Pump Performance

Overview

Pump performance characterizes the hydraulic and mechanical behavior of centrifugal pumps across their operating range. Understanding performance curves, affinity laws, and efficiency characteristics is essential for proper pump selection, system design, and troubleshooting in HVAC hydronic applications. The performance of a centrifugal pump is determined by the interaction between fluid properties, impeller geometry, rotational speed, and system hydraulic resistance.

Fundamental Performance Relationships

Head-Capacity Relationship

The fundamental pump curve relates total dynamic head (TDH) to volumetric flow rate:

Total Dynamic Head:

TDH = Hd - Hs = (Pd - Ps)/ρg + (Vd² - Vs²)/2g + (Zd - Zs)

Where:

• TDH = Total dynamic head (ft or m)
• Hd = Discharge head (ft or m)
• Hs = Suction head (ft or m)
• Pd, Ps = Discharge and suction pressures (lbf/ft² or Pa)
• ρ = Fluid density (lbm/ft³ or kg/m³)
• g = Gravitational acceleration (32.2 ft/s² or 9.81 m/s²)
• Vd, Vs = Discharge and suction velocities (ft/s or m/s)
• Zd, Zs = Discharge and suction elevations (ft or m)

Hydraulic Power

The power transferred to the fluid (water horsepower):

Water Horsepower (WHP):

WHP = (Q × TDH × SG)/(3960)  [US units]

WHP = (Q × TDH × ρ × g)/1000  [SI units]

Where:

• Q = Flow rate (gpm or L/s)
• TDH = Total dynamic head (ft or m)
• SG = Specific gravity (dimensionless)
• 3960 = Conversion constant (US customary)

Brake Horsepower

The actual power input required at the pump shaft:

Brake Horsepower (BHP):

BHP = WHP/ηp

BHP = (Q × TDH × SG)/(3960 × ηp)  [US units]

Where:

• ηp = Pump efficiency (decimal)

Pump Efficiency

Pump efficiency represents the ratio of hydraulic power output to mechanical power input:

Pump Efficiency:

ηp = WHP/BHP = (Q × TDH × SG)/(3960 × BHP)

Typical efficiency ranges for HVAC pumps:

Pump Characteristic Curves

Head-Capacity Curve

The H-Q curve shows the relationship between total head and flow rate at constant speed. Curve shape depends on impeller design:

Curve Classifications:

1. Steep Curve (High Specific Speed)

   • Head drops significantly with increasing flow
   • Stable operation across wide flow range
   • Preferred for variable flow systems
   • Common in HVAC applications

2. Flat Curve (Low Specific Speed)

   • Head relatively constant across flow range
   • Less sensitive to flow variations
   • May have unstable region at low flows
   • Used for constant pressure applications

3. Drooping Curve

   • Head rises to peak then drops
   • Unstable operation possible
   • Multiple operating points possible
   • Generally avoided in HVAC

Power Curve

The BHP-Q curve shows brake horsepower versus flow rate:

Power Characteristics:

• Non-Overloading: BHP peaks at or before design point, then decreases
• Overloading: BHP continues to rise with increasing flow
• HVAC Preference: Non-overloading characteristic to prevent motor overload

Maximum BHP:

BHP_max = (Motor HP × Service Factor)

Motor must be sized for maximum BHP across operating range, typically:

Motor HP ≥ BHP_max/0.95

Efficiency Curve

The ηp-Q curve shows pump efficiency versus flow rate:

Efficiency Characteristics:

• Peak efficiency occurs at Best Efficiency Point (BEP)
• Efficiency drops off at flows above and below BEP
• Operating range typically 70-130% of BEP flow
• Preferred operating range: 85-110% of BEP flow

Part-Load Efficiency:

Modern variable speed pumps maintain higher efficiency at reduced flows through speed reduction rather than throttling.

Net Positive Suction Head Required (NPSHr)

The NPSHr-Q curve shows minimum suction head required to prevent cavitation:

NPSHr Characteristics:

• Increases with flow rate (approximately Q²)
• Must maintain NPSHa > NPSHr + safety margin
• Typical safety margin: 3-5 ft (0.9-1.5 m)
• Critical for high-temperature water applications

Affinity Laws

The affinity laws predict pump performance changes with impeller diameter and rotational speed variations.

Speed Change (Constant Impeller Diameter)

Flow Rate:

Q₂/Q₁ = N₂/N₁

Head:

H₂/H₁ = (N₂/N₁)²

Power:

BHP₂/BHP₁ = (N₂/N₁)³

Where:

• N = Pump speed (rpm)
• Subscripts 1, 2 = Initial and final conditions

Impeller Diameter Change (Constant Speed)

Flow Rate:

Q₂/Q₁ = D₂/D₁

Head:

H₂/H₁ = (D₂/D₁)²

Power:

BHP₂/BHP₁ = (D₂/D₁)³

Where:

• D = Impeller diameter (in or mm)

Application Limitations

Affinity laws are accurate for:

• Speed changes: ±50% of design speed
• Diameter changes: ±5% of design diameter
• Same fluid properties
• Geometrically similar impellers

Accuracy decreases outside these ranges due to Reynolds number effects and efficiency changes.

