Dimensional/Scale/Dynamic

Question 1

Variables for dimensional analysis

Answer 1

• lengths
• velocities
• densities (and gravity)
• viscosity
• pressure (only in pipe flow)

Question 2

Dimension of viscosity

Answer 2

L2T-1

Question 3

Dimension of pressure

Answer 3

ML-1T-2

Question 4

Dimension of gravity

Answer 4

LT-2

Question 5

Important forces

Answer 5

gravity = ρg
pressure = -∇p
viscous = µ∇2u

Question 6

reynolds number

Answer 6

UL/v

Question 7

Dimensional Analysis Process

Answer 7

1. write down dependant and independent variables and their dimensions
2. choose repeating variables (not viscosity and not be able to form a dimensionless group themselves)
3. form dimensionless groups
4. write function of dimensionless groups

Question 8

Scale Analysis

Answer 8

find out some terms are unimportant and ignore them (trying to get 2 forces)

Question 9

Scale Analysis Process

Answer 9

1. choose values for velocity and length scales
2. sub into eqn (remove all + - and =s)
3. divide all terms by inertial term U2/L
4. Sub in order of magnitude estimates
5. remove insignificant terms (1000 times smaller)

Question 10

Dynamic Similarity

Answer 10

All dimensionless parameters must be equal

Question 11

Dynamic Similarity Process

Answer 11

1. get values for actual and experimental parameters
2. use dimensionless numbers to solve for unknowns
3. Calculate Re for all
4. if all the same (or all sufficiently large >10,000) they are dynamically similar

Question 12

How to make things dynamically similar

Answer 12

1. change viscosity
2. instead of scaling dimensions use similar aspect ratio