SME
Process Dynamics & Control · Problem type
Time constant of a mixing tank
Use this for “A 2000 L stirred tank is fed 100 L/min. What is its time constant?”
Diagram
This is an example. Type your own values to start a new problem.
τ (min)
=
V (L)
÷
q (L/min)
Formulas
τ
=
V
q
20
=
2,000
100
Assumptions
•
Constant volume: the flow out equals the flow in.
•
Well mixed, so the outlet has the tank’s own composition or temperature.
•
A change in the feed reaches 63.2% of its effect at the outlet after one τ.
Step-by-step
WE KNOW
V = 2,000 L, q = 100 L/min
FIND
time constant (τ)
Step 1 · Find time constant (τ)
Use τ = V ÷ q
The
tank’s
balance
gives
τ
dc
dt
+
c
=
cᵢₙ
with
τ
=
V
q
:
the
time
the
flow
takes
to
fill
the
tank
once.
τ
=
2,000
100
τ
=
20
min
Check
Put the numbers back in. Both sides should match.
20
=
2,000
100
✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.