2.1. Determine the Equation of the Streamline

Try these first

1. 1.

   Define uniform flow in your own words.

   Hint

   Think about how it relates to space.

2. 2.

   What is a streamline?

   Hint

   Consider how fluids flow along lines.

3. 3.

   What defines uniform flow?

   • Fluid properties change with time
   • Fluid properties are constant in space
   • Fluid properties are only variable along a streamline

   Hint

   Think of flows you can observe.

4. 4.

   True or False: A streamline can intersect itself.

   • True
   • False

   Hint

   Consider the basic definition of streamlines.

5. 5.

   Given a velocity field defined by u=5x, v=-2y, w=3z, derive the equations of the streamlines passing through the point (2,1,3).

   Hint

   Start with separating the variables and integrating each part.

6. 6.

   Evaluate how changes in terrain affect non-uniform flow near a riverbank. Discuss what parameters would vary.

   Hint

   Consider physical effects of terrain on flow characteristics.