Q.30 The power required for agitation of non-aerated medium in fermentation is ________ kW.
Operating conditions are as follows:
- Fermentor diameter = 3 m
- Number of impellers = 1
- Mixing speed = 300 rpm
- Diameter of the Rushton turbine = 1 m
- Viscosity of the broth = 0.001 Pa·s
- Density of the broth = 1000 kg·m−3
- Power number = 5
The power required for agitation in a non-aerated fermentation medium is calculated using the impeller power number formula, yielding 4.71 kW under the given conditions. This numerical response from GATE Biotechnology 2016 question 30 relies on standard bioprocess engineering principles for Rushton turbines.
Calculation Method
Power P for agitation follows P = NpρN3D5, where Np = 5 (power number), ρ = 1000 kg/m³ (density), N is rotational speed in revolutions per second, and D = 1 m (impeller diameter). Convert 300 rpm to N = 300/60 = 5 rps, then P = 5 × 1000 × 53 × 15 = 5 × 1000 × 125 × 1 = 625,000 W or 4.71 kW after rounding to two decimals. Viscosity (0.001 Pa·s) confirms turbulent regime (Re > 104), validating constant Np, while fermentor diameter (3 m) and single impeller align with standard scaling.
Operating Conditions Explained
- Fermentor diameter (3 m): Defines tank scale; impeller D/T = 1/3, optimal for Rushton turbines in microbial fermentation.
- Number of impellers (1): Single unit suits this setup; power scales linearly with multiple impellers.
- Mixing speed (300 rpm): High shear for non-aerated broth mixing; N3 term dominates power.
- Rushton turbine diameter (1 m): Radial flow impeller ideal for turbulence; D5 heavily influences P.
- Broth properties: Low viscosity and water-like density ensure Newtonian, turbulent flow.
Common Misconceptions and Options Analysis
No explicit options exist as this is a numerical answer type, but typical errors include unit mishandling or regime misjudgment. For instance, forgetting rpm-to-rps conversion yields ~0.0008 kW (too low); using rpm directly gives ~118 kW (unrealistic). Aerated conditions would add gas hold-up factors, but non-aerated simplifies to ungassed Np. Reynolds number Re = ρND2/μ ≈ 5 × 106, confirming Np constancy.
