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    p=\frac{F}{A}

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    Gas type
    Chem. Formula
    Volume %
    Partial pressure [hPa]
    Nitrogen
    N2
    78.09
    780.9
    Oxygen
    O2
    20.95
    209.5
    Water vapor
    H2O
    < 2.3
    < 23.3
    Argon
    Ar
    9.3·10 -1
    9.3
    Carbon dioxide
    CO2
    3.0·10-2
    3.0·10-1
    Neon
    Ne
    1.8·10 -3
    1.8·10-2
    Hydrogen
    H2
    < 1·10-3
    < 1·10-2
    Helium
    He
    5.0·10 -4
    5.0·10-3
    Methan
    CH4
    2.0·10-4
    2.0·10-3
    Krypton
    Kr
    1.1·10 -4
    1.1·10-3
    Carbon monoxide
    CO
    < 1.6·10-5
    < 1.6·10-4
    Xenon
    Xe
    9.0·10 -6
    9.0 . 10-5
    Nitrous oxide
    N2O
    5.0·10 -6
    5.0·10-5
    Ammonia
    NH3
    2.6·10-6
    2.6·10-5
    Ozone
    O3
    2.0·10-6
    2.0·10-5
    Hydrogen peroxide
    H2O 2
    4.0·10-8
    4.0·10-7
    Iodine
    I2
    3.5·10-9
    3.5·10-8
    Radon
    Rn
    7.0·10 -18
    7.0·10-17

    Pressure range
    Pressure hPa
    Pressure Pa
    Number density per cm3
    Mean free path in m
    Atmospheric pressure
    1,013.25
    101,325
    2.7·1019
    6.8·10-8
    Low vacuum (LV)
    300…1
    30,000…100
    1019…1016
    10-8…10-4
    Medium vacuum (MV)
    1…10-3
    100…10-1
    1016 …1013
    10-4…10-1
    High vacuum (HV)
    10-3…10-8
    10-1…10-6
    1013…108
    10-1…104
    Ultra-high vacuum (UHV)
    10-8…10-11
    10-6…10-9
    108…105
    104…107
    Extremely high vacuum (XHV)
    <10-11
    <10-9
    <105
    >107

     
    Pa
    bar
    hPa
    µbar
    Torr
    micron
    atm
    at
    mm WS
    psi
    psf
    Pa
    1
    1·10-5
    1·10-2
    10
    7.5·10-3
    7.5
    9.87·10-6
    1.02·10-5
    0.102
    1.45·10-4
    2.09·10-2
    bar
    1·105
    1
    1·103
    1·106
    750
    7.5·105
    0.987
    1.02
    1.02·104
    14.5
    2.09·103
    hPa
    100
    1·10-3
    1
    1,000
    0.75
    750
    9.87·10-4
    1.02·10-3
    10.2
    1.45·10-2
    2.09
    µbar
    0.1
    1·10-6
    1·10-3
    1
    7.5·10-4
    0.75
    9.87·10-7
    1.02·10-6
    1.02·10-6
    1.45·10-5
    2.09·10-3
    Torr
    1.33·102
    1.33·10-3
    1.33
    1,330
    1
    1,000
    1.32·10-3
    1.36·10-3
    13.6
    1.93·10-2
    2.78
    micron
    0.133
    1.33·10-6
    1.33·10-3
    1.33
    1·10-3
    1
    1.32·10-6
    1.36·10-6
    1.36·10-2
    1.93·10-5
    2.78·10-3
    atm
    1.01·105
    1.013
    1,013
    1.01·106
    760
    7.6·105
    1
    1.03
    1.03·104
    14.7
    2.12·103
    at
    9.81·104
    0.981
    981
    9.81·105
    735.6
    7.36·105
    0.968
    1
    1·10-4
    14.2
    2.04·103
    mm WS
    9.81
    9.81·10-5
    9.81·10-2
    98.1
    7.36·10-2
    73.6
    9.68·10-5
    1·10-4
    1
    1.42·10-3
    0.204
    psi
    6.89·103
    6.89·10-2
    68.9
    6.89·104
    51.71
    5.17·104
    6.8·10-2
    7.02·10-2
    702
    1
    144
    psf
    47.8
    4.78·10-4
    0.478
    478
    0.359
    359
    4.72·10-4
    4.87·10-4
    4.87
    6.94·10-3
    1

