Please keep at least one language enabled. || కనీసం ఒక భాషను ఎంచుకోండి.
Question 1
ప్రశ్న 1
Which arrangement is correctly described as pipes connected in series?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Pipes are in series when the outlet of one pipe leads into the next pipe in succession. For steady incompressible flow without withdrawal or addition at the intermediate connections, the same discharge passes through every series pipe. The individual pipes may have different lengths, diameters and friction factors. Their individual head losses generally differ because their hydraulic resistances differ. Therefore Option A correctly defines a series-pipe arrangement.
వివరణ:
Question 2
ప్రశ్న 2
Three pipes are connected in series and no flow enters or leaves at either intermediate junction. If the steady discharge in the first pipe is Q, what are the discharges in the second and third pipes?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Conservation of mass applies at each intermediate junction. With an incompressible fluid and no external inflow or withdrawal, the volumetric discharge entering a junction must equal the discharge leaving it. Consequently the discharge remains the same through every pipe in a simple series system. The velocities may nevertheless differ if the pipe diameters differ. Therefore both downstream pipes carry discharge Q and Option B is correct.
వివరణ:
Question 3
ప్రశ్న 3
For several pipes connected in series between two end points, with no pump or turbine between the intermediate junctions, how is the total frictional head loss related to the individual pipe losses?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Mechanical-energy loss accumulates as the fluid passes successively through each pipe. Therefore the head losses of the individual series segments are added. For three pipes, for example, hL,total = hL1 + hL2 + hL3. The same discharge passes through all three pipes, but each loss may differ because of its own resistance. Hence Option A is correct.
వివరణ:
Question 4
ప్రశ్న 4
Which pair of conditions applies to two steady incompressible-flow pipes connected in parallel between the same two junctions A and B?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Continuity at the upstream junction requires the total discharge to equal the sum of the branch discharges. Because both branches begin and end at the same hydraulic nodes, each path has the same difference in total head between those nodes. Therefore the head loss through one branch equals the head loss through the other when no machine introduces a different head change in a branch. The discharges themselves need not be equal unless the branch resistances are equal. Hence Option B is correct.
వివరణ:
Question 5
ప్రశ్న 5
For a circular pipe using Darcy-Weisbach with a specified constant Darcy friction factor f, the loss is written as hL = RQ². Which expression gives R?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Darcy-Weisbach gives hL = f(L/D)V²/(2g). For a circular pipe, V = 4Q/(πD²). Substitution gives V² = 16Q²/(π²D⁴). Combining the expressions yields hL = [8fL/(gπ²D⁵)]Q². Therefore R = 8fL/(gπ²D⁵), making Option A correct.
వివరణ:
Question 6
ప్రశ్న 6
If two pipes having quadratic resistance coefficients R1 and R2 are connected in series so that hL = RQ² for each pipe, what is the equivalent resistance Req of the series combination?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The same discharge Q passes through both series pipes. Their losses are h1 = R1Q² and h2 = R2Q². The total loss is their sum, giving htotal = (R1 + R2)Q². Comparing this with htotal = ReqQ² gives Req = R1 + R2. Therefore Option A is correct.
వివరణ:
Question 7
ప్రశ్న 7
Two pipes obey hL = RQ² and are connected in parallel between the same two nodes. Which relation gives their equivalent resistance Req?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The head loss h is the same through both parallel branches. Therefore Q1 = √(h/R1) and Q2 = √(h/R2). The total discharge is Q = √h[1/√R1 + 1/√R2]. For an equivalent pipe Q = √(h/Req). Equating these expressions gives 1/√Req = 1/√R1 + 1/√R2, so Option B is correct.
వివరణ:
Question 8
ప్రశ్న 8
What is meant by an equivalent pipe replacing a given compound pipe system between two specified end points?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
An equivalent pipe is intended to reproduce the hydraulic behavior of the original system between selected terminal points. For the same operating condition, it must carry the same total discharge while producing the same total head loss. Its length, diameter and friction factor are chosen or related to satisfy this requirement. It need not have the same diameter as any individual pipe in the original system. Therefore Option A is correct.
