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\begin{align}

\frac{ds}{dt} = -k_1es + (k_{-1} - k_3)c_1 + k_{-3}c_2\\

\frac{dc_1}{dt} = k_1se - (k_{-1} + k_2 + k_3s)c_1 + (k_{-3} + k_4)c_2\\

\frac{dc_2}{dt} = k_3sc_1 - (k_{-3} + k_4)c_2\\

\frac{de}{dt} = -k_1se + (k_{-1} + k_2)c_1\\

\frac{dp}{dt} = k_2c_2 + k_4c_2

\end{align}

How can I use the pi theorem to non-dimensionalize the above? I have the solution and I have read about the pi theorem but I don't understand how to use it.

I can narrow down the 5 equations to just 3.

\begin{align}

\frac{ds}{dt} =& -k_1e_0s + (k_{-1} + k_1s - k_3s)c_1 + (k_1s + k_{-3})c_2,\notag\\

\frac{dc_1}{dt} =& k_1e_0s - (k_{-1} + k_2 +k_1s +k_3s)c_1 + (k_{-3} + k_4 - k_1s)c_2,\notag\\

\frac{dc_2}{dt} =& k_3sc_1 - (k_{-3} + k_4)c_2,\notag

\end{align}

\frac{ds}{dt} = -k_1es + (k_{-1} - k_3)c_1 + k_{-3}c_2\\

\frac{dc_1}{dt} = k_1se - (k_{-1} + k_2 + k_3s)c_1 + (k_{-3} + k_4)c_2\\

\frac{dc_2}{dt} = k_3sc_1 - (k_{-3} + k_4)c_2\\

\frac{de}{dt} = -k_1se + (k_{-1} + k_2)c_1\\

\frac{dp}{dt} = k_2c_2 + k_4c_2

\end{align}

How can I use the pi theorem to non-dimensionalize the above? I have the solution and I have read about the pi theorem but I don't understand how to use it.

I can narrow down the 5 equations to just 3.

\begin{align}

\frac{ds}{dt} =& -k_1e_0s + (k_{-1} + k_1s - k_3s)c_1 + (k_1s + k_{-3})c_2,\notag\\

\frac{dc_1}{dt} =& k_1e_0s - (k_{-1} + k_2 +k_1s +k_3s)c_1 + (k_{-3} + k_4 - k_1s)c_2,\notag\\

\frac{dc_2}{dt} =& k_3sc_1 - (k_{-3} + k_4)c_2,\notag

\end{align}

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