11.1.3. Stream Function and Vorticity Analysis

Try these first

1. 1.

   What does the stream function represent in fluid flow?

   Hint

   Think about how fluid flows along curves.

2. 2.

   Define vorticity in the context of fluid dynamics.

   Hint

   Consider rotation around a point in fluid.

3. 3.

   What does a stream function indicate in fluid motion?

   • Represent velocity directly
   • Shows flow patterns
   • Calculates pressure gradient

   Hint

   Consider the role of streamlines.

4. 4.

   Vorticity is a measure of what?

   • True
   • False

   Hint

   Think of rotation in fluids.

5. 5.

   A water flow between two parallel plates has the velocity described by u = h^2/(2μ)(1 - (y^2/h^2)). Calculate the wall shear stress at y = h.

   Hint

   Consider the relationship to the viscosity and velocity gradient.

6. 6.

   If the vorticity is not zero in a flow field, can you find the velocity potential function? Justify your answer.

   Hint

   Reflect on irrotational flow characteristics.