dimensional analysis

Question 1

define dimension

Answer 1

a measure of a physical quantity (without numerical values)

Question 2

define unit

Answer 2

quantifying a dimension

Question 3

define dimensional homogenity

Answer 3

every additive term in an equation must have the same dimensions

Question 4

what is buckinghams working rule?

Answer 4

if there are n variables in a problem, and the variables contain m primary dimensions, then then the equation relating all the variables will have n-m groups

Question 5

true or false: independent variable = cause, dependent variable = effect

Answer 5

true

Question 6

when choosing repeating variables, what must be considered?

Answer 6

• no repeating variables can be dimensionless
• no two repeating variables should have the same dimensions
• cannot pick a dependent variable as a repeating variable
• avoid obscure variables as repeating variables appear in all dimensionless groups

Question 7

define geometric similarity

Answer 7

model must be same shape as prototype, but may be scaled by some constant scale factor

Question 8

define kinematic similarity

Answer 8

velocity at any point in the model must be scaled by a constant scale factor to the velocity at the corresponding point in the prototype

Question 9

define dynamic similarity

Answer 9

all forces in model scaled by constant scale factor to corresponding forces in prototype (force-scale equivalence)

Question 10

how can we ensure complete similarity between a model and prototype?

Answer 10

each pi group in the model must equal each pi group in the prototype