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A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model is
- a)0.1 m3/s
- b)0.15 m3/s
- c)0.2 m3/s
- d)0.25 m3/s
Correct answer is option 'A'. Can you explain this answer?
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A pipe of diameter 1.5 m is required to transport an oil of relative d...
The Reynolds number must be the same in the model and prototype for similar pipe flows
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A pipe of diameter 1.5 m is required to transport an oil of relative d...
°C is used as a model, what will be the flow rate of water in the model?
Assuming that the flow is laminar and the pipes are of equal length, the flow rate of water in the model can be determined using the principle of dynamic similarity. This principle states that for two systems to be dynamically similar, their dimensionless variables must be equal.
In this case, the dimensionless variables are:
Reynolds number (Re) = (ρVD)/μ
where ρ is the density of the fluid, V is the velocity, D is the diameter of the pipe, and μ is the dynamic viscosity.
For the oil flow in the large pipe:
Re = (0.9 x 1000 x 3)/(3.14 x 0.75 x 10^-2) = 2,859,574
For the water flow in the model:
Re = (1000 x V x 0.15)/(0.001 x 3 x 10^-2)
where we have used the fact that the kinematic viscosity of water is approximately 1 cSt = 0.001 m^2/s.
Equating the two Reynolds numbers, we get:
2,859,574 = (1000 x V x 0.15)/(0.001 x 3 x 10^-2)
Solving for V, we get:
V = 0.85 m/s
Therefore, the flow rate of water in the model pipe will be:
Q = AV = (3.14 x 0.075^2/4) x 0.85 = 0.15 m^3/s
Assuming that the flow is laminar and the pipes are of equal length, the flow rate of water in the model can be determined using the principle of dynamic similarity. This principle states that for two systems to be dynamically similar, their dimensionless variables must be equal.
In this case, the dimensionless variables are:
Reynolds number (Re) = (ρVD)/μ
where ρ is the density of the fluid, V is the velocity, D is the diameter of the pipe, and μ is the dynamic viscosity.
For the oil flow in the large pipe:
Re = (0.9 x 1000 x 3)/(3.14 x 0.75 x 10^-2) = 2,859,574
For the water flow in the model:
Re = (1000 x V x 0.15)/(0.001 x 3 x 10^-2)
where we have used the fact that the kinematic viscosity of water is approximately 1 cSt = 0.001 m^2/s.
Equating the two Reynolds numbers, we get:
2,859,574 = (1000 x V x 0.15)/(0.001 x 3 x 10^-2)
Solving for V, we get:
V = 0.85 m/s
Therefore, the flow rate of water in the model pipe will be:
Q = AV = (3.14 x 0.075^2/4) x 0.85 = 0.15 m^3/s
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A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer?
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A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer?.
A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A pipe of diameter 1.5 m is required to transport an oil of relative density 0,9 and kinematic viscosity = 3 x 10-2 stoke at a rate of 3 m3/s. if a 15 cm diameter pipe with water at 20°C (n = 0.01 stoke) is used to model the above flow, the discharge in the model isa)0.1 m3/sb)0.15 m3/sc)0.2 m3/sd)0.25 m3/sCorrect answer is option 'A'. Can you explain this answer?.
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