వివరణ:
Question 9
ప్రశ్న 9
Two pipes are connected in series and carry Q = 0.040 m³/s. Pipe 1 has f = 0.020, L = 100 m and D = 0.20 m; Pipe 2 has f = 0.025, L = 80 m and D = 0.15 m. Using Darcy-Weisbach and g = 9.81 m/s², what is the total major head loss?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The same discharge passes through both series pipes, but their velocities differ because their diameters differ. Using Darcy-Weisbach, Pipe 1 has a head loss of approximately 0.826 m. Pipe 2 has a head loss of approximately 3.482 m. Series losses add, so the total is 0.826 + 3.482 = approximately 4.308 m. Therefore the total head loss is about 4.31 m and Option C is correct.
వివరణ:
Question 10
ప్రశ్న 10
Two circular pipes of lengths 100 m and 80 m and diameters 200 mm and 150 mm respectively are connected in series. They have the same Darcy friction factor. If they are replaced by one equivalent pipe of total length 180 m having the same friction factor, what is the equivalent diameter approximately, neglecting minor losses?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
With the same discharge and Darcy friction factor, each pipe loss is proportional to L/D⁵. Equivalence therefore requires Le/De⁵ = L1/D1⁵ + L2/D2⁵. Substituting Le = 180 m, L1 = 100 m, D1 = 0.20 m, L2 = 80 m and D2 = 0.15 m gives De approximately 0.16748 m. This is about 167.5 mm. Therefore Option B is correct.
వివరణ:
Question 11
ప్రశ్న 11
Two pipes of equal length and equal Darcy friction factor are connected in series and carry the same discharge. Their diameters are D1 = 200 mm and D2 = 100 mm. What is hL2/hL1 when minor losses are neglected?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
At the same discharge, Darcy-Weisbach loss in a circular pipe is proportional to L/D⁵ when friction factor is fixed. The lengths and friction factors are equal in this question. Therefore hL2/hL1 = (D1/D2)⁵. The diameter ratio is 200/100 = 2, and 2⁵ = 32. Hence Option D is correct.
వివరణ:
Question 12
ప్రశ్న 12
Two parallel branches have quadratic resistance coefficients R1 and R2, with hL = RQ². What is the discharge ratio Q1/Q2?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Both branches connect the same two nodes, so they have the same head loss. Hence R1Q1² = R2Q2². Rearranging gives Q1²/Q2² = R2/R1. Taking the positive square root for flows in the same prescribed direction gives Q1/Q2 = √(R2/R1). Therefore Option C is correct.
వివరణ:
Question 13
ప్రశ్న 13
Two parallel circular pipes have equal lengths and equal constant Darcy friction factors. Their diameters are 200 mm and 100 mm. What is the ratio of their discharges Q200/Q100 under the same head loss?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For fixed f and L, pipe resistance varies as 1/D⁵. Equal head loss therefore gives Q proportional to 1/√R and hence to D^(5/2). The discharge ratio is thus (0.20/0.10)^(5/2). This equals 2^(2.5), or approximately 5.657. Therefore Option C is correct.
వివరణ:
Question 14
ప్రశ్న 14
Two parallel branches have resistances R1 = 1000 s²/m⁵ and R2 = 4000 s²/m⁵ in the relation hL = RQ². If the total discharge is 0.060 m³/s, what are Q1 and Q2?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Equal head loss requires R1Q1² = R2Q2². Therefore Q1/Q2 = √(4000/1000) = 2. Continuity also requires Q1 + Q2 = 0.060 m³/s. Solving these two equations gives Q2 = 0.020 m³/s and Q1 = 0.040 m³/s. Hence Option B is correct.
వివరణ:
Question 15
ప్రశ్న 15
For the parallel branches R1 = 1000 s²/m⁵ and R2 = 4000 s²/m⁵, what is their equivalent quadratic resistance Req?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For quadratic branch losses, 1/√Req = 1/√R1 + 1/√R2. Here 1/√1000 plus 1/√4000 equals three times 1/√4000. Solving the relation gives Req approximately 444.44 s²/m⁵. As expected, the equivalent resistance of parallel paths is smaller than either individual branch resistance. Therefore Option B is correct.
వివరణ:
Question 16
ప్రశ్న 16
Three identical parallel pipes each have resistance R in the relation hL = RQ². What is the equivalent resistance of the three-pipe combination?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Each identical branch experiences the same head loss and therefore carries the same discharge. If each branch carries q, the total discharge is 3q. The common head loss is Rq² = R(Q/3)². Therefore hL = (R/9)Q² for the complete combination. Hence the equivalent resistance is R/9 and Option D is correct.
