1. Overview & Key Concepts
Centrifugal pumps convert rotational energy from motors into fluid pressure through impeller rotation. Proper sizing requires matching pump performance to system hydraulic requirements.
Essential Parameters
| Parameter | Symbol | Common Units | Definition |
|---|---|---|---|
| Flow Rate | Q | gpm, BPD, m³/h | Volume per time |
| Total Dynamic Head | TDH | ft, m | Total head pump must develop |
| NPSH Available | NPSHa | ft, m | Suction head above vapor pressure |
| NPSH Required | NPSHr | ft, m | Head needed to prevent cavitation |
| Brake Horsepower | BHP | HP, kW | Shaft power required |
| Efficiency | η | % | Hydraulic power / shaft power |
| Specific Speed | Ns | dimensionless | Pump type indicator |
Why Use Head Instead of Pressure?
Head-Pressure Relationship:
H (ft) = P (psi) × 2.31 / SG
H (m) = P (kPa) / (SG × 9.81)
Key Advantage: Head is independent of fluid density. A pump develops the same head for water (SG=1.0) or oil (SG=0.85), but different pressures. This makes pump curves universal—one curve works for any fluid.
Example: A pump developing 100 ft of head produces 43.3 psi with water (SG=1.0) but only 36.8 psi with light oil (SG=0.85). The head is constant; pressure varies with density.
2. Total Dynamic Head
Total Dynamic Head (TDH) represents the total energy per unit weight the pump must add to move fluid through the system.
TDH Components:
TDH = Hstatic + Hpressure + Hfriction
Where:
• Hstatic = Elevation change (Zdischarge - Zsuction)
• Hpressure = Pressure change converted to head
• Hfriction = Friction losses in piping and fittings
Static Head
Simply the vertical elevation difference between suction and discharge points.
Hstatic = Zdischarge - Zsuction
Positive for uphill pumping, negative for downhill
Pressure Head
When pumping into a pressurized vessel or against backpressure:
Hpressure = (Pdischarge - Psuction) × 2.31 / SG
Units: P in psig, H in ft
Friction Losses
Energy lost due to pipe friction and fitting resistance.
Pipe Friction (Darcy-Weisbach Equation)
Hf = f × (L/D) × (V²/2g)
Where:
f = Friction factor (from Moody diagram or Colebrook-White equation)
L = Pipe length (ft)
D = Internal diameter (ft)
V = Fluid velocity (ft/s)
g = 32.174 ft/s²
Friction Factor: Depends on Reynolds number and relative pipe roughness.
For turbulent flow, use Moody diagram or calculate iteratively.
Minor Losses (Fittings, Valves)
| Fitting Type | K Factor |
|---|---|
| 90° Elbow (standard radius) | 0.9 |
| 90° Elbow (long radius) | 0.6 |
| 45° Elbow | 0.4 |
| Tee (flow through run) | 0.6 |
| Tee (flow through branch) | 1.8 |
| Gate Valve (fully open) | 0.2 |
| Globe Valve (fully open) | 10.0 |
| Check Valve (swing type) | 2.0 |
| Pipe entrance (sharp-edged) | 0.5 |
| Pipe exit (sudden expansion) | 1.0 |
Hfitting = K × (V²/2g)
Total fitting losses: Sum all K-values, calculate once using system velocity
Hfittings = Σ(Ki) × (V²/2g)
Velocity Guidelines
| Line Type | Typical Velocity | Maximum |
|---|---|---|
| Suction (clean liquid) | 4–7 ft/s | 8 ft/s |
| Discharge | 8–12 ft/s | 15 ft/s |
| Suction (viscous fluid) | 2–4 ft/s | 5 ft/s |
3. NPSH Analysis
Net Positive Suction Head (NPSH) prevents cavitation—the formation and violent collapse of vapor bubbles that damages pumps and reduces performance.
NPSH Available (System Characteristic)
General Form:
NPSHa = (Psuction,abs - Pvapor) × 2.31/SG + Hs - Hf,suction + Hv
Components:
• Psuction,abs = Absolute pressure at liquid surface (psia)
• Pvapor = Vapor pressure of liquid at pumping temperature (psia)
• Hs = Static head: liquid level above (+) or below (-) pump centerline
• Hf,suction = Friction losses in suction piping only
• Hv = Velocity head at pump suction flange = V²/2g
For atmospheric tanks:
Psuction,abs = Patm = 14.7 psia at sea level
Critical: Use absolute pressures, not gauge!
