Dimensional and Scale Analysis

Question 1

Navier-Stokes equations objective

Answer 1

Model any flow perfectly

Question 2

Buckingham Pi Theorem

Answer 2

All terms in an equation must have the same dimensions

Question 3

Steps of dimensional analysis

Answer 3

1. Write down all the important properties and their associated dimensions
2. Choose repeating variables
3. Form dimensionless groups
4. Write the target dimensionless group as a function of the others

Question 4

Scale analysis objective

Answer 4

Reduce the number of terms in the Navier-Stokes equations using magnitudes of terms

Question 5

Criteria for dropping a term

Answer 5

1000 times smaller

Question 6

Dynamic similarity

Answer 6

If two flows have the same geometry (scale version) and the same dimensionless parameters, then they are governed by identical equations