opcsim.equations.cdf.st¶

opcsim.equations.cdf.st(n, gm, gsd, dmin=None, dmax=10.0)¶

Evaluate the total surface area of the particles between two diameters.

The CDF of the lognormal distribution is calculated using equation 8.11 from Seinfeld and Pandis.

Mathematically, it is represented as:

\[S_t=π∫_{-∞}^{∞}D_p^2n_N^e(ln D_p)d lnD_p \;\;(\mu m^2 cm^{-3})\]

Parameters

nfloat: Total number of particles in units of #/cc
gmfloat: Median particle diameter (geometric mean) in units of \(\mu m\).
gsdfloat: Geometric Standard Deviation of the distribution.
dminfloat: The minimum particle diameter in microns. Default value is 0 \(\mu m\).
dmaxfloat: The maximum particle diameter in microns. Default value is 10 \(\mu m\).

Returns

Surface Area | float: Returns the total surface area of particles between \(D_{min}\) and \(D_{max}\) in units of \(\mu m^2 \; cm^{-3}\)

See also

Examples

Integrate a sample distribution between 0 and 2.5 microns:

>>> d = opcsim.AerosolDistribution()
>>> d.add_mode(1e3, 100, 1.5, "mode 1")
>>> n = opcsim.equations.cdf.st(1e3, 0.1, 1.5, dmax=2.5)