opcsim.equations.cdf.vt¶

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

Evaluate the total volume of the particles between two diameters.

The CDF of the lognormal distribution is calculated using equation 8.12 from Seinfeld and Pandis.

Mathematically, it is represented as:

\[V_t=\frac{π}{6}∫_{-∞}^{∞}D_p^3n_N^e(ln D_p)d lnD_p \;\;(\mu m^3 cm^{-3})\]

Parameters

nfloat: Total aerosol number concentration 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

Volume | float: Returns the total volume of particles between \(D_{min}\) and \(D_{max}\) in units of \(\mu m^3 cm^{-3}\)

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.vt(1e3, 0.1, 1.5, dmax=2.5)