Calculator

Gas flow status

• Viscous flow: Known as continuous flow, frequent collisions between gas molecules occur much more than collisions with the walls of pipe. Mean free path of a gas molecule is significantly shorter than the inner diameter of pipe.
• Transition flow: Known as knudsen flow, mean free path of a gas molecule is roughly equal to the inner diameter of pipe. This flow happens in between viscous flow and molecular flow.
• Molecular flow: Mean free path of a gas molecule is significantly greater than the inner diameter of pipe.

Conductance

There is the physical effect of pipe, fittings, valves in the vacuum system. All these components connected between chamber and pump are resistance to gas flow and will reduce the pumping speed of pump (S).

• Conductance of circular straight pipe for air at 20 ℃:

Viscous flow: $C_{v} = 135 (D^{4} / L) * P_{ave}$ (L/sec)

Transition flow: $C_{t} = 135 (D^{4} / L) * P_{ave} + 12.1 D^{3}/L$ (L/sec)

Molecular flow: $C_{m} = 12.1 D^{3} / L$ (L/sec)

$C_{v}$: Conductance of pipe in viscous flow
$C_{t}$: Conductance of pipe in transition flow in between viscous and molecular (L/sec)
$C_{m}$: Conductance of pipe in molecular flow
$D$: Pipe inner diameter (cm)
$P_{ave}$: Average pressure in pipe
$L$: Length of pipe (cm)

Pumping speed of pump: S

A pump name usually uses the peak pumping speed, so it can be misunderstood as having this value in all pressure ranges. But the pumping speed of pump is not a constant value.

For example, as shown below, if there is a pump named FV300, this pump has a peak pumping speed of 300 m³/hr only at ATM and does not have a value of 300 m³/hr in all pressure ranges.

Please keep in mind that the pumping speed is not a constant value, but a variable value depending on the pressure.

Effective pumping speed at chamber: S_eff

By the flow resistance in a pipe, the effective pumping speed working at chamber ($S_{eff}$) is always less than the pumping speed of pump ($S$).

$1/S_{eff}=1/S+1/C$

$S_{eff}=(S·C)/(S+C)$

$S_{eff}$: Effective pumping speed at chamber
$S$: Pumping speed of pump
$C$: Total conductance of pipe

$C$ is the total conductance of piping in the vacuum system consisted of various components such as pipes, fittings, valves.

• In serial connection, the total conductance $C$ is:

$1/C=1/C_{1}+1/C_{2}+1/C_{3}+\ldots+1/C_{N}$

• In parallel connection, the total conductance $C$ is:

$C=C_{1}+C_{2}+C_{3}+C_{4}+\ldots+C_{N}$

Vacuum throughput (flow/pressure) calculation

The chamber pressure estmation according to the gas flow rate is one of the important tasks in configuring and designing a vacuum system. Through the throughput simulation of the configured system, it can be estimated whether the chamber pressure is maintained lower than the desired pressure. Gas is based on N2 at room temp.

Formula

It is used the equation below to calculate throughput (flow/pressure):

$Q=P·S_{eff}$

$Q$: Throughput
$S_{eff}$: Effective pumping speed at chamber
$P$: Pressure

Note: The effective pumping speed at chamber (S) is actual pumping speed working at chamber combined with pumping speed of pump (S) and total conductance of pipe (C).

Vacuum throughput (flow/pressure) manual calculation
w/o pipe conductance

• Pump: FV300
• Requirement: maintain ≤ 50 mbar chamber pressure under 50 slm gas flow

Calculation with pumping speed

$Q=P·S_{eff}$

$Q1=1.0E+03·3.0E+02=3.0E+05\ \mathrm{mbar}·\mathrm{m^{3}/hr}=4.9E+03\ \mathrm{slm}$

$Q2=6.0E+01·2.3E+02=1.4E+04\ \mathrm{mbar}·\mathrm{m^{3}/hr}=2.3E+02\ \mathrm{slm}$

$Q3=2.0E+00·1.5E+02=3.0E+02\ \mathrm{mbar}·\mathrm{m^{3}/hr}=4.9E+00\ \mathrm{slm}$

