Roots Blower Displacement

Roots blower displacement is the fixed volume of air trapped and moved per revolution – the fundamental characteristic that defines a positive displacement machine. Displacement is determined by rotor geometry (lobe profile, diameter, and length). It determines theoretical flow at a given speed. Actual flow is displacement × RPM, minus slipback losses.

Based on field data, understanding displacement is essential for blower selection, capacity calculation, and performance analysis. This guide covers displacement definition, calculation, factors affecting displacement, and practical applications.

Table of Contents

• What Is Roots Blower Displacement?

• How Displacement is Determined

• Theoretical vs Actual Flow

• Displacement and Speed

• Factors Affecting Displacement

• Displacement and Efficiency

• Displacement vs Pressure

• Selection Guide

• Frequently Asked Questions

• Final Thoughts

What Is Roots Blower Displacement?

Roots blower displacement is the fixed volume of air trapped between the rotors and casing and moved from inlet to discharge with each revolution. It is the fundamental characteristic of positive displacement machines – the volume per revolution is fixed by rotor geometry.

Key concepts:

• Displacement is fixed – determined by rotor design

• Theoretical flow = displacement × RPM

• Actual flow = theoretical flow – slipback losses

• Displacement is independent of pressure

Based on field data, displacement is the starting point for blower sizing. It determines the blower's capacity at a given speed. Understanding displacement is essential for proper blower selection.

How Displacement is Determined

Displacement is determined by:

1. Rotor lobe profile.

• Number of lobes (2 or 3)

• Lobe shape (straight or helical)

• Lobe geometry

2. Rotor diameter.

• Larger diameter = more displacement

• Typical: 100–500 mm

3. Rotor length.

• Longer rotors = more displacement

• Typical: 100–500 mm

4. Casing geometry.

• Matches rotor profile

• Creates sealed volume

Displacement formula:
Displacement (ft³/rev) = rotor area × rotor length × number of lobes per revolution

For a typical 3-lobe rotor, displacement is approximately:

• 200 mm diameter, 300 mm length: 0.65 ft³/rev

• 300 mm diameter, 400 mm length: 1.5 ft³/rev

• 400 mm diameter, 500 mm length: 3.0 ft³/rev

Theoretical flow:
Theoretical flow (ACFM) = displacement (ft³/rev) × RPM

Example:
Displacement = 0.65 ft³/rev, RPM = 1,800
Theoretical flow = 0.65 × 1,800 = 1,170 ACFM

Theoretical vs Actual Flow

Theoretical flow:

• Displacement × RPM

• No losses

• Maximum possible flow

Actual flow:

• Theoretical flow – slipback losses

• Slipback increases with pressure

• Slipback increases with clearance

Slipback:

• Air leaks through tip clearance

• From discharge back to inlet

• Increases with pressure

• Increases with clearance

Actual flow formula:
Actual flow = displacement × RPM – slipback

Typical values:

• At 5 psig: actual flow = 98% of theoretical

• At 8 psig: actual flow = 95–97% of theoretical

• At 12 psig: actual flow = 92–95% of theoretical

• At 15 psig: actual flow = 88–92% of theoretical

Example:
Displacement = 0.65 ft³/rev, RPM = 1,800, pressure = 8 psig
Theoretical flow = 1,170 ACFM
Slipback = 40 ACFM (3.5%)
Actual flow = 1,130 ACFM

Displacement and Speed

Flow is proportional to speed:
Flow = displacement × RPM

• Doubling speed doubles flow

• Reducing speed reduces flow

• Linear relationship

Speed ranges:

• Typical: 1,000–3,000 RPM

• Maximum: depends on blower size

• VFD: 30–100% speed

Speed vs flow example:

Why this matters:

• VFD controls flow by changing speed

• Flow is proportional to speed – linear control

• Displacement is fixed – speed determines flow

Factors Affecting Displacement

What affects displacement:

1. Rotor geometry (fixed).

• Determined at manufacture

• Cannot be changed

• Larger blowers have more displacement

2. Rotor wear (decreases displacement).

• Wear reduces lobe volume

• Increases clearance

• Reduces effective displacement

3. Coating (increases effective displacement).

• Coating restores clearance

• Hard chrome extends life

• Maintains displacement

4. Temperature (minor effect).

• Thermal expansion changes clearances

• Affects slipback more than displacement

What does NOT affect displacement:

• Pressure (displacement is fixed)

• Speed (displacement is fixed)

• Temperature (minor effect)

Displacement vs clearance:

• Clearance does not change displacement

• Clearance affects slipback (actual flow)

• Tighter clearance = less slipback = more actual flow

Displacement and Efficiency

How displacement affects efficiency:

1. Volumetric efficiency.
ηv = actual flow / theoretical flow × 100%

• New blower: 92–96%

• Worn blower: 85–90%

2. Slipback loss.

• Increases with clearance

• Increases with pressure

• Reduces actual flow

3. Displacement utilization.

• Actual flow = displacement × RPM × ηv

• ηv decreases with pressure and wear

Example:
Displacement = 0.65 ft³/rev, RPM = 1,800
Theoretical flow = 1,170 ACFM
ηv = 95%
Actual flow = 1,170 × 0.95 = 1,112 ACFM

Efficiency impact:

• 10% efficiency loss = 10% flow loss

• Flow loss = capacity loss

• Capacity loss = process impact

Displacement vs Pressure

Displacement is independent of pressure:

• Displacement is fixed

• Pressure does not change displacement

• Pressure affects slipback (actual flow)

Pressure effect on actual flow:

Key insight:

• Displacement is fixed – pressure does not change it

• Slipback increases with pressure – actual flow drops

• Higher pressure = lower actual flow (same speed)

Selection Guide

Using displacement for selection:

Step 1 – Determine required flow.
ACFM at operating conditions.

