Positive Displacement Pumps | Skills Pool
Positive Displacement Pumps Design and analyze gear, piston, and screw pumps with volumetric efficiency
Positive displacement (PD) pumps move fluid by trapping a fixed volume and forcing it into a discharge pipe. Unlike centrifugal pumps, they deliver nearly constant flow regardless of discharge pressure.
Types of Positive Displacement Pumps
Gear Pumps
External Gear Pumps
Two meshing gears rotate in opposite directions
Fluid trapped between gear teeth and casing
Simple, reliable, good for clean, viscous fluids
Flow proportional to speed
Typical efficiency: 80-95%
Internal Gear Pumps
One gear inside another
Crescent-shaped seal between gears
Smoother flow, less pulsation
Good for viscous fluids
Compact design
Piston Pumps (Reciprocating)
Single-Acting Piston
Fluid displaced on one stroke only
High pulsation
Simple construction
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Fluid displaced on both strokes
Reduced pulsation
Higher efficiency
Multi-Piston (Triplex, Quintuplex)
Multiple pistons offset in phase
Smoother flow
Common in high-pressure applications
Typical efficiency: 85-95%
Diaphragm Pumps Air-Operated Double Diaphragm (AODD)
Two flexible diaphragms
Air pressure drives operation
Self-priming, can run dry
Excellent for slurries and solids
Lower efficiency (~30-70%)
Diaphragm actuated by mechanical linkage
Higher efficiency than AODD
Good for metering applications
Screw Pumps Single Screw (Progressive Cavity)
Rotor rotates within stator
Continuous, non-pulsating flow
Excellent for viscous, shear-sensitive fluids
Self-priming
Two or three intermeshing screws
Low pulsation
Good for high-pressure applications
Typical efficiency: 75-90%
Lobe Pumps
Two or more lobes rotate in opposite directions
Gentle handling of product
Common in food, pharmaceutical industries
Easy to clean (sanitary designs)
Typical efficiency: 50-80%
Key Characteristics
Constant Flow Behavior
Flow rate independent of discharge pressure
Flow proportional to speed only
Q = N × V_d
Q = volumetric flow rate
N = pump speed (rpm)
V_d = displacement per revolution
Flow decreases slightly with pressure (slip)
Efficiency varies with operating conditions
Volumetric Efficiency Volumetric efficiency accounts for internal leakage (slip):
η_v = Q_actual / Q_theoretical
η_v = (Q_theoretical - Q_slip) / Q_theoretical
Factors affecting volumetric efficiency:
Clearances and wear
Fluid viscosity (higher = better sealing)
Differential pressure (higher = more leakage)
Operating speed
Slip and Leakage Slip Flow:
Q_slip = C × ΔP / μ
C = slip coefficient (depends on clearances)
ΔP = differential pressure
μ = dynamic viscosity
Viscous fluids: less slip, higher efficiency
High pressures: more slip, lower efficiency
Worn pumps: increased clearances, more slip
Pulsation
Discrete volume displacement
Reciprocating motion
Gear tooth engagement/disengagement
Pulsation Index:
PI = (Q_max - Q_min) / Q_avg × 100%
Typical Pulsation Levels:
Single piston: Very high (100%+)
Duplex piston: High (~50-60%)
Triplex piston: Moderate (~10-20%)
Gear pumps: Low to moderate (~5-15%)
Screw pumps: Very low (<5%)
Self-Priming Capability Most PD pumps are self-priming:
Create vacuum on suction side
Can lift fluid from below pump
Can evacuate air from suction line
Maximum suction lift ~8m (limited by atmospheric pressure)
Requires reasonable seal condition
May need priming for high-viscosity fluids
Design Calculations
Displacement Per Revolution Gear Pump:
V_d = 2 × π × b × (D_o² - D_i²) / 4
b = gear width
D_o = outer diameter
D_i = inner (root) diameter
Piston Pump:
V_d = (π × d² / 4) × L × n
d = piston diameter
L = stroke length
n = number of pistons (single-acting) or 2n (double-acting)
Screw Pump:
V_d = 4 × A_c × p
A_c = cavity area
p = pitch
Theoretical Flow Rate Q_theoretical = V_d × N / 60
Q_theoretical in m³/s or L/min
V_d in m³ or L
N in rpm
Actual Flow Rate (Accounting for Slip) Q_actual = η_v × Q_theoretical
Q_actual = Q_theoretical - Q_slip
Slip as function of pressure and viscosity:
Q_actual = Q_theoretical - (C × ΔP / μ)
Specify desired flow at operating pressure
Account for expected volumetric efficiency
Select pump with adequate theoretical capacity
Power Requirements Hydraulic Power:
P_hydraulic = Q × ΔP
P in Watts
Q in m³/s
ΔP in Pa
Brake Power (Shaft Power):
P_brake = P_hydraulic / η_overall
η_v = volumetric efficiency
η_m = mechanical efficiency (bearings, seals)
Typical Overall Efficiencies:
Gear pumps: 70-85%
Piston pumps: 80-90%
Screw pumps: 70-85%
Diaphragm pumps: 30-70%
Motor Power (with safety factor):
P_motor = P_brake × SF
NPSH Requirements PD pumps generally require lower NPSH than centrifugal pumps:
NPSH_required = P_atm/ρg - h_suction - h_friction - P_vapor/ρg - safety_margin
0.5-2 m for most PD pumps
Higher for high-speed pumps
Lower for slow-speed pumps
When to Use PD vs Centrifugal Pumps
Choose Positive Displacement When:
