Dimensionless Anaylsis Flashcards
What are dimensions (give examples)
these are qualitative description (L, M, T)
What are (physical) quantities?
quantitative description (numerical value and measuring unit
What kind of quantities do we know?
primary and scondary quantities
When is a process consider as completely similar?
similar geometrical space and if all the dimensionless numbers have the same numerical value
what types of similarities do we have?
geometric, kinematic and dynamic
what is a geometric similarity?
similarity of shape, ratio of all corresponding linear dimensions in model and prototype are equal
kinematic similarity
similarity of motion,
ratio of velocities
dynamic similarity
similarity of forces, ratio of forces
which type of model do we have?
true and distored models
difference between the true and distored models?
true models have the same scale ratios in very direction, while distorted model have different scales in different directions used
example of primary quantities
lengt, mass, time, thermodynamic temperature
amount of substance
electric current
luminous intensity
give the base dimenion and the SI base unit of lengt, mass, time,
length: BD =L, SI =m
mass: BD=M, SI=kg
time: BD=T, SI=s
give the base dimenion and the SI base unit of thermodynamic temperature
amount of substance
thermodynamic temperature: BD: SI =K
amount of substance: BD=N, SI=mol
give the base dimenion and the SI base unit of electric current
luminous intensity
electric current: BD: I SI =A
luminous intensity: BD=J, SI=cd
secondary quantities, exsamples
know the unit and dimensions
force, pressure, energy and power
what is the fundamental principle of the dimensional analysis
a validity should be obtain, by obtaining a dimensionally homogenous systems of dimensions
Name three advantages of the DA?
- consideration of that parameters that are really needed, it lowers the
experimental workload - compression of the statement
- guarantee of a secure scaling (up and down)
Issues with the DA?
- all (important) parameters considered? –> There is no way to prove whether or
not all the variables have been included - Gross errors in the final dimensionless numbers result either when extraneous
variables are included or when important variables are omitted.
What are basic dimension?
this are independent dimension which caanot be formed from a combination of other dimensions
which principle is used in Da?
Buckingham-Pi Theorem
What is Buckingham-Pi Theorem ?
it is the number of variables in a problem minus the number of reference dimension (BD)
What are reference dimension?
dimensions used to describe all the influence variables
what is the method of repeating variables?
used to obtain the PI-terms, whereby the B-PI is just for the number of PI we need.
What does the PI-theorem tells us?
just the number of dimensionless numbers and not the form
How can we obtain the form?
form is specified by the user, experiments
what do you have to do before determining the numbers of Pi-terms
- List all the independent variables involved in the problem
- Each variable in terms of basic dimensions
How do you determine the number of PI-terms
using the Buckingham-PI Theorem
How do you select the repeating variables?
- do not include the dependent variables
- all reference dimensions must be represented in the repeating parameters
- each must be dimensionally independent
(cannot be combined to form one, cannnot form dimensionless numbers)
what should the number of repeating variables be?
number of repeating is equal to the number of reference dimensions
How do we get the non repeating variables dimensionless numbers?
We used the repeating variables to make the nonrepeating variables
equation to determine the number of PI-terms
PI-terms=n(vairaibles)-r (repeating variables)
How do you form the PI-terms?
by taking each of the non repeating varibales and multiplying by the repeatings variables
Focus now on examples
Do you know the BU-PI-Theorem now?
