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There is a normalized form, though it's properly called the dimensionless Euler equations. The way to do it is define: scale time $t_0$ scale density $\rho_0$ scale length $L_0$ and then derive the scales from these: $$ v_0 = \frac{L_0}{t_0},\quad p_0=\rho_0v_0^2 $$ NB: it is possible to use other combinations, but I find that these are often the ...

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