Reference ID: MET-C76F | Process Engineering Reference Sheets Calculation Guide
Introduction & Context
Centrifugal acceleration—expressed as a multiple of gravitational acceleration g—is the key scaling parameter that determines phase-separation performance in rotating equipment. In process engineering it governs:
Solid–liquid separation in decanter and screen-bowl centrifuges
Liquid–liquid extraction in podbielniak and disc-stack centrifuges
Cell harvesting and inclusion-body recovery in bioprocess trains
De-sanding and de-watering of produced water in upstream oil & gas
The dimensionless “RCF” (Relative Centrifugal Force) quantifies how much stronger the radial acceleration is compared with gravity; matching an RCF specification to a physical bowl geometry therefore fixes the required shaft speed. The calculation below converts a target RCF into the corresponding rotational speed in revolutions per minute (rpm) for any given bowl diameter, and you can also explore how this principle applies to grinding media in our ball mill critical speed guide.
🚀 Skip the Manual Math!
Use our interactive Centrifugal Acceleration (G-Force) Calculation to compute these parameters instantly online, or download the offline Excel calculation.
Convert practical geometry to SI units
Bowl diameter D is usually quoted in centimetres; the effective radius is
\[ r = \frac{D}{200} \quad [\text{m}] \]
Relate RCF to angular velocity
By definition
\[ \text{RCF} = \frac{a_{\text{centrifugal}}}{g} = \frac{r\,\omega^{2}}{g} \]
Solving for angular velocity gives
\[ \omega = \sqrt{\frac{\text{RCF} \cdot g}{r}} \quad [\text{rad s}^{-1}] \]
Convert angular velocity to rpm
\[ N = \frac{60\,\omega}{2\pi} \quad [\text{rpm}] \]
Variable
Description
SI Unit
RCF
Relative Centrifugal Force (dimensionless)
—
g
Gravitational acceleration
m s-2
r
Bowl inside radius
m
\(\omega\)
Angular velocity
rad s-1
N
Rotational speed
rpm
The Python snippet implements the above sequence and includes a guard against non-positive radius or RCF values. Replace the hard-coded inputs with live data to obtain the required shaft speed for any centrifuge geometry and target RCF.
Use the formula G = 1.118 × 10⁻⁵ × R × N² where R is the bowl radius in mm and N is the rotational speed in RPM.
Measure the inside radius from the axis of rotation to the inner wall.
Plug the values into the equation; the constant 1.118 × 10⁻⁵ already accounts for unit conversion.
Round the result to two significant figures for plant reporting.
Use the pool surface radius (air–liquid interface) for settling calculations and the inner bowl radius for structural checks.
Pool surface radius determines the effective G-force on settling particles.
Inner bowl radius gives the maximum stress on the shell.
Always state which radius was used in your calculation note.
Maintain constant sigma factor (Σ) rather than constant G-force.
Match pilot Σ to full-scale Σ to keep separation performance.
If bowl geometry differs, adjust RPM so the new Σ equals the pilot value.
Limit continuous operation to 80% of the manufacturer’s maximum G-force rating.
Reserve the remaining 20% for start-up transients and minor speed overshoots.
Document the margin in the safety case file.
Re-verify if bowl wall thickness is reduced by corrosion or polishing.
Worked Example – Sizing a Lab-Scale Centrifuge Bowl
A pilot-plant engineer needs to spin a 12 cm diameter bowl at a Relative Centrifugal Field (RCF) of 10,000 g to clarify a recombinant protein broth. Determine the required rotational speed in revolutions per minute (rpm).
Knowns
Bowl diameter = 12.0 cm
Target RCF = 10,000 g
Standard gravity, g = 9.807 m s⁻²
Step-by-Step Calculation
Convert bowl diameter to radius:
\( r = \frac{12.0\ \text{cm}}{2} = 6.0\ \text{cm} = 0.060\ \text{m} \)
Use the RCF definition:
\[ \text{RCF} = \frac{r\omega^{2}}{g} \]
