7.2.3. Vector Notations and Dimensions

Try these first

1. 1.

   What is a vector?

   Hint

   Think about how forces and velocity are represented.

2. 2.

   Define a Newtonian fluid.

   Hint

   Consider fluids like water and oil.

3. 3.

   What defines a Newtonian fluid?

   • A fluid with variable viscosity
   • A fluid with constant viscosity
   • A gas under pressure

   Hint

   Consider common examples of fluids.

4. 4.

   True or False: The divergence of a vector field measures the net flow into a control volume.

   • True
   • False

   Hint

   Visualize fluid flowing in and out of a container.

5. 5.

   Demonstrate the derivation of the Navier-Stokes equations applying both vector notations and dimensional analysis.

   Hint

   Focus on the fundamental principles of conservation of momentum and mass.

6. 6.

   Evaluate a real-world fluid flow scenario using the principles of vector notation and differentiating between fluid types.

   Hint

   Consider performing a dimensional analysis to compare behaviors.