Detailed explanation of the calculation formula for the air volume of Roots blower (with calculation examples attached)**
The air volume calculation of Roots blower is the core link of equipment selection and operation management. The following are the wind volume calculation formulas for 5 different scenarios, including theoretical derivation, simplified calculation, and on-site measurement methods, with typical calculation cases attached.
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**1、 Basic theoretical formula (calculation)**
**Formula * *:
\[
Q=V_g \ times n \ times 60 \ times \ eta-v \ quad (\ text {unit: m3/min})
\]
**Parameter Description * *:
-Vg: displacement per revolution of impeller (m3/r)
-Two leaf type:\ ( V_g \approx (\pi D^2/4 - 2A)L \)
-Three leaf type:\ ( V_g \approx (\pi D^2/4 - 3A)L \)
(D: Impeller diameter, A： Single leaf cross-sectional area, L： Impeller length)
-* * n * *: Speed (r/min)
-* * η v * *: volumetric efficiency (0.85~0.95, take the lower value at high pressure)
case
Three leaf fan D=300mm, L=400mm，n=1450r/min，ηv=0.9
Calculated as:\ ( V_g \approx 0.028 \, \text{m3/r} \)，\( Q = 0.028 \times 1450 \times 60 \times 0.9 \approx 21.9 \, \text{m3/min} \)
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**2、 Power reverse calculation formula (selection estimation)**
**Formula * *:
\[
Q=\ frac {P \ times 6120 \ times \ eta} {\ Delta P} \ quad (\ text {unit: m3/min})
\]
**Parameter Description * *:
-* * P * *: Motor power (kW)
-Δ P: Import and Export Pressure Difference (kPa)
-* * η * *: Mechanical efficiency (0.6~0.75)
case
37kW fan, ΔP=49kPa，η=0.7
Calculated as:\ ( Q = \frac{37 \times 6120 \times 0.7}{49} \approx 20.1 \, \text{m3/min} \)
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**3、 Speed regulation formula (frequency conversion condition)**
**Formula * *:
\[
Q_2=Q_1 \ times \ frac {n2} {n1} \ quad (\ text {linear relationship})
\]
case
Original working condition: Q=20m3/min（n=1450r/min）
After frequency conversion: n=1200r/min
Calculated as:\ ( Q_2 = 20 \times \frac{1200}{1450} \approx 16.6 \, \text{m3/min} \)
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**4、 Gas state correction formula**
**Formula * *:
\[
Q_ {\ text {actual}}=Q_ {\ text {standard condition}} \ times \ frac {273} {273+T} \ times \ frac {P_ {\ text {atm}}}+\ Delta P} {P_ {\ text {atm}}}}
\]
**Parameter Description * *:
-* * T * *: Gas temperature (℃)
-Patm: Local atmospheric pressure (kPa)
case
Standard air flow rate of 10Nm3/min, temperature of 40 ℃, Δ P=50kPa (altitude 0m)
Calculated as:\ (Q_ {\ text {actual}}=10 \ times \ frac {273} {313} \ times \ frac {101.3+50} {101.3} \ estimate 8.7 \, \ text {m3/min} \)
---
**5、 On site measurement formula (nozzle method)**
**Formula * *:
\[
Q=1.11 \ times C \ times d ^ 2 \ times \ sqrt {\ frac {\ Delta h} {\ rho}} \ quad (\ text {unit: m3/min})
\]
**Parameter Description * *:
-* * C * *: nozzle coefficient (0.98-0.99)
-* * d * *: nozzle diameter (m)
-Δ h: Differential pressure (Pa)
-* * ρ * *: Gas density (kg/m3)
case
d=0.1m，Δh=500Pa，ρ=1.2kg/m3
Calculated as:\ ( Q \approx 1.11 \times 0.99 \times 0.1^2 \times \sqrt{\frac{500}{1.2}} \approx 12.5 \, \text{m3/min} \)
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**6、 Quick selection checklist (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 |
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**7、 Key precautions**
1. * * Pressure effect * *: The air volume decreases with the increase of back pressure (internal leakage increases under high pressure)
2. * * Altitude correction * *: For every 1000m increase in altitude, the mass air volume decreases by about 10
3. * * Temperature impact * *: The actual air volume decreases by about 12% compared to the standard condition at 40 ℃
**Typical error * *: Failure to consider changes in gas density, resulting in a smaller selection (such as high-temperature flue gas conditions). It is recommended to use the operating air volume (m3/min) instead of the standard air volume (Nm3/min) for calculation.
