Freestream Velocity Given Radial Velocity Calculator

Formula Used:

\[ V_{\infty} = \frac{\mu}{2\pi r^3} - \frac{V_r}{\cos(\theta)} \]

Doublet Strength (μ):

m³/s

Radial Coordinate (r):

Radial Velocity (Vr):

m/s

Polar Angle (θ):

rad

Freestream Velocity (V∞):

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1. What is Freestream Velocity?

Freestream Velocity is the velocity of air far upstream of an aerodynamic body, that is before the body has a chance to deflect, slow down or compress the air. It represents the undisturbed flow velocity in fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ V_{\infty} = \frac{\mu}{2\pi r^3} - \frac{V_r}{\cos(\theta)} \]

Where:

\( V_{\infty} \) — Freestream Velocity (m/s)
\( \mu \) — Doublet Strength (m³/s)
\( r \) — Radial Coordinate (m)
\( V_r \) — Radial Velocity (m/s)
\( \theta \) — Polar Angle (rad)

Explanation: This formula calculates the freestream velocity based on doublet strength, radial coordinate, radial velocity, and polar angle in a flow field.

3. Importance of Freestream Velocity Calculation

Details: Calculating freestream velocity is crucial in aerodynamics and fluid dynamics for analyzing flow patterns around objects, designing aerodynamic surfaces, and understanding potential flow theory applications.

4. Using the Calculator

Tips: Enter doublet strength in m³/s, radial coordinate in meters, radial velocity in m/s, and polar angle in radians. Ensure radial coordinate > 0 and polar angle is within valid range (-π/2 < θ < π/2).

5. Frequently Asked Questions (FAQ)

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

Q2: Why is the polar angle important in this calculation?
A: The polar angle determines the direction component of the radial velocity relative to the freestream direction, affecting the velocity decomposition.

Q3: What are typical values for doublet strength?
A: Doublet strength values vary widely depending on the specific flow configuration, but are typically positive values measured in cubic meters per second.

Q4: When is this formula applicable?
A: This formula is derived from potential flow theory and is applicable for incompressible, irrotational flow around doublet configurations.

Q5: What are the limitations of this calculation?
A: This calculation assumes ideal potential flow conditions and may not account for viscous effects, compressibility, or real fluid behavior in practical applications.