code: def vertical_velocity_pressure(w, pressure, temperature, mixing=0):
      r
      rho = density(pressure, temperature, mixing)
      return (- mpconsts.g * rho * w).to('Pa/s')
docs: r"""Calculate omega from w assuming hydrostatic conditions.
  
      This function converts vertical velocity with respect to height
      :math:`\left(w = \frac{Dz}{Dt}\right)` to that
      with respect to pressure :math:`\left(\omega = \frac{Dp}{Dt}\right)`
      assuming hydrostatic conditions on the synoptic scale.
      By Equation 7.33 in [Hobbs2006]_,
  
      .. math: \omega \simeq -\rho g w
  
      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
      ----------
      w: `pint.Quantity`
          Vertical velocity in terms of height
      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 pressure (in Pascals / second)
  
      See Also
      --------
      density, vertical_velocity