వివరణ:
Question 17
ప్రశ్న 17
Two pipes having resistances 500 s²/m⁵ and 1500 s²/m⁵ are connected in series. If the available head difference across the combination is 8.0 m and hL = RQ², what discharge flows?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Series resistances add, giving Req = 500 + 1500 = 2000 s²/m⁵. The system equation is therefore 8.0 = 2000Q². This gives Q² = 0.004. Taking the positive root gives Q = approximately 0.06325 m³/s. Therefore Option B is correct.
వివరణ:
Question 18
ప్రశ్న 18
Two parallel pipes have the same length and the same constant Darcy friction factor. Their diameters are 150 mm and 100 mm, and their combined discharge is 0.030 m³/s. What are the approximate branch discharges?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For equal length and friction factor, branch discharge under equal head loss is proportional to D^(5/2). The ratio Q150/Q100 is therefore 1.5^(5/2), which is approximately 2.756. Combining this ratio with Q150 + Q100 = 0.030 m³/s gives Q150 approximately 0.02201 m³/s. The smaller branch consequently carries approximately 0.00799 m³/s. Therefore Option C is correct.
వివరణ:
Question 19
ప్రశ్న 19
The two parallel pipes in the preceding type of system each have length 100 m and Darcy friction factor 0.020, with diameters 150 mm and 100 mm. If their branch discharges are approximately 0.02201 m³/s and 0.00799 m³/s respectively, what common head loss do they have? Take g = 9.81 m/s².
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Each branch head loss must be calculated using its own discharge and diameter. Applying Darcy-Weisbach to the 150 mm branch gives approximately 1.054 m. Independently applying it to the 100 mm branch with its smaller discharge also gives approximately 1.054 m. Their equality confirms the required parallel-flow condition between the same two nodes. Therefore Option B is correct.
వివరణ:
Question 20
ప్రశ్న 20
Three parallel branches obey hL = RQ² and have resistances 400, 900 and 3600 s²/m⁵. If the common head loss between their end nodes is 9.0 m, what is the total discharge?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
For each parallel branch, Q = √(hL/R). The three discharges are √(9/400) = 0.15 m³/s, √(9/900) = 0.10 m³/s and √(9/3600) = 0.05 m³/s. Continuity requires the total discharge to equal the sum of these branch flows. Their sum is 0.30 m³/s. Therefore Option D is correct.
వివరణ:
Question 21
ప్రశ్న 21
A pipe of resistance 100 s²/m⁵ is in series with two identical parallel pipes, each of resistance 400 s²/m⁵. All losses obey hL = RQ². What is the equivalent resistance of the complete arrangement?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The two identical parallel pipes each have resistance 400 s²/m⁵. Two identical quadratic-resistance branches in parallel have an equivalent resistance R/4, giving 100 s²/m⁵. This parallel group is then connected in series with the first 100 s²/m⁵ pipe. Series resistances add, giving a total equivalent resistance of 200 s²/m⁵. Therefore Option B is correct.
వివరణ:
Question 22
ప్రశ్న 22
For the system consisting of a 100 s²/m⁵ pipe in series with two identical 400 s²/m⁵ parallel branches, the total equivalent resistance is 200 s²/m⁵. If 8.0 m of head is available across the complete system, what total discharge flows and what discharge passes through each identical branch?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
The complete system obeys 8 = 200Q². Therefore Q² = 0.04 and the total series flow is Q = 0.20 m³/s. This total flow reaches the parallel junction and divides equally because the two branch resistances are identical. Each branch therefore carries 0.10 m³/s. Hence Option B is correct.
వివరణ:
Question 23
ప్రశ్న 23
Two identical pipes are connected in parallel between reservoirs that maintain a fixed head difference. If one branch is completely closed while the other pipe and the reservoir heads remain unchanged, what happens to the total discharge under the same quadratic resistance law?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
With both identical branches open under a fixed head difference, each carries the same discharge q. The total discharge is therefore 2q. Closing one branch does not change the imposed head difference across the remaining identical branch under the stated reservoir condition. The remaining branch consequently still carries q. The system total therefore falls from 2q to q, which is one-half, so Option B is correct.
