7.2 Positive Displacement Pumps (Gear, Vane, Piston, Diaphragm)

Fundamental Mechanics & PD vs Centrifugal Comparison

Positive Displacement (PD) pumps operate on a fundamentally different mechanical principle than dynamic centrifugal pumps. Rather than accelerating liquid to create velocity head, a positive displacement pump traps a fixed, discrete volume of fluid in a expanding cavity on the suction side, physically seals off the cavity, and mechanically forces that fluid volume out through the discharge port. Because fluid is physically displaced into the discharge line with each shaft revolution or reciprocating stroke, a PD pump produces a nearly constant volumetric flow rate (Q) regardless of variations in system discharge head (H).

Kinematic & Hydraulic Comparison

• Pressure vs Flow Characteristic: Centrifugal pumps exhibit a variable head-capacity curve where flow decreases significantly as system head increases. In contrast, positive displacement pumps exhibit a steep, nearly vertical Q vs H curve; flow rate remains constant even as discharge pressure escalates dramatically.
• Internal Slip Dynamics: Internal slip refers to the high-pressure discharge fluid leaking backward to the low-pressure suction side across small internal mechanical running clearances (such as gear tooth tip clearances or piston ring gaps). In centrifugal pumps, slip dominates performance at high head. In PD pumps, internal slip is minimal when pumping viscous fluids, but increases slightly as discharge pressure increases or when pumping ultra-low viscosity fluids.
• Viscosity Responsiveness: High fluid viscosity severely degrades centrifugal pump performance by causing extreme hydraulic friction drag on impellers. Conversely, positive displacement pumps excel at pumping high-viscosity liquids (e.g., heavy oils, resins, polymers, molasses); higher viscosity actually reduces internal slip across running clearances, raising the pump's volumetric efficiency.

Rotary Positive Displacement Pumps

Rotary PD pumps utilize rotating components (gears, vanes, lobes, or screws) to transfer fluid continuously without pulsating reciprocating motion. They are widely specified for industrial hydraulic systems, lubrication skids, and viscous chemical transfer:

External Gear Pumps

External gear pumps feature two identical interlocking spur or helical gears (one driven gear and one idler gear) supported by shafts inside a precision-machined housing.

• Operation: As gear teeth unmesh on the suction side, a low-pressure void is created, drawing fluid into the housing. Fluid is trapped within the pockets between adjacent gear teeth and the interior casing wall, and carried around the outer perimeter to the discharge port. As gear teeth mesh together on the discharge side, fluid is squeezed out under pressure.
• Characteristics: Compact, simple, economical design capable of high operating pressures (up to 210 bar / 3000 PSI). Shafts are supported by sleeve bushings lubricated by the pumped fluid.

Internal Gear Pumps

Internal gear pumps feature an externally toothed inner drive gear (rotor) meshing inside a larger internally toothed outer gear (idler), separated by a stationary crescent-shaped divider seal.

• Operation: Fluid enters the suction port where teeth unmesh. The crescent divider splits the fluid flow, sealing the liquid trapped between rotor teeth and idler teeth as it passes around to the discharge port, where teeth re-mesh to force liquid out.
• Characteristics: Exceptional self-priming ability and gentle pumping action suitable for sensitive, high-viscosity shear-susceptible liquids across a wide temperature range.

Sliding Vane Pumps

Sliding vane pumps consist of an eccentric rotor spinning inside a cylindrical cam ring housing. Slots in the rotor house rectangular vanes that slide radially outward under spring pressure or centrifugal force to maintain continuous contact with the casing wall.

• Operation: As the eccentric rotor turns, the expanding volume between adjacent vanes on the suction side draws in liquid. As vanes approach the narrow side of the housing, the trapped volume shrinks, compressing fluid out the discharge port.
• Characteristics: Vanes automatically extend outward to compensate for tip wear, maintaining high volumetric efficiency throughout their service life. Ideal for low-viscosity fluids (propane, solvents, fuel oils).

Progressive Cavity Pumps (Single Screw)

Progressive cavity pumps feature a precision-machined single-external helix metallic rotor turning eccentrically inside a double-internal helix elastomeric stator.

• Operation: As the rotor turns within the resilient stator, discrete progressing cavities form and move axially from suction to discharge. Flow is completely non-pulsating, continuous, and proportional to speed.
• Characteristics: Outstanding capability for pumping extremely heavy slurries, abrasive pastes, municipal sludge, and high-solids mixtures without shearing suspended particles.