    p\cdot V=\mbox{const.}

    V=\mbox{const.}\cdot T

    p\cdot V=\frac{m}{M}\cdot R\cdot T

    p\cdot V=\frac{N}{N_{A}}\cdot R\cdot T=N\cdot k\cdot T\quad\mbox{where }k=\frac{R}{N_{A}}

    p=n\cdot k\cdot T

    c_{w}=\sqrt{\frac{2\cdot R\cdot T}{M}}\quad\mbox{oder}\quad c_{w}=\sqrt{\frac{2\cdot k\cdot T}{m}}

    \overline{c}=\sqrt{\frac{8\cdot R\cdot T}{\pi\cdot M}}\quad\mbox{oder}\quad\overline{c}=\sqrt{\frac{8\cdot k\cdot T}{\pi\cdot m}}

    Gas
    Chemical Symbol
    Molar Mass [g mol-1]
    Mean Velocity [m s-1]
    Mach Number
    Hydrogen
    H2
    2
    1,754
    5.3
    Helium
    He
    4
    1,245
    3.7
    Water vapor
    H2O
    18
    585
    1.8
    Nitrogen
    N2
    28
    470
    1.4
    Air
     
    29
    464
    1.4
    Argon
    Ar
    40
    394
    1.2
    Carbon dioxide
    CO2
    44
    375
    1.1

  • 1_2_img_1_4_mean_free_path_between_two_collisions

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    \bar{l}=\frac{k\cdot T}{\sqrt2\cdot\pi\cdot p\cdot d_{m}^2}

    \bar{l}\cdot p=\frac{k\cdot T}{\sqrt2\cdot\pi\cdot d_{m}^2}

    Gas
    Chemical Symbol
    𝑙¯⋅𝑝
    [m hPa]
    𝑙¯⋅𝑝
    [m Pa]
    Hydrogen
    H2
    11.5·10-5
    11.5·10-3
    Nitrogen
    N2
    5.9·10-5
    5.9·10-3
    Oxygen
    O2
    6.5·10-5
    6.5·10-3
    Helium
    He
    17.5·10-5
    17.5·10-3
    Neon
    Ne
    12.7·10-5
    12.7·10-3
    Argon
    Ar
    6.4·10-5
    6.4·10-3
    Air
     
    6.7·10-5
    6.7·10-3
    Krypton
    Kr
    4.9·10-5
    4.9·10-3
    Xenon
    Xe
    3.6·10-5
    3.6·10-3
    Mercury
    Hg
    3.1·10-5
    3.1·10-3
    Water vapor
    H2O
    6.8·10-5
    6.8·10-3
    Carbon monoxide
    CO
    6.8·10-5
    6.0·10-3
    Carbon dioxide
    CO2
    4.0·10-5
    4.0·10-3
    Hydrogen chloride
    HCl
    3.3·10-5
    3.3·10-3
    Ammonia
    NH3
    3.2·10-5
    3.2·10-3
    Chlorine
    Cl2
    2.1·10-5
    2.1·10-3

    Pressure [Pa]
    Pressure [hPa]
    Mean free path [m]
    1·105
    1·103
    5.9·10-8
    1·104
    1·102
    5.9·10-7
    1·103
    1·101
    5.9·10-6
    1·102
    1·100
    5.9·10-5
    1·101
    1·10-1
    5.9·10-4
    1·100
    1·10-2
    5.9·10-3
    1·10-1
    1·10-3
    5.9·10-2
    1·10-2
    1·10-4
    5.9·10-1
    1·10-3
    1·10-5
    5.9·100
    1·10-4
    1·10-6
    5.9·101
    1·10-5
    1·10-7
    5.9·102
    1·10-6
    1·10-8
    5.9·103
    1·10-7
    1·10-9
    5.9·104
    1·10-8
    1·10-10
    5.9·105
    1·10-9
    1·10-11
    5.9·106
    1·10-10
    1·10-12
    5.9·107

  • 1_2_img_1_5_molecular_number_density

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    \mathit{Kn}=\frac{\bar{l}}{d}

