Stream Function For Semi-Infinite Body Calculator

Stream Function Formula:

\[ \psi = V_{\infty} \times r \times \sin(\theta) + \frac{\Lambda}{2\pi} \times \theta \]

Freestream Velocity (V∞):

m/s

Radial Coordinate (r):

Polar Angle (θ):

rad

Source Strength (Λ):

m²/s

Stream Function (ψ):

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Stream Function for Semi-Infinite Body?

The Stream Function for a semi-infinite body represents the flow pattern around a body that extends infinitely in one direction. It combines freestream flow with a source to model fluid behavior around such bodies in potential flow theory.

2. How Does the Calculator Work?

The calculator uses the Stream Function formula:

\[ \psi = V_{\infty} \times r \times \sin(\theta) + \frac{\Lambda}{2\pi} \times \theta \]

Where:

\( \psi \) — Stream Function (m²/s)
\( V_{\infty} \) — Freestream Velocity (m/s)
\( r \) — Radial Coordinate (m)
\( \theta \) — Polar Angle (rad)
\( \Lambda \) — Source Strength (m²/s)
\( \pi \) — Mathematical constant pi (approximately 3.14159)
\( \sin \) — Trigonometric sine function

Explanation: The equation combines the freestream flow component with the source flow component to determine the complete stream function for the flow field.

3. Importance of Stream Function Calculation

Details: Stream function calculations are essential in fluid dynamics for analyzing potential flow patterns, determining streamlines, and understanding flow behavior around various body shapes in aerodynamics and hydrodynamics.

4. Using the Calculator

Tips: Enter freestream velocity in m/s, radial coordinate in meters, polar angle in radians, and source strength in m²/s. All values must be positive and valid.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of stream function?
A: Stream function represents the flow rate between streamlines. Constant stream function values define streamlines, and the difference between stream functions gives the flow rate between those streamlines.

Q2: When is this semi-infinite body model applicable?
A: This model is used in potential flow theory to approximate flow around bodies that are long compared to their cross-sectional dimensions, such as airfoils or slender bodies.

Q3: What are the limitations of this model?
A: This model assumes inviscid, incompressible, irrotational flow and may not accurately represent real fluid behavior with viscosity effects, separation, or compressibility.

Q4: How does source strength affect the flow field?

A: Source strength determines the magnitude of fluid emanating from the source point. Higher source strength creates stronger radial outflow from the source location.

Q5: Can this calculator be used for three-dimensional flows?
A: No, this specific stream function formulation is for two-dimensional potential flow. Three-dimensional flows require different mathematical approaches.