KEVOS® MAKEOS · Strength
Centrifuge Bowl Check (Self Hoop Stress, Liquid Ring Pressure, Total Hoop Stress, Speed Limit)
For a spinning centrifuge bowl or basket holding a ring of liquid, how high is the hoop stress from its own spin and from the liquid pressure, and how fast may it run?
Check of a thin cylindrical centrifuge bowl: the acceleration at the wall as a multiple of gravity (as the centrifugal force tool), the hoop stress from the spinning shell itself (density × rim speed squared), the pressure the spinning liquid ring puts on the wall, the hoop stress from that pressure (as the thick cylinder tool’s thin-wall value), the total hoop stress, and the highest speed for your allowable stress, since every stress grows with the square of the speed.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Bowl inside radius | mm | Inside radius of the bowl wall. |
| Wall thickness | mm | Wall thickness of the bowl. |
| Speed | rpm | Running speed. |
| Bowl material density | kg/m³ | Density of the bowl material. |
| Liquid density | kg/m³ | Density of the liquid or slurry. |
| Radius of the liquid surface | mm | Radius of the free liquid surface (the liquid fills the ring from here to the wall; equal to the wall radius when empty). |
| Allowable hoop stress | MPa | Allowable hoop stress for the bowl material, joints and duty. |
Method and formulas
- ω = 2π n ÷ 60; g-level = ω² r ÷ g (as the centrifugal force tool).
- Shell self stress = ρ_s v² at the mean wall radius; liquid pressure at the wall p = ρ_l ω² (r² − r₀²) ÷ 2.
- Liquid hoop stress = p (D + t) ÷ 2t (the thin-wall value of the thick cylinder tool); speed limit = n √(allowable ÷ total).
- Example: 1,118.2 g at the wall; 22.041 + 36.993 = 59.034 MPa; the limit is 2,603 rpm.
Limitations
- Thin plain cylinder; perforations in a basket raise the stress and the bowl ends, hubs and joints need their own checks.
- Liquid ring only; solids cake in a basket add pressure as a denser ring.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check a centrifuge bowl before raising the speed
- Size the wall of a spinning drum
- Find the safe speed limit for a bowl
Who it is for
- Design engineers
- Process engineers
- Safety engineers
What you get
- Wall acceleration as g
- Hoop stress from the shell and from the liquid
- Total stress and speed limit
Interpreting the result
- Every stress in a spinning bowl rises with the square of the speed: 10% more speed means 21% more stress.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 187–190, 290–294. Topic reference; no source tables or recommended settings are reproduced.
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