Elevation Effect: Atmospheric pressure decreases with elevation. At 5,000 ft, Patm = 12.2 psia (vs 14.7 at sea level), reducing NPSHa by ~6 ft of water. Always correct for site elevation.
NPSH Required (Pump Characteristic)
NPSHr comes from pump manufacturer's certified test curves. Cannot be calculated—must be obtained from pump datasheet. Typical estimation for preliminary design:
NPSHr ≈ σ × H
Where σ (Thoma parameter) depends on specific speed:
• Ns < 2000: σ ≈ 0.08
• Ns 2000-5000: σ ≈ 0.12
• Ns > 5000: σ ≈ 0.16
Note: This is rough estimate only. Always use manufacturer data.
NPSH Margin Requirements (ANSI/HI 9.6.1-2017)
| Service Condition | Minimum Margin |
|---|---|
| Normal service (general) | NPSHa - NPSHr ≥ 3 ft (or 35% of NPSHr, whichever is greater) |
| API 610 process pumps | NPSHa/NPSHr ≥ 1.3 |
| Temperature > 300°F | NPSHa/NPSHr ≥ 2.0 |
| Hydrocarbons near bubble point | NPSHa/NPSHr ≥ 2.0 |
Vapor Pressure Data (Selected Fluids)
| Fluid | Temperature (°F) | Pvapor (psia) |
|---|---|---|
| Water | 60 | 0.26 |
| Water | 80 | 0.51 |
| Water | 100 | 0.95 |
| Water | 180 | 7.5 |
| Water | 212 | 14.7 |
| Gasoline (typical) | 100 | 7–10 |
| Propane | 60 | 92 |
| Butane | 60 | 23 |
⚠️ Cavitation Symptoms: Loud crackling/rumbling noise, severe vibration, sudden drop in flow and head, rapid impeller erosion damage. If suspected, immediately reduce flow or increase NPSHa.
Improving NPSH Available
- Raise liquid level: Increase static head (flooded suction preferred)
- Lower pump elevation: Reduces static lift or increases submergence
- Increase suction pressure: Pressurize suction vessel
- Reduce suction losses: Larger pipe, fewer fittings, shorter run
- Lower liquid temperature: Reduces vapor pressure
- Use booster pump: Add low-NPSH inducer or vertical can pump
4. Power & Motor Sizing
Hydraulic Power (Water Horsepower)
The theoretical power required to move the fluid, assuming 100% efficiency:
WHP = (Q × H × SG) / 3960
Where:
Q = Flow rate (gpm)
H = Total head (ft)
SG = Specific gravity
3960 = Conversion constant
Alternative (using pressure):
WHP = (Q × ΔP) / 1714
Where ΔP in psi, Q in gpm
Brake Horsepower (Shaft Power)
Actual power required at the pump shaft, accounting for pump losses:
BHP = WHP / ηpump
Or combined:
BHP = (Q × H × SG) / (3960 × ηpump)
Where ηpump = pump efficiency as decimal (e.g., 0.75 for 75%)
Typical Pump Efficiency by Size
| Flow Range (gpm) | Typical Efficiency Range | Notes |
|---|---|---|
| < 50 | 40–60% | Small pumps, high relative losses |
| 50–200 | 60–70% | Medium pumps |
| 200–1000 | 70–80% | Large single-stage |
| 1000–5000 | 78–88% | Large/multistage |
| > 5000 | 82–92% | Very large centrifugal |
Motor Sizing
Motor HP = BHP × SF / ηmotor
Where:
SF = Safety factor (typically 1.10–1.25 per API 610)
ηmotor = Motor efficiency (0.90–0.96 for standard motors)
Then select next standard NEMA motor size:
5, 7.5, 10, 15, 20, 25, 30, 40, 50, 60, 75, 100, 125, 150, 200, 250...
Note: NEMA motors have 1.15 service factor, meaning they can handle 15% overload continuously.
