Q.85. A continuous bacterial culture carried out in a chemostat is set to a flow rate of 𝟒𝟎𝐦𝐥/𝐡𝐫. The culture volume is equivalent to that of a cubical container having 10 cm sides. The dilution rate (in 𝐡𝐫−𝟏, rounded off to two decimal places) of this system is ____ .
The dilution rate (D) in a chemostat is calculated as the
flow rate divided by the culture volume.
For this setup, the dilution rate is:
0.04 hr−1.
Key Concepts
A chemostat maintains bacterial growth at steady state by balancing
the inflow of fresh medium and the outflow of culture.
At steady state:
D = μ
where D is the dilution rate and μ is the specific growth rate,
provided that D < μmax (maximum growth rate).
The dilution rate is defined as:
D = F / V
where:
- F = flow rate (volume per unit time)
- V = culture volume
Step-by-Step Calculation
1. Calculate Culture Volume
The culture vessel is a cube with side length 10 cm.
V = 10 × 10 × 10 = 1000 cm3
Since:
1 cm3 = 1 mL
V = 1000 mL = 1 L
2. Convert Flow Rate
Flow rate:
F = 40 mL/hr = 0.040 L/hr
3. Calculate Dilution Rate
D = F / V
D = 40 mL/hr ÷ 1000 mL = 0.04 hr−1
Rounded to two decimal places:
D = 0.04 hr−1
Final Answer
The dilution rate of the chemostat is 0.04 hr−1.
Why This Formula Is Correct
The formula D = F / V directly represents the fraction of culture
volume replaced per hour.
Using consistent units (mL or L) is essential to avoid errors.
Common Mistakes
- Unit mismatch: Forgetting that 1 cm3 = 1 mL.
- Decimal error: Writing 0.40 instead of 0.04.
- Confusing residence time:
Residence time = 1 / D, not D itself.
Applications in Bioprocess Engineering
Dilution rate is a critical design parameter in
continuous fermentation, wastewater treatment,
and industrial bioreactors.
Accurate calculation ensures stable operation without washout.