Specific Speed

Specific speed characterizes impeller geometry and performance characteristics.

Pump Specific Speed (Ns)

Definition:

Ns = (N × Q^0.5)/H^0.75  [US units]

Ns = (N × Q^0.5)/(H^0.75)  [SI units, dimensionless]

Where:

• N = Rotational speed (rpm)
• Q = Flow rate at BEP (gpm or m³/s)
• H = Head per stage at BEP (ft or m)

For multi-stage pumps:

H = Total head/Number of stages

Specific Speed Characteristics

Suction Specific Speed (S)

Suction specific speed characterizes cavitation performance:

Definition:

S = (N × Q^0.5)/(NPSHr)^0.75

Performance Criteria:

• S < 8,500: Excellent suction performance
• S = 8,500-11,000: Good suction performance
• S = 11,000-13,000: Average performance, higher cavitation risk
• S > 13,000: Poor suction performance, requires careful NPSH analysis

Higher suction specific speed indicates greater susceptibility to cavitation and erosion.

Net Positive Suction Head (NPSH)

NPSH Available (NPSHa)

The absolute pressure head available at pump suction:

Closed System (HVAC Typical):

NPSHa = Ps/ρg + Vs²/2g - Pvp/ρg

Open System:

NPSHa = Pa/ρg ± Zs - hfs - Pvp/ρg + Vs²/2g

Where:

• Ps = Suction pressure (absolute) (lbf/ft² or Pa)
• Pa = Atmospheric pressure (absolute) (lbf/ft² or Pa)
• Zs = Static suction lift (+) or head (-) (ft or m)
• hfs = Friction loss in suction piping (ft or m)
• Pvp = Vapor pressure of fluid at pumping temperature (lbf/ft² or Pa)
• Vs = Velocity at pump suction (ft/s or m/s)

NPSH Required (NPSHr)

The minimum suction head required to prevent cavitation, determined by pump manufacturer through testing per HI standards.

Cavitation Prevention

Design Criteria:

NPSHa ≥ NPSHr + Safety Margin

Safety Margin = 3-5 ft (general HVAC)
Safety Margin = 5-10 ft (hot water >200°F)
Safety Margin = 10+ ft (critical services)

Temperature Effects on NPSH

Vapor pressure increases exponentially with temperature:

High-temperature applications require careful NPSH analysis and often require suction pressurization.

System Operating Point

System Curve

The system head curve represents total head required versus flow rate:

System Head Equation:

Hs = Hstatic + Hfriction = Hstatic + K × Q²

Where:

• Hstatic = Static head (elevation + pressure differences) (ft or m)
• K = System resistance coefficient
• Q = Flow rate (gpm or L/s)

Operating Point Determination

The pump operates where the pump curve intersects the system curve:

Graphical Method:

1. Plot pump H-Q curve
2. Plot system H-Q curve
3. Intersection = operating point

Analytical Method:

Hpump(Q) = Hsystem(Q)

Solve iteratively for Q, then determine H, BHP, and ηp at operating point.

Multiple Operating Points

Parallel pump operation creates combined pump curves:

• System may have multiple stable operating points
• Unstable operating points occur on negatively sloped regions
• Control valves shift system curve to maintain design flow

Pump Performance Testing

Field Testing per HI/ASHRAE Standards

Required Measurements:

1. Flow Rate:

   • Calibrated flow meters (±2% accuracy)
   • Ultrasonic flow measurement
   • Pressure drop across known restriction

2. Pressure:

   • Calibrated gauges at suction and discharge
   • Piezometer taps per HI standards
   • Compound gauge on suction for vacuum conditions

3. Power:

   • True RMS wattmeter for VFD applications
   • Current and voltage measurement with power factor
   • Motor nameplate efficiency correction

4. Temperature:

   • Suction and discharge temperature
   • Required for density and viscosity corrections

Performance Calculations

Measured Head:

H = (Pd - Ps)/(ρg) + (Zd - Zs)

Velocity head typically negligible in HVAC systems (pipe velocities 4-12 ft/s).

Wire-to-Water Efficiency:

ηww = (Q × H × ρ × g)/(Pin × 1000)

Where Pin = electrical power input (kW)

Acceptance Criteria

Per HI 14.6 and ASHRAE Guideline 22:

Series and Parallel Operation

Series Operation

Pumps in series add heads at constant flow rate:

Combined Performance:

Htotal = H₁ + H₂ + ... + Hn (at constant Q)

Applications:

• High-rise buildings requiring pressure boost
• Multi-stage pumps
• Overcoming high static head

Considerations:

• Each pump must handle full system flow
• Downstream pump sees elevated suction pressure
• NPSHa increases for downstream pumps

Parallel Operation

Pumps in parallel add flow rates at constant head:

Combined Performance:

Qtotal = Q₁ + Q₂ + ... + Qn (at constant H)

Applications:

• Variable flow systems with lead-lag control
• Redundancy (N+1 configuration)
• Energy efficiency at part load

Considerations:

• Pumps must have similar H-Q curves (within 5%)
• Operating point shifts with pump staging
• Check valves prevent reverse flow through idle pumps
• Individual pump flow less than 50% of total in 2-pump configuration

Parallel Pump Flow Distribution

For two identical pumps:

Q_each = Qtotal/2 (ideal)

For dissimilar pumps, flow splits based on individual pump curves at system head.