Example Calculation
Given:
- Flow Q = 500 gpm
- Total head H = 250 ft
- Specific gravity SG = 0.85
- Pump efficiency η = 75%
- Motor efficiency = 94%
- Safety factor = 1.15
Calculate:
WHP = (500 × 250 × 0.85) / 3960 = 26.89 HP
BHP = 26.89 / 0.75 = 35.85 HP
Motor HP = 35.85 × 1.15 / 0.94 = 43.9 HP
Selected motor: 50 HP (next standard size)
BHP = 26.89 / 0.75 = 35.85 HP
Motor HP = 35.85 × 1.15 / 0.94 = 43.9 HP
Selected motor: 50 HP (next standard size)
5. Pump Selection
Specific Speed and Pump Type
Specific speed (Ns) indicates the most efficient pump type for given conditions:
Ns = N × √Q / H0.75
Where:
N = Rotational speed (rpm)
Q = Flow at BEP (gpm)
H = Head per stage (ft)
| Ns Range | Pump Type | Characteristics |
|---|---|---|
| < 1000 | Radial flow | High head, low flow, narrow impeller |
| 1000–2000 | Francis vane | Medium head, moderate flow |
| 2000–4000 | Mixed flow | Medium head, high flow |
| 4000–7000 | Axial flow | Low head, very high flow |
| > 7000 | Propeller | Very low head, extremely high flow |
API 610 Pump Classifications
| Type | Description | Typical Application |
|---|---|---|
| OH1 | Overhung, centerline mounted, flexible coupling | Process pumps, moderate service |
| OH2 | Overhung, centerline mounted, close-coupled | Light duty, clean fluids |
| BB1 | Between bearings, single stage, radially split | Large flows, general service |
| BB2 | Between bearings, two stage, radially split | Medium head applications |
| BB3 | Between bearings, multistage, axially split | High pressure (> 600 ft) |
| BB5 | Between bearings, barrel type, multistage | Very high pressure (> 1500 ft) |
| VS1 | Vertical suspended, single casing | Sump drainage, low NPSH |
Selection Guidelines
- Operating range: Select pump where duty point falls at 80–110% of BEP flow
- NPSH margin: Verify adequate margin per API 610 requirements
- Speed: 1800 rpm (4-pole) typical for reliability; 3600 rpm (2-pole) for smaller pumps
- Head range: Single stage < 600 ft; multistage for higher heads (~300 ft/stage)
- Materials: 316 SS standard; higher alloys for corrosive service
- Sealing: Mechanical seal standard; API Plan 11 minimum for hydrocarbons
Pump Types by Application
| Application | Recommended Type |
|---|---|
| Pipeline transfer (< 600 ft) | Single-stage BB1 or OH1 |
| Pipeline transfer (> 600 ft) | Multistage BB3 or BB5 |
| Process circulation | ANSI centrifugal or OH2 |
| High viscosity (> 500 cP) | Positive displacement (gear, screw, PC) |
| Metering/dosing | API 674 reciprocating |
| Low NPSH available | VS1 vertical can or inducer pump |
| Slurries/solids | Recessed impeller or rubber-lined |
Affinity Laws
Relationships for speed or impeller diameter changes:
Flow: Q₂/Q₁ = (N₂/N₁) = (D₂/D₁)
Head: H₂/H₁ = (N₂/N₁)² = (D₂/D₁)²
Power: BHP₂/BHP₁ = (N₂/N₁)³ = (D₂/D₁)³
Where:
N = Speed (rpm)
D = Impeller diameter
Energy Savings: Reducing speed by 20% decreases power by ~50% (cube law). Variable frequency drives (VFDs) offer dramatic energy savings for systems with varying flow requirements.
Common Mistakes to Avoid
- ❌ Using gauge pressure instead of absolute pressure in NPSH calculations
- ❌ Forgetting to account for friction losses in suction piping
- ❌ Selecting pump at shutoff or runout (far from BEP)
- ❌ Ignoring site elevation effect on atmospheric pressure
- ❌ Using water vapor pressure for hydrocarbons
- ❌ Not verifying NPSH margin per API 610 criteria
- ❌ Forgetting velocity head in NPSH calculation
Key Standards & References
- API 610 (12th Ed, 2010) – Centrifugal Pumps for Petroleum, Petrochemical and Natural Gas Industries
- API 674 (3rd Ed, 2010) – Positive Displacement Pumps - Reciprocating
- ANSI/HI 9.6.1-2017 – Rotodynamic Pumps - Guideline for NPSH Margin
- ANSI/HI 9.6.7-2015 – Effects of Liquid Viscosity on Rotodynamic Pump Performance
- HI 1.3 – Rotodynamic Centrifugal Pumps for Design and Application
- Crane TP-410 – Flow of Fluids Through Valves, Fittings, and Pipe
- Cameron Hydraulic Data – Industry reference handbook
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