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Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.
- a)1.56 m/s
- b)0.165 m/s
- c)0.1246 m/s
- d)1.65 m/s
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pi...
In this case, Reynolds similarity law is applicable
Referring to oil with a subscript p and water with a suffix m
∴
Referring to oil with a subscript p and water with a suffix m
∴
Most Upvoted Answer
Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pi...
Given data:
Density of oil = 917 kg/m³
Dynamic viscosity of oil = 0.29 Pa.s
Velocity of oil = 2 m/s
Diameter of oil pipe = 15 cm
Density of water = 998 kg/m³
Dynamic viscosity of water = 1.31 × 10^-3 Pa.s
Diameter of water pipe = 1 cm
To find: Velocity of water to make the two flows dynamically similar
Kinematic viscosity of oil can be calculated as:
Kinematic viscosity of oil = Dynamic viscosity of oil / Density of oil
= 0.29 / 917
= 3.17 × 10^-4 m²/s
Reynolds number for oil flow can be calculated as:
Re = (Density of oil × Velocity of oil × Diameter of oil pipe) / Dynamic viscosity of oil
= (917 × 2 × 0.15) / 0.29
= 950.17
Now, to make the flow of water dynamically similar to the flow of oil, the Reynolds number should be the same for both fluids. Hence, the Reynolds number for water flow should also be 950.17.
The velocity of water can be calculated using the Reynolds number equation for laminar flow:
Re = (Density of water × Velocity of water × Diameter of water pipe) / Dynamic viscosity of water
950.17 = (998 × V × 0.01) / 1.31 × 10^-3
V = 0.1246 m/s
Therefore, the velocity of water required to make the two flows dynamically similar is 0.1246 m/s. The correct answer is option C.
Density of oil = 917 kg/m³
Dynamic viscosity of oil = 0.29 Pa.s
Velocity of oil = 2 m/s
Diameter of oil pipe = 15 cm
Density of water = 998 kg/m³
Dynamic viscosity of water = 1.31 × 10^-3 Pa.s
Diameter of water pipe = 1 cm
To find: Velocity of water to make the two flows dynamically similar
Kinematic viscosity of oil can be calculated as:
Kinematic viscosity of oil = Dynamic viscosity of oil / Density of oil
= 0.29 / 917
= 3.17 × 10^-4 m²/s
Reynolds number for oil flow can be calculated as:
Re = (Density of oil × Velocity of oil × Diameter of oil pipe) / Dynamic viscosity of oil
= (917 × 2 × 0.15) / 0.29
= 950.17
Now, to make the flow of water dynamically similar to the flow of oil, the Reynolds number should be the same for both fluids. Hence, the Reynolds number for water flow should also be 950.17.
The velocity of water can be calculated using the Reynolds number equation for laminar flow:
Re = (Density of water × Velocity of water × Diameter of water pipe) / Dynamic viscosity of water
950.17 = (998 × V × 0.01) / 1.31 × 10^-3
V = 0.1246 m/s
Therefore, the velocity of water required to make the two flows dynamically similar is 0.1246 m/s. The correct answer is option C.
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Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer?
Question Description
Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. 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 Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer?.
Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. 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 Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer?.
Solutions for Oil of density 917 kg/m3 and dynamic viscosity 0.29 Pa.s flows in a pipe of diameter 15 cm at a velocity of 2 m/s. What would be the velocity of flow of water in a 1 cm diameter pipe to make the two flows dynamically similar? The density and viscosity of water can be taken as 998 kg/m3 and 1.31 x 10-3 Pa.s respectivley.a)1.56 m/sb)0.165 m/sc)0.1246 m/sd)1.65 m/sCorrect answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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