**Detailed Explanation of the Calculation Method for Roots Fan Airflow (Theory+Example)**
The calculation of air volume for Roots blowers is a crucial step in selection, operation, and maintenance. This article will systematically introduce four methods for calculating air volume, including theoretical formulas, on-site measurement methods, selection calculation cases, and key factors affecting air volume, and provide practical solutions.
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**1、 Theoretical air volume calculation formula**
**1. Basic theoretical formula**
Roots blower belongs to positive displacement blower, and its theoretical air volume (Q) is determined by the geometric volume and speed of the impeller
\[
Q=V_g \ times n \ times 60 \ quad (\ text {unit: m3/min})
\]
-Vg: Geometric volume discharged by the impeller per revolution (m3/r)
-Two blade Roots blower: Vg ≈ (π D2/4-2A) L
-Three leaf Roots blower: Vg ≈ (π D2/4-3A) L
(D: Impeller diameter, A： Single leaf cross-sectional area, L： Impeller length)
-* * n * *: Fan speed (r/min)
**Note: The actual air volume may decrease by 5-15 due to internal leakage, which needs to be multiplied by the volumetric efficiency (η≈ 0.85~0.95).
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**2. Simplify practical formulas**
If the impeller parameters cannot be obtained, the motor power (P) and pressure (Δ P) can be used to estimate:
\[
Q ≈ \ frac {P \ times 6120 \ times \ eta} {\ Delta P} \ quad (\ text {unit: m3/min})
\]
-* * η * *: Comprehensive efficiency (usually 0.6~0.75)
-Δ P: Import and Export Pressure Difference (kPa)
---
**2、 On site air volume measurement method**
**1. Nozzle method (ISO 1217 standard)**
**Step * *:
1. Install standard nozzles (diameter d) in the outlet pipeline;
2. Measure the pressure difference Δ h (Pa) before and after the nozzle;
3. Calculate air volume:
\[
Q = 1.11 \times C \times d^2 \sqrt{\frac{\Delta h}{\rho}}
\]
-* * C * *: nozzle coefficient (0.98-0.99)
-* * ρ * *: Air density (1.2kg/m3, at 20 ℃)
case
The nozzle of a certain fan has a diameter of 100mm, Δh=500Pa， The measured Q is approximately 12.5m3/min.
---
**2. Anemometer method**
-Measure the cross-sectional wind speed v (m/s) of the pipeline using a hot wire anemometer or pitot tube;
-Calculate air volume:
\[
Q=v \ times A \ times 60 \ quad (A: cross-sectional area of the pipeline, m2)
\]
---
**3、 Selection calculation example**
**Case 1: Given power and pressure, calculate air volume**
**Requirement * *: A certain sewage treatment plant uses a 37kW Roots blower with a pressure of 49kPa, η=0.7。
**Calculation * *:
\[
Q = \frac{37 \times 6120 \times 0.7}{49} ≈ 20.1 \, \text{m3/min}
\]
**Selection * *: Choose a model with an air volume of 20m3/min (such as -200).
---
**Case 2: Given the rotational speed and impeller parameters, calculate the air volume**
**Parameter * *: Three leaf fan, Vg=0.025m3/r，n=1450r/min，η=0.9。
**Calculation * *:
\[
Q = 0.025 \times 1450 \times 60 \times 0.9 ≈ 19.6 \, \text{m3/min}
\]
---
**4、 Key factors affecting air volume**
|* * Factor * * | * * Impact Law * * | * * Solution * *|
|------------------|-----------------------------|---------------------------|
|* * Speed reduction * * | Linear decrease in air volume (Q ∝ n) | Variable frequency speed regulation or replacement of pulley|
|* * Pipeline resistance increases * * | Back pressure increases, actual air volume decreases | Clean filter/increase pipe diameter|
|* * Temperature increase * * | Air density decreases, mass air volume decreases | Increase fan speed or cool intake air|
|* * Impeller wear * * | Increased internal leakage, reduced volumetric efficiency | Replace impeller or adjust clearance|
---
**5、 Frequently Asked Questions and Answers**
**Q1: What is the difference between air volume units Nm3/min and m3/min**
-Nm3/min: Air volume under standard conditions (0 ℃, 1atm);
-* * m3/min * *: The actual airflow under working conditions needs to be converted according to the gas state equation:
\[
Q_ {\ text {actual}}=Q_ {\ text {standard}} \ times \ frac {273+T} {273} \ times \ frac {P_ {\ text {atm}}} {P_ {\ text {atm}}}+\ Delta P}
\]
(T: Temperature ℃, ΔP： Gauge pressure (kPa)
**Q2: Why does the same wind turbine have a higher air volume in winter than in summer**
-In winter, the air density is high (low temperature+dry), and the mass flow rate increases by about 5-10.
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**6、 Conclusion**
1. * * Theoretical calculation * *: Prioritize the use of the impeller volume formula (Q=Vg × n × 60 × η);
2. * * On site measurement * *: The nozzle method has the highest accuracy, while the anemometer method is the most convenient;
3. * * Selection points * *: It is necessary to calculate comprehensively based on pressure, temperature, and speed;
4. * * Maintenance suggestion * *: Regularly check the impeller clearance and pipeline resistance to avoid air volume attenuation.
**Attachment: Quick selection table (at a pressure of 49kPa)**
|Power (kW) | Theoretical air volume (m3/min) | Applicable models|
|------------|-------------------|---------------|
| 7.5 | 5~6 | CSR-80 |
| 15 | 10~12 | CSR-125 |
| 30 | 20~22 | CSR-200 |
| 55 | 40~45 | CSR-300 |
If specific model performance curves or customized calculations are required, further analysis of operating parameters can be provided.
