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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]?
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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.
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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]?
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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]?.
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