Step 2 – Select blower size.
Choose displacement that delivers required flow at available speed.

Step 3 – Verify at operating pressure.
Account for slipback – actual flow = displacement × RPM – slipback.

Step 4 – Check speed range.
Speed must be within blower range (1,000–3,000 RPM typical).

Step 5 – Confirm with manufacturer.
Manufacturer capacity charts show actual flow at pressure.

Selection example:

• Required flow: 1,000 ACFM at 8 psig

• Blower displacement: 0.65 ft³/rev

• Required RPM: 1,000 / (0.65 × 0.95) = 1,619 RPM

• Select blower with speed range including 1,619 RPM

Frequently Asked Questions

1. What is roots blower displacement?
Displacement is the fixed volume of air trapped and moved per revolution. It is determined by rotor geometry – lobe profile, diameter, and length. Displacement is fixed at manufacture and does not change with pressure or speed.

2. How is displacement calculated?
Displacement (ft³/rev) = rotor area × rotor length × number of lobes per revolution. For a typical 200 mm rotor, displacement is 0.5–0.8 ft³/rev. Larger rotors have more displacement.

3. How does displacement affect flow?
Flow = displacement × RPM. Doubling speed doubles flow. Flow is proportional to speed – linear relationship. VFD controls flow by changing speed.

4. What is the difference between theoretical and actual flow?
Theoretical flow = displacement × RPM (no losses). Actual flow = theoretical flow – slipback (leakage through tip clearance). Slipback increases with pressure and clearance. Actual flow is less than theoretical.

5. Does pressure affect displacement?
No – displacement is fixed. Pressure does not change displacement. Pressure affects slipback – higher pressure = more slipback = less actual flow.

6. Does speed affect displacement?
No – displacement is fixed. Speed affects flow – flow = displacement × RPM. Displacement is constant; speed determines flow.

7. How does rotor wear affect displacement?
Rotor wear increases clearance and reduces effective displacement. Worn rotors have more slipback. Actual flow decreases. Replace rotors when clearance >0.35 mm.

8. How is displacement related to blower size?
Larger blowers have more displacement. Displacement increases with rotor diameter and length. Displacement determines flow capacity at a given speed.

9. What is the typical displacement of a roots blower?
Depends on blower size. 200 mm rotor: 0.5–0.8 ft³/rev. 300 mm rotor: 1.0–1.5 ft³/rev. 400 mm rotor: 2.0–3.0 ft³/rev. Check manufacturer data.

10. How does displacement affect efficiency?
Volumetric efficiency = actual flow / theoretical flow × 100%. Tighter clearance = less slipback = higher efficiency. Displacement itself does not change – clearance affects slipback.

11. What is the relationship between displacement and horsepower?
Power = flow × pressure / efficiency. Displacement determines flow at a given speed. Higher displacement = more flow = more power (at same pressure).

12. Can displacement be increased?
No – displacement is fixed by rotor geometry. To increase flow, increase speed. To increase capacity, select larger blower. Displacement cannot be changed without replacing rotors.

13. How does temperature affect displacement?
Temperature has minor effect – thermal expansion changes clearances, affecting slipback. Displacement itself is essentially constant. Temperature correction is for flow measurement (ACFM vs SCFM).

14. What is the difference between displacement and displacement volume?
Same concept. Displacement is volume per revolution. Displacement volume is total volume trapped and moved. Used interchangeably.

15. How do I select a blower based on displacement?
Calculate required flow at operating conditions. Account for slipback (pressure loss). Select displacement and speed that deliver required flow. Use manufacturer capacity charts for accurate selection.

Final Thoughts

After decades of roots blower displacement analysis, here is my practical advice:

Displacement is fixed. It is determined by rotor geometry – lobe profile, diameter, and length. Displacement does not change with pressure, speed, or operating conditions. It is the fundamental characteristic of positive displacement machines.

Flow = displacement × RPM. Flow is proportional to speed. VFD controls flow by changing speed. Linear relationship – easy to control.

Slipback affects actual flow. Displacement determines theoretical flow. Slipback (leakage through clearance) reduces actual flow. Tighter clearance = less slipback = more actual flow. Replace worn rotors to maintain flow.

The bottom line. Roots blower displacement is the foundation of blower sizing and selection. Zhanggu and other manufacturers provide displacement data for their blowers. Use displacement to calculate theoretical flow. Account for slipback to determine actual flow. The investment in correct sizing pays back through reliable operation.