High-Pressure Applications
ΔP > 10-20 bar
PD pumps maintain efficiency at high pressure
Centrifugal pumps become impractical
Viscous Fluids
μ > 100 cP
PD efficiency improves with viscosity
Centrifugal efficiency drops dramatically
Constant Flow Required
Metering and dosing
Flow independent of pressure variations
Predictable delivery
Low Flow, High Pressure
Centrifugal pumps inefficient at low flow
PD pumps excel in this range
Self-Priming Required
Suction lift needed
Air entrainment possible
Dry-run capability
Shear-Sensitive Fluids
Food products, polymers
Use lobe or progressive cavity pumps
Gentle handling
Choose Centrifugal When:
High Flow, Low Pressure
Q > 100 m³/h, ΔP < 10 bar
More economical
Simpler maintenance
Low Viscosity Fluids
μ < 50 cP (water-like)
Centrifugal pumps efficient
Less expensive
Continuous, Smooth Flow
No pulsation acceptable
Variable flow needed
Throttling control
Particulate Handling
Large solids
PD pumps can jam
Centrifugal more forgiving
Lower Initial Cost
Simple installation
Standard motors
Lower maintenance
Pulsation Dampening
Vibration and noise
Inaccurate flow measurement
Pressure spikes
System fatigue
Dampening Methods 1. Pulsation Dampener (Accumulator)
Gas-Charged Bladder Type:
Bladder separates gas and fluid
Gas compresses during pressure peaks
Gas expands during pressure valleys
Smooth flow output
Sizing:
V_dampener = (Q_theoretical × C_d) / (η_p × f)
C_d = dampening coefficient (typically 5-10)
η_p = pulsation reduction efficiency (0.9-0.95)
f = pump frequency (Hz)
Gas Pre-Charge Pressure:
P_precharge = 0.6 × P_operating (typical)
Triplex Pump (3 pistons at 120°):
Pulsation reduced ~90%
Common in high-pressure applications
Quintuplex Pump (5 pistons at 72°):
Pulsation reduced ~95%
Smoother than triplex
Simple expansion chamber on discharge:
Gas cushion absorbs pulsation
Requires regular air charging
Lower cost than bladder type
4. Flexible Discharge Line
Hose instead of rigid pipe (short section)
Elasticity absorbs pulses
Simple, low cost
Limited effectiveness
Restrictor orifice
Creates back pressure
Dampens pressure fluctuations
Energy loss
Design Considerations Critical Frequencies:
Avoid resonance with system natural frequency:
N = pump speed (rpm)
n = number of pistons or pumping chambers
Close to pump discharge
Before flow meter (if smooth flow required)
Consider accessibility for maintenance
Check bladder integrity
Verify gas pre-charge pressure
Inspect for leaks
Application Selection Guide
High-Pressure Chemical Injection Recommended: Plunger pump (triplex)
High pressure capability (up to 1000+ bar)
Good metering accuracy
Pulsation dampener required
Viscous Oil Transfer Recommended: Gear pump or screw pump
Handles high viscosity well
Self-priming
Relatively smooth flow
Slurry and Solids Recommended: Diaphragm pump or progressive cavity
Can handle solids
Won't jam easily
Gentle action
Food and Pharmaceutical Recommended: Lobe pump or sanitary diaphragm
Hygienic design
Easy to clean
Gentle product handling
Metering and Dosing Recommended: Diaphragm metering pump or plunger pump
Excellent accuracy
Adjustable stroke
Handles chemicals
General Water Transfer Recommended: Centrifugal pump
Lower cost
Lower maintenance
Adequate for low viscosity
Design Example Workflow
Define Requirements:
Flow rate (actual, at operating pressure)
Differential pressure
Fluid properties (density, viscosity)
Operating conditions
Select Pump Type:
Based on application guide above
Consider fluid compatibility
Evaluate cost constraints
Calculate Theoretical Capacity:
Account for volumetric efficiency
Q_theoretical = Q_actual / η_v
Size Displacement:
V_d = Q_theoretical × 60 / N
Choose operating speed N
Calculate Power:
P_hydraulic = Q × ΔP
P_brake = P_hydraulic / η_overall
P_motor = P_brake × SF
Check NPSH:
NPSH_available > NPSH_required + margin
Size suction piping appropriately
Evaluate Pulsation:
Calculate pulsation index
Determine if dampening needed
Size dampener if required
Verify Operating Range:
Minimum/maximum speed
Pressure limitations
Viscosity range
Flow rate vs. speed (check for increased slip)
Discharge pressure
Power consumption (increased = wear)
Vibration levels
Temperature
Reduced flow at same speed
Increased power consumption
Increased noise/vibration
Reduced volumetric efficiency
Replace seals/gaskets per schedule
Monitor clearances in gear pumps
Check valve seats in piston pumps
Inspect diaphragms regularly
Summary Positive displacement pumps are essential for:
High-pressure applications
Viscous fluid handling
Metering and constant flow
Self-priming requirements
Key design considerations:
Account for volumetric efficiency (slip)
Size for actual flow needed
Consider pulsation dampening
Match pump type to application
Trade-offs vs. centrifugal:
Higher pressure capability
Better viscosity handling
Pulsating flow
Higher initial cost
More maintenance
02
Gear Pumps
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