UPSC Exam > UPSC Questions > A smooth flat plate 2 m wide and 2 m long is ...
Start Learning for Free
A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]?
Most Upvoted Answer
A smooth flat plate 2 m wide and 2 m long is subjected to flow of wate...
Introduction
The boundary layer is a crucial concept in fluid mechanics, particularly when analyzing the flow over surfaces like a flat plate. In this scenario, we have a smooth flat plate subjected to a uniform flow of water.
Given Parameters
- Plate dimensions: 2 m wide and 2 m long
- Flow velocity: 2 m/s
- Density of water (p): 898 kg/m³
- Kinematic viscosity (v): 1 x 10-6 m²/s
- Thickness of the boundary layer at the edge: 1.76 mm
Boundary Layer Development
- The boundary layer forms as the fluid flows over the flat plate, affecting the velocity profile.
- Near the leading edge, the flow is affected by viscosity, leading to a velocity gradient where the fluid velocity transitions from zero at the surface (due to the no-slip condition) to the free stream velocity.
Laminar Boundary Layer Thickness
- The thickness of the laminar boundary layer can be estimated using the relationship:
- δ = 5 x (L / √(Re))
- Where δ is the boundary layer thickness, L is the length of the plate, and Re is the Reynolds number.
Reynolds Number Calculation
- The Reynolds number (Re) is defined as:
- Re = (U * L) / v
- For our case:
- U = 2 m/s, L = 2 m, v = 1 x 10-6 m²/s
- Re = (2 * 2) / (1 x 10-6) = 4,000,000
Conclusion
- The calculated boundary layer thickness of 1.76 mm indicates the region where viscous effects are significant.
- Understanding this concept is vital for applications in aerodynamics and hydrodynamics, influencing drag and heat transfer characteristics.
The boundary layer is a crucial concept in fluid mechanics, particularly when analyzing the flow over surfaces like a flat plate. In this scenario, we have a smooth flat plate subjected to a uniform flow of water.
Given Parameters
- Plate dimensions: 2 m wide and 2 m long
- Flow velocity: 2 m/s
- Density of water (p): 898 kg/m³
- Kinematic viscosity (v): 1 x 10-6 m²/s
- Thickness of the boundary layer at the edge: 1.76 mm
Boundary Layer Development
- The boundary layer forms as the fluid flows over the flat plate, affecting the velocity profile.
- Near the leading edge, the flow is affected by viscosity, leading to a velocity gradient where the fluid velocity transitions from zero at the surface (due to the no-slip condition) to the free stream velocity.
Laminar Boundary Layer Thickness
- The thickness of the laminar boundary layer can be estimated using the relationship:
- δ = 5 x (L / √(Re))
- Where δ is the boundary layer thickness, L is the length of the plate, and Re is the Reynolds number.
Reynolds Number Calculation
- The Reynolds number (Re) is defined as:
- Re = (U * L) / v
- For our case:
- U = 2 m/s, L = 2 m, v = 1 x 10-6 m²/s
- Re = (2 * 2) / (1 x 10-6) = 4,000,000
Conclusion
- The calculated boundary layer thickness of 1.76 mm indicates the region where viscous effects are significant.
- Understanding this concept is vital for applications in aerodynamics and hydrodynamics, influencing drag and heat transfer characteristics.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Similar UPSC Doubts
Top Courses for UPSCView all
A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]?
Question Description
A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]?.
A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]?.
Solutions for A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? defined & explained in the simplest way possible. Besides giving the explanation of
A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]?, a detailed solution for A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? has been provided alongside types of A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? theory, EduRev gives you an
ample number of questions to practice A smooth flat plate 2 m wide and 2 m long is subjected to flow of water along its length at a uniform velocity of 2 m/s. The thickness of boundary layer at the edge of laminar boundary layer will be 1.76 mm. [p = 898 kg/m³, v = 1 x 10-6 m²/s]? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup