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The Surface Pressure Coefficient quantifies the local pressure variation on a cylinder's surface due to lift generation in non-lifting flow conditions. It represents the dimensionless pressure difference relative to the freestream pressure.
The calculator uses the formula:
Where:
Explanation: This formula describes the pressure distribution around a circular cylinder in potential flow theory, where the pressure coefficient varies sinusoidally with the polar angle.
Details: The surface pressure coefficient is crucial in aerodynamics and fluid mechanics for analyzing pressure distributions around bodies, predicting flow separation points, and understanding lift and drag characteristics in inviscid flow conditions.
Tips: Enter the polar angle in radians. The angle should be between 0 and 2π radians (0-360 degrees) for meaningful results in the context of circular cylinder flow.
Q1: What does a negative pressure coefficient indicate?
A: A negative pressure coefficient indicates that the local pressure is lower than the freestream pressure, which typically occurs on the upper surface of bodies where flow acceleration occurs.
Q2: How does this relate to real fluid flow?
A: This formula represents ideal potential flow theory. In real viscous flows, the actual pressure distribution may differ due to boundary layer effects and flow separation.
Q3: What is the range of possible values for Cp?
A: For non-lifting flow over a circular cylinder, the pressure coefficient ranges from +1 (stagnation point) to -3 (at θ = π/2 and 3π/2).
Q4: How is polar angle measured?
A: Polar angle is typically measured from the forward stagnation point (θ = 0) in the counterclockwise direction around the cylinder.
Q5: Can this formula be used for lifting flows?
A: No, this specific formula is for non-lifting flow. Lifting flows over circular cylinders require additional terms to account for circulation.