code: def vertical_velocity(omega, pressure, temperature, mixing=0):
      r
      rho = density(pressure, temperature, mixing)
      return (omega / (- mpconsts.g * rho)).to('m/s')
docs: r"""Calculate w from omega assuming hydrostatic conditions.
  
      This function converts vertical velocity with respect to pressure
      :math:`\left(\omega = \frac{Dp}{Dt}\right)` to that with respect to height
      :math:`\left(w = \frac{Dz}{Dt}\right)` assuming hydrostatic conditions on
      the synoptic scale. By Equation 7.33 in [Hobbs2006]_,
  
      .. math: \omega \simeq -\rho g w
  
      so that
  
      .. math w \simeq \frac{- \omega}{\rho g}
  
      Density (:math:`\rho`) is calculated using the :func:`density` function,
      from the given pressure and temperature. If `mixing` is given, the virtual
      temperature correction is used, otherwise, dry air is assumed.
  
      Parameters
      ----------
      omega: `pint.Quantity`
          Vertical velocity in terms of pressure
      pressure: `pint.Quantity`
          Total atmospheric pressure
      temperature: `pint.Quantity`
          Air temperature
      mixing: `pint.Quantity`, optional
          Mixing ratio of air
  
      Returns
      -------
      `pint.Quantity`
          Vertical velocity in terms of height (in meters / second)
  
      See Also
      --------
      density, vertical_velocity_pressure