Reciprocating Positive Displacement Pumps & Relief Valves

Reciprocating PD pumps utilize a back-and-forth stroke action produced by a crankshaft, eccentric drive, or linear pneumatic cylinder to displace fluid past suction and discharge check valves:

Piston & Plunger Pumps

• Piston Pumps: A cylindrical piston fitted with dynamic high-pressure packing rings moves back and forth inside a cylinder liner. On the retraction stroke, negative pressure opens the suction check valve, filling the cylinder cavity. On the forward stroke, the suction valve snaps shut and the discharge check valve opens, forcing fluid into the piping.
• Plunger Pumps: A smooth stationary ceramic or hardened steel plunger passes through stationary high-pressure packing glands into a fluid chamber. Used for extreme pressure applications (up to 700 bar / 10,000 PSI) such as hydro-blasting, waterjet cutting, and boiler chemical injection.

Diaphragm Pumps

Diaphragm pumps replace reciprocating metal pistons with a flexible elastomeric or PTFE diaphragm clamped inside a fluid chamber. The diaphragm is flexed back and forth by a mechanical linkage, hydraulic oil pulse, or compressed air (Air-Operated Double Diaphragm - AODD pumps).

• Key Advantage: Because the flexible diaphragm completely separates the pumped fluid from driver linkages, there are no dynamic shaft seals or packing glands to leak. Diaphragm pumps provide zero-leakage containment for toxic, corrosive, reactive, or carcinogenic chemicals.

Mandatory Pressure Relief Valve (PRV) Requirement

Because positive displacement pumps deliver a fixed volume per revolution regardless of head, a positive displacement pump operating against a closed discharge line will produce theoretically infinite pressure rise.

• Catastrophic Failure Modes: If a discharge isolation valve is accidentally closed while a PD pump is running, pressure will instantaneously exceed component yield limits, resulting in fractured pump casings, ruptured discharge piping, destroyed mechanical seals, or electric motor burn-out.
• Mandatory Installation Standard: Industrial standards require an inline Pressure Relief Valve (PRV) installed directly on the discharge line upstream of any isolation valve. The relief valve discharge must be piped back to the suction supply reservoir (or drain skid) to vent excess fluid safely if system pressure exceeds design setpoint.

Displacement Calculations, Volumetric Efficiency & Dry-Run Hazards

Flow Rate & Volumetric Efficiency Formulas

The theoretical flow rate (Q_theoretical) delivered by a positive displacement pump is determined directly by its internal geometric displacement per revolution (D_rev) and driver rotational speed (N): $Q_{\text{theoretical}} = \frac{D_{\text{rev}} \text{ (in}^3/\text{rev)} \times N \text{ (RPM)}}{231 \text{ (in}^3/\text{gal)}}$

Due to internal fluid slip across internal running clearances, actual measured flow rate (Q_actual) is slightly lower than theoretical flow. The ratio is defined as Volumetric Efficiency (η_v): $\eta_v = \left(\frac{Q_{\text{actual}}}{Q_{\text{theoretical}}}\right) \times 100\%$

Engineering Calculation Example

An external gear pump with a liquid displacement of 4.62 in³/rev operates at 1750 RPM. If a calibrated flow meter measures an actual discharge of 31.5 GPM under load:

1. Theoretical Flow Rate: $Q_{\text{theoretical}} = \frac{4.62 \times 1750}{231} = \frac{8085}{231} = 35.0\text{ GPM}$
2. Volumetric Efficiency: $\eta_v = \left(\frac{31.5}{35.0}\right) \times 100\% = 90.0\%$ (The remaining 10% or 3.5 GPM represents internal slip back to suction).

Self-Priming Ability vs Dry-Running Damage Risks

Because rotary and reciprocating PD pumps maintain tight mechanical tolerances, they create strong internal vacuum levels capable of evacuating air from dry suction piping—making them inherently self-priming.

• Dry-Running Hazard: Despite their self-priming capability, positive displacement pumps must never be operated dry. Internal components (gear teeth, sliding vanes, progressive cavity stators, plungers, and dynamic packing) rely entirely on the pumped liquid film for thermal cooling and hydrodynamic lubrication.
• Thermal Seizure Mechanism: Operating a PD pump dry causes instantaneous metallic or elastomeric friction heat generation. Progressive cavity rubber stators expand and melt within 30 seconds; sliding vanes chatter and shatter; external gear teeth heat, expand axially, and gall against end plates, resulting in complete mechanical pump destruction.