PARTIAL: the selected-input arithmetic is valid: Qth = VdN, Q = ηvQth, selected slip is Qth − Q and Ph = ΔpQ. The normalized drawing is explicitly non-contact and does not establish a sealing nip, carried pockets, displacement geometry or historical “form 2” mapping.
PARTIAL · Selected Lobe-Pump Arithmetic
PARTIAL: calculate valid selected-input flow arithmetic beside a non-contact lobe schematic that makes no sealing or carried-pocket claim.
Equation Used
- Displacement per revolution is constant at the selected value.
- Volumetric efficiency is a valid user-supplied operating-point value.
- Selected slip is only the arithmetic difference between theoretical and delivered flow.
- Mechanical losses, inlet limitations, fluid behavior, dynamics and ratings are excluded.
The normalized twin-lobe drawing is intentionally non-contact. It does not define conjugate rotor profiles, clearances, displacement chambers, timing or a particular manufacturer's wet-end geometry.
Selected positive-displacement model
Displacement per revolution and shaft speed set ideal volumetric throughput. A user-supplied operating-point efficiency partitions that throughput into selected delivered flow and slip.
The twin-lobe animation is illustrative. It does not define actual displacement chambers, rotor timing, clearances, ports, seals or inlet conditions for a specific pump.
What the calculator determines
Select displacement, speed, volumetric efficiency and pressure rise. The calculator returns theoretical flow, selected delivered flow, the arithmetic difference labeled slip and hydraulic output.
The inputs are not ratings. Verify manufacturer pump curves, viscosity and temperature corrections, inlet requirements, speed and pressure limits, relief protection, driver capacity and cleaning requirements for the actual equipment.
Bounded selected-input identities
Qth = VdN. Q = ηvQth. Qslip = Qth − Q. Ph = ΔpQ. With flow in L/min and pressure in bar, Ph = QΔp/600 kW.
The equations do not predict ηv from pressure, viscosity, clearance or speed and do not calculate shaft input power.
Selected-input example
For 100 cc/rev, 300 rpm and 90% selected volumetric efficiency, theoretical flow is 30.0 L/min, delivered flow is 27.0 L/min and the arithmetic slip difference is 3.0 L/min. At 10 bar pressure rise, hydraulic output is 0.450 kW.
These values follow from selected inputs and do not rate or select a real lobe pump.
Scope and correction boundary
The original arithmetic calculator is preserved because its identities are valid when volumetric efficiency is independently supplied. The former article added universal speeds, clearances, materials, pressure limits, cavitation behavior, failure diagnoses and product recommendations not determined by the inputs.
Those claims, the fabricated molasses example and unrelated video are removed. The selected pressure does not authorize operation at that pressure.
Questions
Does the calculator predict volumetric efficiency?
No. It is a selected input that should come from manufacturer or measured operating-point data.
Is slip independently modeled?
No. It is defined here only as theoretical flow minus selected delivered flow.
Is hydraulic output the motor input?
No. Actual shaft input is higher after mechanical and other losses.
Does the model check cavitation or safe operation?
No. Use the actual manufacturer's curves and installation requirements.
Technical references
- Hydraulic Institute — pump standards and system guidance.
- OpenStax College Physics, Flow Rate — volumetric-flow definitions.
- NIST Special Publication 811 — SI unit and conversion guidance.
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