  • 1_2_img_1_6_profiles_of_various_types_of_flow_regimes

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    Re=\frac{\rho\cdot\nu\cdot l}{\eta}

  • 1_2_img_1_7_flow_ranges_in_vacuum_as_function_of_p___d

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    Viscous flow
    Knudsen flow
    Molecular flow
     
    Low vacuum
    Medium vacuum
    High / Ultra-high vacuum
    Pressure range [hPa]
    103…1
    1…10-3
    < 10-3 bzw. < 10-7
    Pressure range [Pa]
    105…10 2
    102…10 -1
    < 10-1 bzw. < 10-5
    Knudsen number
    Kn < 0.01
    0.01 < Kn < 0.5
    Kn > 0.5
    Reynolds number

    Re < 2,300: laminar
    Re > 4,000: turbulent
     
     
    p · d [hPa cm]
    p · d > 0.6
    0.6 > p · d > 0.01
    p · d < 0.01

    q_{pV}=\frac{p\cdot V}{t}=\frac{m\cdot R\cdot T}{M\cdot t}

    q_{pV}=S\cdot p=\frac{dV}{dt}\cdot p

    S=\frac{dV}{dt}

     
    Pa m3 / s = W
    mbar l / s
    Torr l / s
    atm cm3 / s
    lusec
    sccm
    slm
    Mol / s
    Pa m3 / s
    1
    10
    7.5
    9.87
    7.5·103
    592
    0.592
    4.41·10-4
    mbar l / s
    0.1
    1
    0.75
    0.987
    750
    59.2
    5.92·10-2
    4.41·10-5
    Torr l / s
    0.133
    1.33
    1
    1.32
    1,000
    78.9
    7.89·10-2
    5.85·10-5
    atm cm3 / s
    0.101
    1.01
    0.76
    1
    760
    59.8
    5.98·10-2
    4.45·10-5
    lusec
    1.33·10-4
    1.33·10-3
    10-3
    1.32·10-3
    1
    7.89·10-2
    7.89·10-5
    5.86·10-8
    sccm
    1.69·10-3
    1.69·10-2
    1.27·10-2
    1.67·10-2
    12.7
    1
    10-3
    7.45·10-7
    slm
    1.69
    16.9
    12.7
    16.7
    1.27·104
    1,000
    1
    7.45·10-4
    Mol / s
    2.27·103
    2.27·104
    1.7·104
    2.24·104
    1.7·107
    1.34·106
    1.34·103
    1

    C=\frac{l}{W}=\frac{q_{pV}}{\Delta p}

    R=\frac{U}{I}\mbox{ or }\frac{1}{R}=\frac{I}{U}

    C_{\mbox{ges}}=C_1+C_2+...+C_{n}

    \frac{1}{C_{\mbox{ges}}}=\frac{1}{C_1}+\frac{1}{C_2}+...+\frac{1}{C_{n}}

  • 1_2_img_1_8_conductance_smooth_round_pipe_as_function_of_mean_pressure_in_pipe

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    q_{pV}=15.7\cdot d^2\cdot p_{a}

    q_{pV}=A\cdot\frac{\bar{c}}{4}\cdot(p_1-p_2)

    C_{\mathrm{or,\,mol}}=A\cdot\frac{\bar{c}}{4}=A\cdot\sqrt{\frac{kT}{2\pi m_0}}

    q_{pV}=A\cdot\frac{\bar{c}}{4}\cdot(p_1-p_2)

    C_{\mathrm{pipe,\,lam}}=\frac{\pi\cdot d^4}{256\cdot\eta\cdot l}\cdot(p_1+p_2)=\frac{\pi\cdot d^4}{128\cdot\eta\cdot l}\cdot\bar{p}

    q_{pV}=A\cdot\frac{\bar{c}}{4}\cdot(p_1-p_2)

    C_{\mathrm{pipe,\,mol}}=C_{\mathrm{orifice,\,mol}}\cdot P_{\mathrm{pipe,\,mol}}

    P_{\mathrm{pipe,\,mol}}=\frac43\cdot\frac{d}{l}

    C_{\mathrm{pipe,\,mol}}=\frac{\bar{c}\cdot\pi\cdot d^3}{12\cdot l}

    C_{\mathrm{pipe,\,mol}}=12.1\cdot\frac{d^3}{l}