Stirred Tank Energy Input per Unit Mass (E)
Results
Impeller Reynolds Number (Rei):
Flow Regime:
Power Number (Po):
Unaerated Power Input (P): W
Gassed Power Input (PG): W
Energy Input per Unit Mass (E): W/kg
Note: Power calculations (P, PG, E) are typically complex in the transitional regime and require specific correlations not included here.
Note: Laminar flow calculation (Po = c·Rei-1) is only implemented for Disc Turbine (c=100) and Propeller (c=40). Results for other impellers in laminar flow may not be accurate.
Calculation Explanation
This calculator determines the energy input per unit mass (E) for stirred tanks based on operating conditions and impeller type. It first calculates the impeller Reynolds number (Rei) to identify the flow regime.
1. Impeller Reynolds Number (Rei):
Rei = (ρL ⋅ N ⋅ di²) / μL
Where:
- ρL: Liquid Density (kg/m³)
- N: Impeller Speed (rev/s)
- di: Impeller Diameter (m)
- μL: Liquid Viscosity (Pa·s)
2. Flow Regime & Power Number (Po):
- Laminar Flow (Rei < 10): Po = c ⋅ Rei-1
(c ≈ 100 for six-bladed disc turbine, c ≈ 40 for propeller. Specific values for other impellers may vary.)
- Transitional Flow (10 ≤ Rei ≤ 104): Po varies complexly. Standard correlations often not applicable.
- Turbulent Flow (Rei > 104): Po is approximately constant, depending on impeller geometry:
- Propeller: Po ≈ 0.32
- Two-bladed Paddle: Po ≈ 1.70
- Six-bladed Disc Turbine: Po ≈ 6.30
- Five-bladed Prochem®: Po ≈ 1.0
3. Unaerated Power Input (P):
P = Po ⋅ ρ
L ⋅ N³ ⋅ d
i⁵ (Units: W)
(Calculated only for Laminar and Turbulent regimes where Po is defined here.)
4. Gassed Power Input (PG):
If aeration rate Q > 0:
P
G = 0.72 ⋅ [ (P² ⋅ N ⋅ d
i³) / Q
0.56 ]
0.45 (Units: W)
If Q = 0, P
G = P.
Where Q is the Volumetric Aeration Rate (m³/s).
(Calculated only if P is calculated.)
5. Energy Input per Unit Mass (E):
E = P
G / (ρ
L ⋅ V
L) (Units: W/kg)
Where V
L is the Liquid Volume (m³).
(Calculated only if P
G is calculated.)