SME
Material & Energy Balances · Problem type
Degrees of freedom of a unit
Use this for “A splitter has 5 unknowns, 2 balances, 2 specified values and 1 split relation. Can it be solved?”
Diagram
This is an example. Type your own values to start a new problem.
DOF
=
Nᵤ
−
Nb
−
Nₛ
−
Nᵣ
Formulas
DOF = Nᵤ − Nb − Nₛ − Nᵣ
0 = 5 − 2 − 2 − 1
Assumptions
•
The picture is one example, a splitter on a 100 kg/h basis with five lit unknowns; type the counts of your own.
•
In it, two components give two balances, the feed fraction and one outlet flow are specified, and one split relation gives an outlet the feed’s composition.
•
Count a value the problem gives one way, not both: written on the chart (not counted), or as an unknown and a specified value.
•
DOF > 0 needs more information; DOF < 0 is over-specified or inconsistent.
Step-by-step
WE KNOW
Nᵤ = 5, Nb = 2, Nₛ = 2, Nᵣ = 1
FIND
degrees of freedom (DOF)
Step 1 · Find degrees of freedom (DOF)
Use DOF = Nᵤ − Nb − Nₛ − Nᵣ
Each equation or specified value pins one unknown; what is left is free.
DOF = 5 − 2 − 2 − 1
DOF = 0
Check
Put the numbers back in. Both sides should match.
0 = 5 − 2 − 2 − 1 ✓
Topic check
See what you know: 5 questions on this topic
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