Radius of Cylinder for Non-Lifting Flow Calculator

Formula Used:

\[ R = \sqrt{\frac{\kappa}{2\pi V_{\infty}}} \]

Cylinder Radius (R):

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1. What is the Cylinder Radius for Non-Lifting Flow?

The Cylinder Radius for Non-Lifting Flow is determined from the doublet strength and freestream velocity in potential flow theory. It represents the radius of a circular cylinder that would produce the same flow field as a doublet in a uniform stream.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ R = \sqrt{\frac{\kappa}{2\pi V_{\infty}}} \]

Where:

\( R \) — Cylinder Radius (m)
\( \kappa \) — Doublet Strength (m³/s)
\( V_{\infty} \) — Freestream Velocity (m/s)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula derives from potential flow theory where a doublet in a uniform stream creates a flow field identical to that around a circular cylinder.

3. Importance of Cylinder Radius Calculation

Details: Calculating the equivalent cylinder radius is essential in aerodynamics and hydrodynamics for modeling flow around cylindrical objects and understanding flow patterns in non-lifting potential flow scenarios.

4. Using the Calculator

Tips: Enter doublet strength in m³/s and freestream velocity in m/s. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is doublet strength in fluid mechanics?
A: Doublet strength is defined as the product of distance between a source-sink pair and the strength of the source or sink, representing a dipole flow field.

Q2: What does non-lifting flow mean?
A: Non-lifting flow refers to flow patterns where there is no net lift force generated on the body, typical in symmetric potential flow around objects.

Q3: When is this formula applicable?
A: This formula applies to ideal, inviscid, incompressible flow where potential flow theory is valid, typically for high Reynolds number flows.

Q4: Are there limitations to this calculation?
A: Yes, this calculation assumes ideal potential flow and doesn't account for viscous effects, flow separation, or compressibility effects.

Q5: What are typical values for doublet strength?
A: Doublet strength values depend on the specific flow configuration but are typically positive values representing the strength of the dipole flow field.