\documentclass{article}

\usepackage{nomencl,etoolbox,ragged2e,siunitx,mathtools}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}

\newcommand{\DimensUnits}[2]{\hfill\makebox[8em]{#1\hfill}%
\makebox[4em]{#2\hfill}\ignorespaces}
\newcommand{\DefinitionCol}[1]{\hfill\parbox[t]{12em}{#1}\ignorespaces}

\newcommand{\nomsubtitle}[1]{\item[\large\bfseries #1]}

\renewcommand\nomgroup[1]{\def\nomtemp{\csname nomstart#1\endcsname}\nomtemp}

\newcommand{\nomstartR}{\nomsubtitle{Roman Symbols}%
  \item[\bfseries Symbol]%
  \textbf{Description}\DimensUnits{\textbf{Dimensions}}{\textbf{Units}}}
\newcommand{\nomstartG}{\nomsubtitle{Greek Symbols}%
  \item[\bfseries Symbol]%
  \textbf{Description}\DimensUnits{\textbf{Dimensions}}{\textbf{Units}}}
\newcommand{\nomstartD}{\nomsubtitle{Dimensionless Numbers}%
  \item[\bfseries Symbol]\textbf{Description}\DefinitionCol{\textbf{Definition}}}

\renewcommand*{\nompreamble}{\markboth{\nomname}{\nomname}}

\newcommand{\nomdescr}[1]{\parbox[t]{4cm}{\RaggedRight #1}}
\newcommand{\nomwithdim}[5]{\nomenclature[#1]{#2}%
{\nomdescr{#3}\DimensUnits{#4}{#5}}}
\newcommand{\nomtypeR}[5][]{\nomwithdim{R#1}{#2}{#3}{#4}{#5}}
\newcommand{\nomtypeG}[5][]{\nomwithdim{G#1}{#2}{#3}{#4}{#5}}
\newcommand{\nomtypeD}[4][]{\nomenclature[D#1]{#2}{\nomdescr{#3}\DefinitionCol{#4}}}
\makenomenclature

\begin{document}
\mbox{}
\nomtypeR[abc]{\(a,b,c\)}{half axes of ellipsoid}{L}{\si{m}}
\nomtypeR[C]{\(C\)}{dimensionless coefficient (e.g.\ for drag model)}{--}{1}
\nomtypeG{\( \varepsilon_0 \)}{vacuum permittivity}{F/L}{\si{F.m^{-1}}}
\nomtypeD{\( \mathcal A_r \)}{Archimedes number}{\(\displaystyle
\frac{d^3g\rho_c\abs{\Delta\rho}}{\mu_c^2} = \sqrt{\frac{\mathcal
E_0^3}{\mathcal M_0}} \)}
\nomtypeR[CC]{\(\mathbf{C}\)}{another dimensionless coefficient}{--}{1}
\nomtypeR[A]{\(A\)}{a dimensionless coefficient}{--}{1}
\nomtypeR[Z]{\(Z\)}{a dimensionless coefficient}{--}{1}

\printnomenclature[6em]
\end{document}