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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
[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
To determine the thickness of the boundary layer at the edge of a laminar flow over a flat plate, we can use the formula for the boundary layer thickness in laminar flow.
Boundary Layer Thickness Formula
The thickness of the laminar boundary layer (δ) at a distance (L) from the leading edge of a flat plate can be calculated using the formula:
δ = 5 * (ν * L / U)
Where:
- ν = kinematic viscosity (m²/s)
- L = length of the plate (m)
- U = velocity of the flow (m/s)
Given Values
- Width of the plate = 2 m (not needed for thickness calculation)
- Length of the plate, L = 2 m
- Velocity of flow, U = 2 m/s
- Kinematic viscosity, ν = 1 x 10^-6 m²/s
Calculation
1. Substitute the given values into the boundary layer thickness formula:
δ = 5 * (1 x 10^-6 m²/s * 2 m / 2 m/s)
2. Simplify the equation:
δ = 5 * (1 x 10^-6 m²/s)
3. Calculate δ:
δ = 5 x 10^-6 m
δ = 5 x 10^-6 m = 5 mm
Conclusion
The thickness of the boundary layer at the edge of the laminar boundary layer for the given flat plate is approximately 5 mm. This value indicates the region where viscous effects are significant near the surface of the plate, affecting the flow 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 [p = 898 kg/m³, v = 1 x 10-6 m²/s]?
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