1. What is Stream Function for Uniform Incompressible Flow?

The Stream Function for Uniform Incompressible Flow represents the quantity of fluid moving across an imaginary line in a uniform flow field. It is a fundamental concept in fluid dynamics that helps visualize and analyze flow patterns.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( \psi \) — Stream Function (m²/s)
• \( V_{\infty} \) — Freestream Velocity (m/s)
• \( y \) — Distance on Y-Axis (m)

Explanation: The stream function is calculated by multiplying the freestream velocity by the distance measured along the y-axis from the origin.

3. Importance of Stream Function Calculation

Details: The stream function is crucial for analyzing fluid flow patterns, determining flow rates, and solving problems in potential flow theory. It helps in visualizing streamlines and understanding flow behavior around objects.

4. Using the Calculator

Tips: Enter the freestream velocity in m/s and the distance on y-axis in meters. Both values must be positive numbers greater than zero.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of stream function?
A: The stream function represents the volume flow rate between streamlines and helps in visualizing fluid flow patterns without solving complex equations.

Q2: Can this formula be used for compressible flow?
A: No, this specific formula is derived for uniform incompressible flow where density remains constant.

Q3: What are typical values for stream function?
A: Stream function values depend on the specific flow conditions and can range from very small to large values based on velocity and distance scales.

Q4: How does stream function relate to velocity components?
A: For 2D flow, the velocity components can be derived from the stream function as u = ∂ψ/∂y and v = -∂ψ/∂x.

Q5: What are the limitations of this formula?
A: This formula applies only to uniform, incompressible flow and doesn't account for viscosity, turbulence, or three-dimensional effects.