Variable Speed Pump Performance

Speed Reduction Effects

Variable frequency drives (VFDs) enable speed modulation for flow control:

Speed vs. Flow Control:

Power_throttled = Q × H
Power_VFD = Q × (H × (Q/Q_design)²)

Energy savings from VFD operation:

Power_ratio = (N₂/N₁)³

System Curve Impact

Speed reduction shifts pump curve downward along parabolic system curve:

Operating Points:

• 100% speed: Design flow and head
• 75% speed: 75% flow, 56% head, 42% power
• 50% speed: 50% flow, 25% head, 12.5% power

Minimum Speed Constraints

Operational Limits:

1. Minimum Flow: Prevent overheating (typically 30-40% design flow)
2. Motor Cooling: Below 30 Hz, external cooling may be required
3. Bearing Lubrication: Minimum speed varies by pump type
4. Control Stability: Below 20-30% speed, control becomes difficult

Viscosity Effects on Performance

Correction Factors

For fluids with kinematic viscosity > 20 cSt, apply correction factors per HI/ASHRAE:

Head Correction:

H_viscous = H_water × CH

Flow Correction:

Q_viscous = Q_water × CQ

Efficiency Correction:

η_viscous = η_water × Cη

Correction factors obtained from HI viscosity correction charts based on:

• Flow rate at BEP (gpm)
• Head at BEP (ft)
• Kinematic viscosity (cSt)

Glycol Solutions

Common in HVAC freeze protection:

Viscosity decreases with temperature; corrections most significant at low temperatures.

Design Considerations

Pump Sizing Best Practices

1. Operating Point Selection:

   • Target 90-110% of pump BEP
   • Avoid operation below 70% or above 120% of BEP flow
   • Consider future flow requirements (typically 10-20% margin)

2. Head Calculation Accuracy:

   • Include all friction losses (pipe, fittings, valves, coils)
   • Add control valve authority (25-50% of system friction)
   • Include elevation changes and equipment pressure drops
   • Add 5-10% safety factor to calculated head

3. Power and Motor Sizing:

   • Size motor for maximum BHP across operating range
   • Include service factor (typically 1.15)
   • For VFD applications, consider harmonics and derating

4. NPSH Verification:

   • Calculate NPSHa for worst-case conditions (highest temperature)
   • Verify NPSHa > NPSHr + 5 ft minimum
   • For hot water systems, consider suction pressurization

Selection Criteria Priority

Primary Criteria:

1. Flow rate and head at design conditions
2. Operating point near BEP (90-110%)
3. Adequate NPSH margin
4. Non-overloading power characteristic
5. Efficiency at design and part-load conditions

Secondary Criteria:

1. Physical size and weight constraints
2. Installation and maintenance access
3. Noise and vibration levels
4. Manufacturer service and parts availability
5. Life cycle cost analysis

Common Performance Issues

Symptoms and Causes:

References and Standards

Hydraulic Institute (HI):

• HI 1.1-1.5: Centrifugal pump standards
• HI 14.6: Rotodynamic pump acceptance testing
• HI 9.6.7: Effects of liquid viscosity on performance

ASHRAE:

• ASHRAE Guideline 22: Instrumentation for monitoring system performance
• ASHRAE Handbook - HVAC Systems and Equipment: Chapter 44 (Pumps)
• ASHRAE Standard 90.1: Energy efficiency requirements for pump power

Industry Standards:

• ASME PTC 8.2: Centrifugal pump performance testing
• ISO 9906: Rotodynamic pump acceptance testing
• AHRI Standard 11: Performance rating of pumps

Advanced Topics

Wire-to-Water Optimization

Total system efficiency considering pump and motor:

η_system = η_pump × η_motor × η_VFD

Typical values:
η_pump = 75-85%
η_motor = 90-95%
η_VFD = 95-97%

η_system = 65-78%

Optimize by:

• Selecting high-efficiency pumps and motors
• Operating near BEP
• Minimizing system resistance
• Right-sizing to avoid oversizing penalties

Computational Fluid Dynamics (CFD)

Modern pump design uses CFD analysis to:

• Optimize impeller blade geometry
• Predict cavitation inception
• Minimize hydraulic losses
• Analyze recirculation and secondary flows

CFD enables custom impeller design for specific duty points, achieving efficiencies 3-5% higher than standard designs.

Life Cycle Cost Analysis

Total cost of ownership includes:

LCC = Initial Cost + Energy Cost + Maintenance Cost + Downtime Cost

Energy Cost (20-year) = kW × Operating Hours × $/kWh × Escalation Factor

Typically: Energy Cost = 80-90% of LCC

Investment in higher efficiency pumps typically pays back in 2-5 years through energy savings.