$Q5=2.0E-01·8.0E+01=1.6E+01\ \mathrm{mbar}·\mathrm{m^{3}/hr}=2.6E-01\ \mathrm{slm}$

$Q5=8.0E-02·4.0E+01=3.2E+00\ \mathrm{mbar}·\mathrm{m^{3}/hr}=5.3E-02\ \mathrm{slm}$

$Q6=5.2E-02·1.0E+01=5.2E-01\ \mathrm{mbar}·\mathrm{m^{3}/hr}=8.6E-03\ \mathrm{slm}$

$Q7=5.0E-02·1.0E+00=5.0E-02\ \mathrm{mbar}·\mathrm{m^{3}/hr}=8.2E-04\ \mathrm{slm}$

• Requirement: maintain ≤ 50 mbar chamber pressure under 50 slm gas flow
• With FV300, the estimated chamber pressure under 50 slm gas flow will be 15 mbar. So it meets the requirement. By the valve opening control, 50 mbar at chamber under 50 slm gas flow can be achievable.
• Direct connection between chamber and pump without pipe connection, S= S

Vacuum throughput (flow/pressure) manual calculation
w/ pipe conductance

• Pump: FV300
• Pipe: 500 m³/hr (constant conductance*)
• Requirement: maintain ≤ 50 mbar chamber pressure under 50 slm gas flow

$S_{eff}=(S·C)/(S+C)$

$S_{eff}@1.0E+03\ \mathrm{mbar}=188\ \mathrm{m^{3}/hr}$

$S_{eff}@6.0E+01\ \mathrm{mbar}=158\ \mathrm{m^{3}/hr}$

$S_{eff}@2.0E+00\ \mathrm{mbar}=115\ \mathrm{m^{3}/hr}$

$S_{eff}@2.0E-01\ \mathrm{mbar}=69\ \mathrm{m^{3}/hr}$

$S_{eff}@8.0E-02\ \mathrm{mbar}=37\ \mathrm{m^{3}/hr}$

$S_{eff}@5.2E-02\ \mathrm{mbar}=9.8\ \mathrm{m^{3}/hr}$

$S_{eff}@5.2E-02\ \mathrm{mbar}=0.99\ \mathrm{m^{3}/hr}$

Throughput calculation with effective pumping speed

$Q=P·S_{eff}$

$Q1=1.0E+03*1.88E+02=1.9E+05\ \mathrm{mbar}·\mathrm{m^{3}/hr}=3.1E+03\ \mathrm{slm}$

$Q2=6.0E+01*1.58E+02=9.5E+04\ \mathrm{mbar}·\mathrm{m^{3}/hr}=1.6E+02\ \mathrm{slm}$

$Q3=2.0E+00*1.15E+02=2.3E+02\ \mathrm{mbar}·\mathrm{m^{3}/hr}=3.8E+00\ \mathrm{slm}$

$Q4=2.0E-01*6.90E+01=1.4E+01\ \mathrm{mbar}·\mathrm{m^{3}/hr}=2.3E-01\ \mathrm{slm}$

$Q5=8.0E-02*3.70E+01=3.0E+00\ \mathrm{mbar}·\mathrm{m^{3}/hr}=4.9E-02\ \mathrm{slm}$

$Q6=5.2E-02*9.8E+00=5.1E-01\ \mathrm{mbar}·\mathrm{m^{3}/hr}=8.4E-03\ \mathrm{slm}$

$Q7=5.0E-02*9.9E-01=5.0E-02\ \mathrm{mbar}·\mathrm{m^{3}/hr}=8.2E-04\ \mathrm{slm}$

• Requirement: maintain ≤ 50 mbar chamber pressure under 50 slm gas flow
• With FV300 and 500 m³/hr pipe, the estimated chamber pressure under 50 slm gas flow will be 20 mbar. So it meets the requirement. By the valve opening control, 50 mbar at chamber under 50 slm gas flow can be achievable.
• The pipe conductance, 500 m³/hr is considered as a constant value in all pressure range. So the pump throughput calculation in this way is much closer than the previous way but still gap from the reality.
• Conductance of pipes are variable values depend on pressure with normally 3 different gas flow status. $C_{v}$, $C_{t}$, $C_{m}$ should be considered for more accurate calculation of pipe conductance.