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Pharma Engineering > Dimensionless Anaylsis > Flashcards

Dimensionless Anaylsis Flashcards

1
Q

What are dimensions (give examples)

A

these are qualitative description (L, M, T)

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2
Q

What are (physical) quantities?

A

quantitative description (numerical value and measuring unit

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3
Q

What kind of quantities do we know?

A

primary and scondary quantities

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4
Q

When is a process consider as completely similar?

A

similar geometrical space and if all the dimensionless numbers have the same numerical value

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5
Q

what types of similarities do we have?

A

geometric, kinematic and dynamic

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6
Q

what is a geometric similarity?

A

similarity of shape, ratio of all corresponding linear dimensions in model and prototype are equal

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7
Q

kinematic similarity

A

similarity of motion,

ratio of velocities

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8
Q

dynamic similarity

A

similarity of forces, ratio of forces

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9
Q

which type of model do we have?

A

true and distored models

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10
Q

difference between the true and distored models?

A

true models have the same scale ratios in very direction, while distorted model have different scales in different directions used

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11
Q

example of primary quantities

A

lengt, mass, time, thermodynamic temperature
amount of substance
electric current
luminous intensity

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12
Q

give the base dimenion and the SI base unit of lengt, mass, time,

A

length: BD =L, SI =m
mass: BD=M, SI=kg
time: BD=T, SI=s

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13
Q

give the base dimenion and the SI base unit of thermodynamic temperature
amount of substance

A

thermodynamic temperature: BD: SI =K

amount of substance: BD=N, SI=mol

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14
Q

give the base dimenion and the SI base unit of electric current
luminous intensity

A

electric current: BD: I SI =A

luminous intensity: BD=J, SI=cd

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15
Q

secondary quantities, exsamples

know the unit and dimensions

A

force, pressure, energy and power

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16
Q

what is the fundamental principle of the dimensional analysis

A

a validity should be obtain, by obtaining a dimensionally homogenous systems of dimensions

17
Q

Name three advantages of the DA?

A
  1. consideration of that parameters that are really needed, it lowers the
    experimental workload
  2. compression of the statement
  3. guarantee of a secure scaling (up and down)
18
Q

Issues with the DA?

A
  1. all (important) parameters considered? –> There is no way to prove whether or
    not all the variables have been included
  2. Gross errors in the final dimensionless numbers result either when extraneous
    variables are included or when important variables are omitted.
19
Q

What are basic dimension?

A

this are independent dimension which caanot be formed from a combination of other dimensions

20
Q

which principle is used in Da?

A

Buckingham-Pi Theorem

21
Q

What is Buckingham-Pi Theorem ?

A

it is the number of variables in a problem minus the number of reference dimension (BD)

22
Q

What are reference dimension?

A

dimensions used to describe all the influence variables

23
Q

what is the method of repeating variables?

A

used to obtain the PI-terms, whereby the B-PI is just for the number of PI we need.

24
Q

What does the PI-theorem tells us?

A

just the number of dimensionless numbers and not the form

25
Q

How can we obtain the form?

A

form is specified by the user, experiments

26
Q

what do you have to do before determining the numbers of Pi-terms

A
  1. List all the independent variables involved in the problem
  2. Each variable in terms of basic dimensions
27
Q

How do you determine the number of PI-terms

A

using the Buckingham-PI Theorem

28
Q

How do you select the repeating variables?

A
  1. do not include the dependent variables
  2. all reference dimensions must be represented in the repeating parameters
  3. each must be dimensionally independent
    (cannot be combined to form one, cannnot form dimensionless numbers)
29
Q

what should the number of repeating variables be?

A

number of repeating is equal to the number of reference dimensions

30
Q

How do we get the non repeating variables dimensionless numbers?

A

We used the repeating variables to make the nonrepeating variables

31
Q

equation to determine the number of PI-terms

A

PI-terms=n(vairaibles)-r (repeating variables)

32
Q

How do you form the PI-terms?

A

by taking each of the non repeating varibales and multiplying by the repeatings variables

33
Q

Focus now on examples

A

Do you know the BU-PI-Theorem now?

Pharma Engineering (8 decks)

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