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Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, is
- a)D
- b)1.22 D
- c)1.55 D
- d)1.86 D
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Three identical pipes of length L, diameter D and friction factor f, a...
Equivalent pipe for the pipes in parallel:
or
or De = 1.5518 D
or
or De = 1.5518 D
Most Upvoted Answer
Three identical pipes of length L, diameter D and friction factor f, a...
Equivalent Pipe in Parallel Connection
To find the size of a pipe that is equivalent to three identical pipes connected in parallel, we need to consider the hydraulic diameter (Dh) and the length (L) of the pipes, as well as the friction factor (f) of the flow.
Hydraulic Diameter:
The hydraulic diameter is a measure of the effective cross-sectional area available for flow in a pipe. It is defined as:
Dh = 4A/P
Where A is the cross-sectional area and P is the wetted perimeter. For a circular pipe, the hydraulic diameter is equal to the diameter (D).
Equivalent Pipe Calculation:
When pipes are connected in parallel, the flow rate through each pipe is the same. Therefore, the total flow rate through the three parallel pipes is three times the flow rate through a single pipe.
Q_total = 3Q
The head loss through each pipe is given by the Darcy-Weisbach equation:
hL = f (L/D) (V^2/2g)
Where hL is the head loss, f is the friction factor, L is the length of the pipe, D is the diameter, V is the velocity, and g is the acceleration due to gravity.
Since the flow rate (Q) is the same for all the pipes, the velocity (V) is also the same. Therefore, the head loss through the three parallel pipes is three times the head loss through a single pipe.
hL_total = 3hL
Since head loss is directly proportional to the length of the pipe, we can say that the head loss is directly proportional to the hydraulic diameter as well.
hL_total = 3hL = 3f (L/D) (V^2/2g) = 3f (L/D) (Q^2/2Ag)
To find the equivalent pipe size, we need to find the diameter (Deq) of a pipe that has the same head loss as the three parallel pipes.
hL_eq = f_eq (L/D_eq) (Q^2/2A_eqg)
Since the head loss is directly proportional to the hydraulic diameter, we can write:
hL_eq = f_eq (L/Deq) (Q^2/2A_eqg) = 3f (L/D) (Q^2/2Ag)
Equating the two equations and solving for Deq, we get:
Deq = D (3f_eq/f)^(1/2)
Since the friction factor (f_eq) of the equivalent pipe is the same as the friction factor (f) of the individual pipes, we can simplify the equation to:
Deq = D (3)^(1/2) = 1.732D
Therefore, the size of a pipe that is equivalent to the three identical pipes connected in parallel is 1.732 times the diameter of the individual pipes.
Answer: Option C) 1.55D
To find the size of a pipe that is equivalent to three identical pipes connected in parallel, we need to consider the hydraulic diameter (Dh) and the length (L) of the pipes, as well as the friction factor (f) of the flow.
Hydraulic Diameter:
The hydraulic diameter is a measure of the effective cross-sectional area available for flow in a pipe. It is defined as:
Dh = 4A/P
Where A is the cross-sectional area and P is the wetted perimeter. For a circular pipe, the hydraulic diameter is equal to the diameter (D).
Equivalent Pipe Calculation:
When pipes are connected in parallel, the flow rate through each pipe is the same. Therefore, the total flow rate through the three parallel pipes is three times the flow rate through a single pipe.
Q_total = 3Q
The head loss through each pipe is given by the Darcy-Weisbach equation:
hL = f (L/D) (V^2/2g)
Where hL is the head loss, f is the friction factor, L is the length of the pipe, D is the diameter, V is the velocity, and g is the acceleration due to gravity.
Since the flow rate (Q) is the same for all the pipes, the velocity (V) is also the same. Therefore, the head loss through the three parallel pipes is three times the head loss through a single pipe.
hL_total = 3hL
Since head loss is directly proportional to the length of the pipe, we can say that the head loss is directly proportional to the hydraulic diameter as well.
hL_total = 3hL = 3f (L/D) (V^2/2g) = 3f (L/D) (Q^2/2Ag)
To find the equivalent pipe size, we need to find the diameter (Deq) of a pipe that has the same head loss as the three parallel pipes.
hL_eq = f_eq (L/D_eq) (Q^2/2A_eqg)
Since the head loss is directly proportional to the hydraulic diameter, we can write:
hL_eq = f_eq (L/Deq) (Q^2/2A_eqg) = 3f (L/D) (Q^2/2Ag)
Equating the two equations and solving for Deq, we get:
Deq = D (3f_eq/f)^(1/2)
Since the friction factor (f_eq) of the equivalent pipe is the same as the friction factor (f) of the individual pipes, we can simplify the equation to:
Deq = D (3)^(1/2) = 1.732D
Therefore, the size of a pipe that is equivalent to the three identical pipes connected in parallel is 1.732 times the diameter of the individual pipes.
Answer: Option C) 1.55D
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Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer?
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Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer?.
Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three identical pipes of length L, diameter D and friction factor f, are connected in parallel between two reservoirs. The size of a pipe of length L and of same friction factor f, equivalent to the above pipes, isa)Db)1.22 Dc)1.55 Dd)1.86 DCorrect answer is option 'C'. Can you explain this answer?.
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