8.2.1. Assumptions in fluid equations

Try these first

1. 1.

   What is the assumption of incompressibility in fluid mechanics?

   Hint

   Consider how density is treated in mass conservation.

2. 2.

   Define a Newtonian fluid.

   Hint

   Think about how viscosity behaves in these fluids.

3. 3.

   What does the assumption of incompressibility imply for fluid density?

   • Density varies significantly
   • Density remains constant
   • Density decreases with velocity

   Hint

   Consider the effects on mass conservation.

4. 4.

   Is a Newtonian fluid characterized by a non-linear relationship between shear stress and velocity gradient?

   • True
   • False

   Hint

   Think of how viscosity behaves in linear terms.

5. 5.

   In a scenario where a fluid flow transition from laminar to turbulent occurs, how would the assumptions regarding incompressibility, Newtonian fluid, and isothermal conditions be affected? Discuss quantitatively.

   Hint

   Think about the dynamics of flow and how they transition.

6. 6.

   Analyze a case study where temperature fluctuations affect the viscosity of a fluid in a heating pipe system. Discuss the necessity of assuming isothermal conditions.

   Hint

   Consider real industrial applications where temperature control is key.