 # Formulas

## 1 Introduction to Vacuum Technology

Formula 1-1
Barometric formula
Formula 1-2
Numerical barometric formula
Formula 1-3
Definition of pressure
Formula 1-4
Boyle-Mariotte law
Formula 1-5
Gay-Lussac’s law
Formula 1-6
General equation of state for ideal gases
Formula 1-7
Equation of state for ideal gases I
Formula 1-8
Equation of state for ideal gases II
Formula 1-9
Most probable speed
Formula 1-10
Most probable speed
Formula 1-11
Mean free path
Formula 1-12
Mean free path II
Formula 1-13
Knudsen number
Formula 1-14
Reynolds number
Formula 1-15
pV throughput
Formula 1-16
Throughput of a vacuum pump
Formula 1-17
Volume flow rate, or pumping speed, of a vacuum pumpe
Formula 1-18
Definition of conductance
Formula 1-19
Ohm’s law
Formula 1-20
Parallel connection conductance
Formula 1-21
Series connection conductivities
Formula 1-22
Blocking of an orifice
Formula 1-23
Orifice flow
Formula 1-24
Orifice conductivity
Formula 1-25
Orifice conductivity for air
Formula 1-26
Conductance of a pipe in laminar flow
Formula 1-27
Conductance of a pipe in laminar flow for air
Formula 1-28
Molecular pipe flow
Formula 1-29
Passage probability for long round pipes
Formula 1-30
Molecular pipe conductivity
Formula 1-31
Molecular pipe conductivity
Formula 1-32
Desorption rate
Formula 1-33
Desorption rate from plastics
Formula 1-34
Permeation
Formula 1-35
Leak rate
Formula 1-36
Ultimate pressure as a function of time

## 2 Basic calculations

Formula 2-1
Formula 2-2
Compression ratio of Roots pump
Formula 2-3
Compression ratio of Roots pump for laminar flow
Formula 2-4
Compression ratio of Roots pump for molecular flow
Formula 2-5
Pumping speed of Roots pumping station with overflow valve open and at high fore-vacuum pressure
Formula 2-6
Pumping speed of Roots pumping station with overflow valve closed and fore-vacuum pressure close to differential pressure
Formula 2-7
Pumping speed of Roots pumping station at high intake pressure
Formula 2-8
Pumping speed of Roots pumping station at low intake pressure
Formula 2-9
Pump-down time
Formula 2-10
Calculating the pumping speed
Formula 2-11
Gas throughput for pumping down vapors
Formula 2-12
Calculation of the condensation surface area
Formula 2-13
Base pressure of a vacuum system
Formula 2-14
Diffusion coefficient (T)

## 4 Vacuum generation

Formula 4-1
Compression ratio
Formula 4-2
Pump combination gas flow
Formula 4-3
Backflow conductance
Formula 4-4
Actual compression ratio
Formula 4-5
Pumping speed recursion formula
Formula 4-6
Water vapor tolerance
Formula 4-7
Water vapor capacity
Formula 4-8
Turbopump compression ratio
Formula 4-9
Turbopump pumping speed
Formula 4-10
Turbopump pumping speed
Formula 4-11
Specific pumping speed
Formula 4-12
Holweck stage pumping speed
Formula 4-13
Holweck stage compression ratio
Formula 4-14
Ultimate pressure

## 6 Mass spectrometers and residual gas analysis

Formula 6-1
Kinetic energy
Formula 6-2
Lorentz force
Formula 6-3
Equilibrium of forces
Formula 6-4
Formula 6-5
Formula 6-6
Stability parameter a
Formula 6-7
Stability parameter q
Formula 6-8
Stability condition U
Formula 6-9
Stability condition V
Formula 6-10
High-pass condition
Formula 6-11
RF power
Formula 6-12
Scatter
Formula 6-13
Ion current

## 8 Contamination management solutions

Formula 8-1
Surface coverage
Formula 8-2
Dose of contamination