2.2. Continuity Equation in Differential Form

Try these first

1. 1.

   Define the continuity equation in terms of fluid flow.

   Hint

   Think about mass conservation.

2. 2.

   What is incompressible flow?

   Hint

   Consider fluids like water.

3. 3.

   What does the continuity equation represent?

   • Mass conservation
   • Energy conservation
   • Momentum conservation

   Hint

   Remember the principle of mass in closed systems.

4. 4.

   True or False: Incompressible flow means the density changes with the flow.

   • True
   • False

   Hint

   Think about common fluids like water.

5. 5.

   A tank has a rectangular base with dimensions 4 m x 3 m and a height of 5 m. Water flows through a pipe from this tank at a rate of 0.5 m³/s. If the pipe diameter changes from 10 cm to 5 cm, calculate the velocity at both sections and discuss how the continuity equation is used.

   Hint

   Use A = πr² for cross-sectional area calculations.

6. 6.

   Design a scenario involving a pipe network used in a municipal water system where the continuity equation needs to be applied to determine pressures and flow rates. Explain your design.

   Hint

   Focus on where water enters and exits different pipe sizes.