How do I use mathmode in tables to write physics formulae?

As mentioned in my comment, \n is not a defined LaTeX macro. I am assuming it was a typo intended as _n. Also, \cdotd should be \cdot d, as appears earlier in your example.

As an aside, I used \dfrac (from the amsmath package) and \arraystretch to make it look better (to my point of view). Also, heeding egreg's suggestion, \mathit{Nu} and \mathit{Re} have been employed.

In the following MWE, I perform the result twice, the first time using tabular and the second time, using array (and tabularx package), as suggested by Au101. The output is the same, but one input syntax may be preferable to the other.

\documentclass{article}
\usepackage{amsmath,tabularx}
\begin{document} 

\begin{table}[]
\centering
\label{my-label}
\renewcommand\arraystretch{1.4}
\begin{tabular}{lr}
Drehmoment               & $ M = l\cdot F $                                  \\
Leistung                 & $ P = \mathit{Ne}\cdot \rho_n^{3}\cdot d_{R}^{5} $         \\
                         & $ P=M\cdot \omega=M\cdot 2\pi \cdot n $           \\
Newtonzahl               & $ \mathit{Ne}=\dfrac{P}{n^{2}\cdot d_{R}^{5}\cdot \rho} $   \\
                         & $ \mathit{Ne}=f(\mathit{Re}) $                                      \\
Reynoldszahl             & $ \mathit{Re}=\dfrac{n\cdot d_{R}^{2} \cdot \rho}{\eta} $    \\
Mischzeit                & $ t_{m}=t_{e}-t_{a} $                             \\
Dimensionslose Mischzeit & $ T_{M}=t_{m}\cdot n $                            \\                     
\end{tabular}

\[
\begin{array}{>{$}l<{$}r}
Drehmoment               &  M = l\cdot F                                   \\
Leistung                 &  P = \mathit{Ne}\cdot \rho_n^{3}\cdot d_{R}^{5}          \\
                         &  P=M\cdot \omega=M\cdot 2\pi \cdot n            \\
Newtonzahl               &  \mathit{Ne}=\dfrac{P}{n^{2}\cdot d_{R}^{5}\cdot \rho}    \\
                         &  \mathit{Ne}=f(\mathit{Re})                                       \\
Reynoldszahl             &  \mathit{Re}=\dfrac{n\cdot d_{R}^{2} \cdot \rho}{\eta}     \\
Mischzeit                &  t_{m}=t_{e}-t_{a}                              \\
Dimensionslose Mischzeit &  T_{M}=t_{m}\cdot n                             \\                     
\end{array}
\]
\end{table}

\end{document}

My mathematician's eyes bleed when seeing all those \cdot symbols. ;-)

A couple of suggestions: define macros for the Newton and Reynolds numbers, that replace \mathit{Ne} and \mathit{Re}. When such a symbol is preceded or followed by another factor, separate them with \,.

With booktabs and a “phantom” trick you can achieve equal height for all rows. I'd much prefer left alignment for the formulas.

A table should have its caption.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\usepackage[ngerman]{babel}
\usepackage{amsmath}
\usepackage{booktabs,array}

\newcommand{\NZ}{\mathit{Ne}} % Newton number
\newcommand{\RZ}{\mathit{Re}} % Reynolds number

\begin{document} 

\begin{table}[htp]
\centering
\caption{Physikalische Formeln\label{my-label}}

\begin{tabular}{l >{$}l<{\vphantom{\dfrac{R^2}{y}}$}}
\toprule
Drehmoment               & M = l F                               \\
Leistung                 & P = \NZ\, \rho_n^{3} d_{R}^{5}        \\
                         & P = M \omega = 2\pi M n               \\
Newtonzahl               & \NZ = \dfrac{P}{n^{2} d_{R}^{5} \rho} \\
                         & \NZ = f(\RZ)                          \\
Reynoldszahl             & \RZ =\dfrac{n d_{R}^{2} \rho}{\eta}   \\
Mischzeit                & t_{m}=t_{e}-t_{a}                     \\
Dimensionslose Mischzeit & T_{M}=t_{m} n                         \\
\bottomrule
\end{tabular}

\end{table}

\end{document}

Just for the sake of variety, here's still another suggestion for how you might typeset the table. In particular, I suggest separating the symbol and the defining formula (formulae in two cases) in separate columns. I further suggest that you right-align rather than left-align the text column and left-align the material in the third column.

Finally, I also suggest fine-tuning the appearance of the d_R term, specifically, snugging up the R to the d via a \! (negative thinspace) directive.

\documentclass{article}
\usepackage{array} % for \newcolumntype macro
\newcolumntype{C}{>{$\displaystyle}c<{$}}
\newcolumntype{L}{>{$\displaystyle}l<{$}}
% Macros for typesetting "Ne" and "Re" in upright Roman (math) font
\newcommand\Ne{\mathrm{Ne}}
\renewcommand\Re{\mathrm{Re}}
\begin{document}
\begin{table}
\renewcommand\arraystretch{1.5}
\centering
\begin{tabular}{rCL}
Drehmoment            & M  & l\cdot F            \\
Leistung              & P  & \Ne\cdot \rho \cdot n^{3}\cdot d_{\!R}^{5} \\
                      &    & M \cdot \omega=M\cdot 2\pi \cdot n         \\[1ex]
Newtonzahl            &\Ne & \frac{P}{n^{2}\cdot d_{\!R}^{5}\cdot \rho} \\[1ex]
                      &    & f(\Re)                                     \\[1ex]
Reynoldszahl          &\Re & \frac{n\cdot d_{\!R}^{2} \cdot \rho}{\eta} \\[1ex]
Mischzeit             &t_m & t_{e}-t_{a}         \\
Dimensionslose Mischzeit & T_{M} & t_{m}\cdot n  \\                     
\end{tabular}
\end{table}
\end{document}