13.1.6. Principle of Homogeneity

Try these first

1. 1.

   Define dimensional homogeneity.

   Hint

   Consider what it means for things to be 'the same' across an equation.

2. 2.

   What is the dimensional formula for velocity?

   Hint

   Think of how velocity is calculated.

3. 3.

   What is dimensional homogeneity?

   • A concept where equations match in dimensions
   • An experimental design method
   • None of the above

   Hint

   Think about the fundamental idea behind dimensional analysis.

4. 4.

   True or False: Reynolds number is used to specify units in fluid dynamics.

   • True
   • False

   Hint

   Consider what dimensionless means.

5. 5.

   Verify if the equation P = ρgh is dimensionally homogeneous, where P is pressure, ρ is density, g is acceleration due to gravity, and h is height.

   Hint

   Break down each term into its fundamental dimensions.

6. 6.

   Analyze how the introduction of a new variable in a fluid dynamics equation would affect its dimensional homogeneity.

   Hint

   Consider the dimensions of the new variable.