Commonly Used Vacuum Calculation Formulas

1. Boyle's Law

Volume V, pressure P, and P·V = constant.

For a gas of a certain mass, when the temperature remains constant, the gas's pressure is inversely proportional to its volume.

That is, P1/P2 = V2/V1.

2. Gay-Lussac's Law

When the pressure P remains constant, the volume V of a given mass of gas is directly proportional to its absolute temperature T:

V1/V2 = T1/T2 = constant

When the pressure remains constant, for a given mass of gas, for every 1℃ increase (or decrease in P), its volume increases (or decreases) by 1/273 compared to its original volume.

3. Charles's Law

When the volume V of a gas remains constant, for a given mass of gas, the pressure P is directly proportional to its absolute temperature T, that is:

P1/P2 = T1/T2

At a constant volume, for a given mass of gas, for every 1℃ increase (or decrease) in temperature, its pressure increases (or decreases) by 1/273 compared to the original pressure.

4. Mean Free Path:

λ = (5 × 10⁻³) / P (cm)

5. Pumping speed:

S = dv/dt (liters/second) or S = Q/P

Q = Flow rate (torr·L/s) P = Pressure (torr) V = Volume (L) t = Time (s)

6. Communication and Navigation: C = Q / (P2 - P1) (liters/second)

7. Vacuum pumping time:

For the calculation formula of pumping time from atmospheric pressure to 1 Torr:

t = 8V/S (empirical formula)

V represents volume, and S represents the pumping speed; typically, t is selected within the range of 5 to 10 minutes.

8. Pump Selection for Maintenance:

S after = S before / 10

9. Estimation of the diffusion pump pumping speed:

S = 3D² (D = diameter in cm)

10. The forepump pumping speed of the Roots pump:

S = (0.1~0.2) S_Luo (l/s)

11. Leakage rate:

Q_leak = V(P2 - P1) / (t2 - t1)

Q Leakage - System leakage rate (mmHg·l/s)

V-System Volume (l)

P1 - Pressure (mmHg) in the system when the vacuum pump stops

P2 - The pressure (mmHg) reached in the vacuum chamber after time t.

t - The time (s) it takes for the pressure to rise from P1 to P2.

12. Selection of the pumping speed for the roughing pump:

S = Q1/P pre (l/s)

S = 2.3V · lg(Pa/P₀) / t

S-Mechanical pump effective pumping speed

Q1 - Vacuum System Leak Rate (Torr·L/s)

P pre - Required pre-vacuum level (Torr)

V - Vacuum system volume (liters)

t - the time required to reach P pre-time

Pa - Atmospheric pressure value (Torr)

13. Selection of the forepump pumping speed:

For transfer pumps whose exhaust port pressure is lower than one atmosphere—such as diffusion pumps, oil booster pumps, Roots pumps, and turbomolecular pumps—these pumps require a forepump during operation to maintain the forepump pressure below the critical value. The selected forepump must be capable of evacuating the maximum gas flow rate of the main pump. According to the principle that the flow rate is constant across all cross-sections in the pipeline:

PnSg≥PgS or

Sg ≥ Pgs/Pn

Sg—Effective pumping speed of the forepump (l/s)

Pn—Critical upstream pressure of the main pump (maximum exhaust pressure) (l/s)

Pg - Maximum operating pressure of the vacuum chamber (Torr)

Effective pumping speed (l/s) of the main pump when operating at Pg.

14. Formula for calculating the pumping speed of a diffusion pump:

S = Q/P = (K·n)/(P·t) (liters/second)

In the formula: S – the pumping speed of the tested pump (l/s)

Number of grid divisions the oil column rises in the n-dropper (grids)

The time (in seconds) required for the oil column to rise by n grid spaces.

P—Pressure measured near the pump inlet (torr)

K-dropper coefficient (Torr·L/s)

K = V0 · (L/n) · (Υ0/Υm) + Pa△Vt

Among them, V0—original volume (liters) of the dropper and vacuum tubing

Length of the L-dropper scale section (mm)

Number of graduations (grads) on the n-dropper scale

Υ0 - Specific gravity of oil (g/cm³)

Specific gravity of mercury (g/cm³)

Pa—Local atmospheric pressure (Torr)

△Vt—The volume (liters/graduation) corresponding to one graduation on the pipette's scale.

15. Geometric pumping speed calculation formula for rotary vane vacuum pumps:

S = πZnLKv(D² - d²) / (24 × 10⁴) (l/s)

In the formula: Z represents the number of rotor blades, n is the rotational speed (revolutions per minute), L is the length of the pump chamber, D is the diameter of the pump chamber, d is the diameter of the rotor (cm), and Kv is the volumetric utilization coefficient (generally taken as 95%).

16. The depth B of the O-ring rubber groove = 0.7D

D is the rubber diameter, and the groove width C = 1.6B.

17. The depth B of the square rubber groove = 0.8A

A is the side length of the square rubber edge, and the groove width C = 1.67B.