Air Flow over a Flat Plate: Velocity and Boundary Layer Thickness

Introduction:
Air flow over a flat plate is a common fluid mechanics problem that is encountered in many engineering applications. In order to understand the behavior of the flow, it is important to study the velocity and boundary layer thickness of the flow.

Velocity of the Flow:
The velocity of the flow over a flat plate can be expressed as a function of the distance from the leading edge of the plate. The velocity profile can be approximated by a power law of the form:

U = U∞(y/d)^n

Where:
• U is the velocity of the flow at a distance y from the leading edge of the plate.
• U∞ is the free stream velocity of the flow.
• d is the boundary layer thickness.
• y is the distance from the leading edge of the plate.
• n is a constant that depends on the type of flow.

Boundary Layer Thickness:
The boundary layer thickness is defined as the distance from the leading edge of the plate to the point where the velocity of the flow is 99% of the free stream velocity. This distance is denoted by the symbol d.

Boundary layer thickness can be calculated using the following formula:

d = 5x/√Re_x

Where:
• d is the boundary layer thickness
• x is the distance from the leading edge of the plate
• Re_x is the Reynolds number at x

Re_x is the ratio of inertial forces to viscous forces and can be calculated as:

Re_x = U∞x/ν

Where:
• U∞ is the free stream velocity
• x is the distance from the leading edge of the plate
• ν is the kinematic viscosity of the fluid

Conclusion:
In conclusion, the velocity and boundary layer thickness of the flow over a flat plate can be expressed as a function of the distance from the leading edge of the plate. The velocity of the flow can be approximated by a power law, while the boundary layer thickness can be calculated using the Reynolds number. These parameters are important for understanding the behavior of the flow and for designing engineering applications that involve air flow over a flat plate.

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