0.815 m సమాధానం: B.
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Question 8 ప్రశ్న 8Answer: B. 0.183 m సమాధానం: B.
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Question 9 ప్రశ్న 9Answer: C. 0.637 m సమాధానం: C.
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Question 10 ప్రశ్న 10Answer: B. (V1 - V2)²/(2g) సమాధానం: B.
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Question 11 ప్రశ్న 11Answer: C. 0.418 m సమాధానం: C.
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Question 12 ప్రశ్న 12Answer: A. K = (1 - A1/A2)² సమాధానం: A.
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Question 13 ప్రశ్న 13Answer: A. The EGL falls because of irreversible loss, while the static pressure can rise because the mean velocity decreases సమాధానం: A.
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Question 14 ప్రశ్న 14Answer: A. A vena contracta forms downstream of the contraction before the stream expands to fill the smaller pipe సమాధానం: A.
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Question 15 ప్రశ్న 15Answer: A. Kc = (1/Cc - 1)² సమాధానం: A.
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Question 16 ప్రశ్న 16Answer: B. 0.306 m సమాధానం: B.
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Question 17 ప్రశ్న 17Answer: B. 0.632 m సమాధానం: B.
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Question 18 ప్రశ్న 18Answer: A. Le = KD/f సమాధానం: A.
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Question 19 ప్రశ్న 19Answer: C. 15 m సమాధానం: C.
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Question 20 ప్రశ్న 20Answer: A. H1 + hp = H2 + ht + Σhmajor + Σhminor సమాధానం: A.
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Question 21 ప్రశ్న 21Answer: C. 0.1298 m³/s సమాధానం: C.
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Question 22 ప్రశ్న 22Answer: B. 0.0269 m³/s సమాధానం: B.
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Question 23 ప్రశ్న 23Answer: C. Velocity head V²/(2g) సమాధానం: C.
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Question 24 ప్రశ్న 24Answer: A. Both drop by the local head loss, while their separation remains the same సమాధానం: A.
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Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.