వివరణ:
Question 24
ప్రశ్న 24
For n identical pipes, each having quadratic resistance R, compare a series arrangement with a parallel arrangement. Which pair of equivalent resistances is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
In series, the same discharge passes through all n pipes and the individual head losses add. The equivalent resistance is therefore nR. In parallel, each identical branch carries Q/n when the total discharge is Q. The common head loss is R(Q/n)², so the equivalent resistance is R/n². Therefore Option A is correct.
వివరణ:
Question 25
ప్రశ్న 25
Consider the following statements about pipe combinations when individual losses are represented by hL = RQ²: I. Series pipes carry the same discharge when there is no intermediate withdrawal or inflow. II. Head losses of series pipes add. III. Parallel branches between the same two nodes have equal end-to-end head loss. IV. For parallel branches, total discharge equals the sum of the branch discharges. Which option is correct?
Select an option first. || ముందుగా ఒక సమాధానాన్ని ఎంచుకోండి.
Explanation:
Statement I follows from continuity through a series connection without intermediate sources or sinks. Statement II follows from the energy equation because the losses accumulate successively along the flow path. Statement III is required because each parallel path connects the same pair of hydraulic nodes. Statement IV is the junction continuity requirement for the divided and recombined flow. Therefore all four statements are correct and Option D is the valid answer.
వివరణ:
Answer Key సమాధానాల పట్టిక
-
Question 1 ప్రశ్న 1Answer: A. Pipes connected successively so that the same flow passes through each pipe సమాధానం: A.
-
Question 2 ప్రశ్న 2Answer: B. Q and Q సమాధానం: B.
-
Question 3 ప్రశ్న 3Answer: A. The total loss is the arithmetic sum of the individual head losses సమాధానం: A.
-
Question 4 ప్రశ్న 4Answer: B. Q = Q1 + Q2 and hL1 = hL2 between A and B సమాధానం: B.
-
Question 5 ప్రశ్న 5Answer: A. R = 8fL/(gπ²D⁵) సమాధానం: A.
-
Question 6 ప్రశ్న 6Answer: A. Req = R1 + R2 సమాధానం: A.
-
Question 7 ప్రశ్న 7Answer: B. 1/√Req = 1/√R1 + 1/√R2 సమాధానం: B.
-
Question 8 ప్రశ్న 8Answer: A. A single pipe that carries the same discharge with the same total head loss between the specified end points under the stated conditions సమాధానం: A.
-
Question 9 ప్రశ్న 9Answer: C. 4.31 m సమాధానం: C.
-
Question 10 ప్రశ్న 10Answer: B. 167.5 mm సమాధానం: B.
-
Question 11 ప్రశ్న 11Answer: D. 32 సమాధానం: D.
-
Question 12 ప్రశ్న 12Answer: C. √(R2/R1) సమాధానం: C.
-
Question 13 ప్రశ్న 13Answer: C. 5.66 సమాధానం: C.
-
Question 14 ప్రశ్న 14Answer: B. Q1 = 0.040 m³/s and Q2 = 0.020 m³/s సమాధానం: B.
-
Question 15 ప్రశ్న 15Answer: B. 444.4 s²/m⁵ సమాధానం: B.
-
Question 16 ప్రశ్న 16Answer: D. R/9 సమాధానం: D.
-
Question 17 ప్రశ్న 17Answer: B. 0.0632 m³/s సమాధానం: B.
-
Question 18 ప్రశ్న 18Answer: C. 0.0220 and 0.0080 m³/s సమాధానం: C.
-
Question 19 ప్రశ్న 19Answer: B. 1.054 m సమాధానం: B.
-
Question 20 ప్రశ్న 20Answer: D. 0.30 m³/s సమాధానం: D.
-
Question 21 ప్రశ్న 21Answer: B. 200 s²/m⁵ సమాధానం: B.
-
Question 22 ప్రశ్న 22Answer: B. Total 0.20 m³/s; each branch 0.10 m³/s సమాధానం: B.
-
Question 23 ప్రశ్న 23Answer: B. It becomes one-half of the original value సమాధానం: B.
-
Question 24 ప్రశ్న 24Answer: A. Series: nR; Parallel: R/n² సమాధానం: A.
-
Question 25 ప్రశ్న 25Answer: D. I, II, III and IV సమాధానం: D.