10.4.1. Approximate Solutions for Navier-Stokes

Try these first

1. 1.

   Define the Navier-Stokes equations and their importance.

   Hint

   What kind of fluids do these equations describe?

2. 2.

   What is meant by irrotational flow?

   Hint

   Think about the flow patterns in an ideal fluid.

3. 3.

   What does the Navier-Stokes equation describe?

   • Solid motion
   • Fluid mechanics
   • Gas pressure

   Hint

   Consider the type of behavior that fluids exhibit.

4. 4.

   Is irrotational flow used only in ideal fluid scenarios?

   • True
   • False

   Hint

   Think about how friction influences flow.

5. 5.

   You have a cylindrical tank with water. Derive the velocity profiles and pressure distributions present when fluid is allowed to flow from a height under gravity.

   Hint

   Consider gravity while integrating Bernoulli's equation.

6. 6.

   In a pipe flow scenario, derive velocity distributions and shear stresses as fluid passes through a varying cross-section.

   Hint

   Think about how conservation of mass applies here.