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The formula calculates the polar angle (angular position) on a circular cylinder surface for non-lifting flow, given the surface pressure coefficient. This relationship is derived from potential flow theory and describes the pressure distribution around a circular cylinder.
The calculator uses the formula:
Where:
Explanation: The formula relates the angular position on the cylinder surface to the local pressure coefficient, which is derived from the inviscid flow solution around a circular cylinder.
Details: Calculating the polar angle from pressure coefficient is important in aerodynamics and hydrodynamics for determining flow separation points, pressure distribution analysis, and understanding the behavior of non-lifting flows around circular bodies.
Tips: Enter the surface pressure coefficient value. The value must be ≤ 1 for a real solution. The calculator returns the polar angle in degrees.
Q1: What is the valid range for surface pressure coefficient?
A: For real solutions, the surface pressure coefficient must be ≤ 1. Values greater than 1 will result in mathematical error.
Q2: What does the polar angle represent?
A: The polar angle represents the angular position measured from the stagnation point on the cylinder surface.
Q3: Is this formula valid for all flow conditions?
A: This formula is derived for ideal, non-lifting, inviscid flow over a circular cylinder and may not accurately represent real viscous flows.
Q4: Can this calculator handle negative pressure coefficients?
A: Yes, negative pressure coefficients are valid inputs as long as they are ≤ 1.
Q5: What are typical applications of this calculation?
A: This calculation is used in theoretical fluid mechanics, aerodynamics education, and preliminary analysis of flow around cylindrical structures.