Screw Pump Sizing and Capacity Calculation Guide

Sizing Process Overview

Step-by-Step Sizing

1. Define process requirements (flow, pressure, fluid)
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2. Calculate theoretical displacement needed
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3. Account for slip (volumetric efficiency)
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4. Select pump size and speed
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5. Verify NPSH and suction conditions
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6. Calculate power requirements
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7. Size motor with appropriate margin
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8. Verify cold start capability

Displacement Calculation

Theoretical Displacement

D = V / N

Where:
D = Displacement (cc/rev or L/rev)
V = Required flow rate (cc/min or L/min)
N = Rotational speed (RPM)

Accounting for Slip

D_actual = V_required / (N × ηv)

Where:
ηv = Volumetric efficiency (typically 0.85-0.95)

Example:
Required flow: 200 L/min
Speed: 1500 RPM
Expected efficiency: 90%

D_actual = 200 / (1500 × 0.90) = 0.148 L/rev = 148 cc/rev

Select next standard size: 150 cc/rev

Volumetric Efficiency

Definition

ηv = Q_actual / Q_theoretical × 100%

Where:
Q_actual = Measured output flow
Q_theoretical = Displacement × Speed

Factors Affecting Efficiency

Efficiency by Viscosity

Efficiency by Pressure

Slip Calculation

What is Slip?

Slip = Theoretical Flow - Actual Flow

Slip% = (Slip / Theoretical Flow) × 100

Or: Slip% = 100 - ηv

Slip Estimation

Slip ∝ ΔP / μ

Where:
ΔP = Differential pressure
μ = Dynamic viscosity

Simplified: S = K × ΔP / μ
K = Pump-specific constant (from manufacturer)

Practical Slip Values

Flow Rate Calculation

Basic Flow Formula

Q = D × N × ηv

Where:
Q = Flow rate (L/min or m³/h)
D = Displacement (L/rev)
N = Speed (RPM)
ηv = Volumetric efficiency (decimal)

Unit Conversions

L/min to m³/h: Multiply by 0.06
m³/h to L/min: Divide by 0.06

cc/rev to L/rev: Divide by 1000

Example Calculation

Given:
- Displacement: 100 cc/rev
- Speed: 1200 RPM
- Viscosity: 300 cSt → ηv = 92%
- Pressure: 20 bar

Q = (100/1000) × 1200 × 0.92
Q = 0.1 × 1200 × 0.92
Q = 110.4 L/min = 6.62 m³/h

Speed Selection

Speed Guidelines by Viscosity

Speed Selection Process

1. Identify viscosity range (operating and cold start)
2. Select speed based on highest viscosity expected
3. Calculate required displacement at selected speed
4. Verify flow meets requirements
5. Consider VFD for variable conditions

Power Calculation

Hydraulic Power

P_hyd = Q × ΔP / 600

Where:
P_hyd = Hydraulic power (kW)
Q = Flow rate (L/min)
ΔP = Differential pressure (bar)

Shaft Power

P_shaft = P_hyd / η_pump

Where:
η_pump = Overall pump efficiency (0.70-0.90)

η_pump = ηv × ηm
ηv = Volumetric efficiency
ηm = Mechanical efficiency (typically 0.90-0.95)

Motor Power

P_motor = P_shaft × SF

Where:
SF = Service factor

Typical SF values:
- Normal duty: 1.15
- Heavy duty: 1.20
- Variable viscosity: 1.25
- Cold start concern: 1.30

Complete Power Example

Given:
- Flow: 100 L/min
- Differential pressure: 30 bar
- Volumetric efficiency: 90%
- Mechanical efficiency: 92%

Step 1: Hydraulic power
P_hyd = 100 × 30 / 600 = 5.0 kW

Step 2: Pump efficiency
η_pump = 0.90 × 0.92 = 0.828 = 82.8%

Step 3: Shaft power
P_shaft = 5.0 / 0.828 = 6.04 kW

Step 4: Motor power (SF = 1.15)
P_motor = 6.04 × 1.15 = 6.95 kW

Select: 7.5 kW motor

NPSH Verification

NPSHa Calculation

NPSHa = (P_source - P_vapor) / (ρ × g) + H_static - H_loss

Where:
P_source = Absolute pressure at source (Pa)
P_vapor = Vapor pressure of fluid (Pa)
ρ = Fluid density (kg/m³)
g = 9.81 m/s²
H_static = Static head (m) - positive if flooded
H_loss = Suction line friction loss (m)

NPSHr for Screw Pumps

NPSH Margin

Required Margin: NPSHa ≥ NPSHr × 1.3 (minimum)

For viscous fluids: NPSHa ≥ NPSHr × 1.5
For critical service: NPSHa ≥ NPSHr × 2.0

Torque Calculation

Starting Torque

T_start = P_shaft × 9550 / N × (μ_cold / μ_hot)

Where:
T_start = Starting torque (Nm)
P_shaft = Shaft power at operating conditions (kW)
N = Speed (RPM)
μ_cold = Cold start viscosity
μ_hot = Operating viscosity

Note: Simplified - actual depends on pump design

Torque Example

Operating condition:
- P_shaft = 6 kW
- Speed = 1200 RPM
- Operating viscosity = 100 cSt

T_operating = 6 × 9550 / 1200 = 47.75 Nm

Cold start (viscosity = 500 cSt):
T_start ≈ 47.75 × (500/100)^0.5 = 47.75 × 2.24 = 107 Nm

Motor must provide adequate starting torque!

Sizing Worksheet

=== SCREW PUMP SIZING WORKSHEET ===

1. PROCESS REQUIREMENTS
Required flow: ___ L/min (___ m³/h)
Differential pressure: ___ bar
Fluid: _______________
Operating temperature: ___ °C
Operating viscosity: ___ cSt
Cold start temperature: ___ °C
Cold start viscosity: ___ cSt

2. PRELIMINARY SIZING
Target speed (based on viscosity): ___ RPM
Estimated volumetric efficiency: ___ %
Required displacement: Q / (N × ηv) = ___ cc/rev

3. PUMP SELECTION
Selected pump model: _______________
Actual displacement: ___ cc/rev
Rated speed: ___ RPM
Calculated flow: ___ L/min

4. EFFICIENCY VERIFICATION
Volumetric efficiency (vendor): ___ %
Mechanical efficiency: ___ %
Overall efficiency: ___ %

5. POWER CALCULATION
Hydraulic power: ___ kW
Shaft power: ___ kW
Service factor: ___
Motor power required: ___ kW
Selected motor: ___ kW

6. NPSH VERIFICATION
NPSHa calculated: ___ m
NPSHr (vendor): ___ m
Margin: ___ (OK if > 1.3)

7. COLD START CHECK
Cold viscosity ratio: ___ ×
Starting torque factor: ___
Motor can start? □ Yes □ No (need VFD/soft start)

8. FINAL SELECTION
Pump model: _______________
Motor: ___ kW, ___ RPM
Speed control: □ Fixed □ VFD

Quick Reference Formulas