Doublet Strength Given Tangential Velocity Calculator

Doublet Strength Formula:

\[ \mu = 4 \pi r^3 \left( \frac{V_\theta}{\sin \theta} - V_\infty \right) \]

Radial Coordinate (r):

Tangential Velocity (Vθ):

m/s

Polar Angle (θ):

rad

Freestream Velocity (V∞):

m/s

Doublet Strength (μ):

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1. What is Doublet Strength?

Doublet Strength (μ) is defined as the product of the distance between a source-sink pair and source or sink strength in potential flow theory. It represents the strength of a doublet in fluid dynamics, which is a combination of a source and sink of equal strength placed infinitesimally close together.

2. How Does the Calculator Work?

The calculator uses the Doublet Strength formula:

\[ \mu = 4 \pi r^3 \left( \frac{V_\theta}{\sin \theta} - V_\infty \right) \]

Where:

\( \mu \) — Doublet Strength (m³/s)
\( r \) — Radial Coordinate (m)
\( V_\theta \) — Tangential Velocity (m/s)
\( \theta \) — Polar Angle (rad)
\( V_\infty \) — Freestream Velocity (m/s)
\( \pi \) — Archimedes' constant (≈3.14159)

Explanation: The formula calculates the doublet strength based on the radial coordinate, tangential velocity component, polar angle, and freestream velocity in potential flow theory.

3. Importance of Doublet Strength Calculation

Details: Doublet strength is crucial in aerodynamics and hydrodynamics for modeling flow around bodies. It helps in analyzing potential flow patterns and understanding the behavior of fluid flow around obstacles.

4. Using the Calculator

Tips: Enter radial coordinate in meters, tangential velocity in m/s, polar angle in radians (0 to π), and freestream velocity in m/s. All values must be valid (r > 0, 0 < θ < π).

5. Frequently Asked Questions (FAQ)

Q1: What is a doublet in fluid dynamics?
A: A doublet is a combination of a source and sink of equal strength placed infinitesimally close together, used to model flow around bodies in potential flow theory.

Q2: What are typical units for doublet strength?
A: Doublet strength is typically measured in cubic meters per second (m³/s).

Q3: When is this formula applicable?
A: This formula is applicable in potential flow theory for incompressible, inviscid flow around axisymmetric bodies.

Q4: What is the physical significance of doublet strength?
A: Doublet strength determines the intensity of the flow disturbance created by the doublet and influences the resulting flow field pattern.

Q5: Can this be used for compressible flow?
A: This specific formula is derived for incompressible flow. For compressible flow, additional factors and modifications would be needed.