2.7. Stream Function

Try these first

1. 1.

   What is the definition of a stream function?

   Hint

   Think about how it relates to flow rates.

2. 2.

   Write the formulas for u and v in terms of the stream function.

   Hint

   One is derived from the y direction, while the other is negative from x.

3. 3.

   What does a stream function represent?

   • It represents pressure.
   • It represents temperature.
   • It represents flow rates across streamlines.

   Hint

   Remember how it maintains consistency in flow across lines.

4. 4.

   In what flow condition is the vorticity zero?

   • True
   • False

   Hint

   Consider what constitutes a rotational flow.

5. 5.

   Consider a velocity potential function φ(x, y) = 2xy + x^2 - 3y^2. Derive the stream function ψ and evaluate it across streamlines defined by y=1, y=2.

   Hint

   Utilize partial derivatives properly.

6. 6.

   Analyze a scenario where a stream function yields divergent velocities in a rectangular domain. Describe how the flow patterns emerge.

   Hint

   List multiple responses regarding velocity behavior dependent on boundary conditions.