Centrifuge Maximum Volumetric Throughput (Φ_v)

Calculation Explanation

This calculator estimates the maximum theoretical volumetric throughput (Φ_v) for a continuous centrifuge, often applied to tubular bowl types, assuming clarification where all particles of diameter d_p are removed. It's derived by substituting Stokes' Law for terminal settling velocity into the centrifuge capacity equation.

Equation (9.10):
Φ_v = [ π ⋅ (r_o² - r_i²) ⋅ ω² ⋅ L ] / [ g ⋅ ln(r_o / r_i) ] ⋅ [ (Δρ ⋅ d_p² ⋅ g) / (18 ⋅ η_l) ]

Where:

• Φ_v: Maximum volumetric throughput (m³/s).
• π: Mathematical constant Pi (≈ 3.14159).
• r_o: Outer radius of the bowl (m).
• r_i: Inner radius of the liquid layer (m).
• ω: Angular velocity of the bowl (rad/s).
• L: Effective length of the bowl (m).
• g: Acceleration due to gravity (≈ 9.81 m/s²).
• ln: Natural logarithm.
• Δρ: Density difference = particle density (ρ_p) - liquid density (ρ_l) (kg/m³).
• d_p: Particle diameter (m).
• η_l: Dynamic viscosity of the liquid (Pa·s or kg/(m·s)).

• Assumes laminar flow (Stokes' Law applies).
• Represents the condition for capturing 100% of particles of size d_p starting at the inner liquid radius r_i.
• Requires consistent SI units (meters, seconds, kilograms, Pascals).
• Ensure r_o > r_i > 0.
• Δρ must be positive for particles to settle outwards towards r_o.