# Fluid Mechanics and order of magnitude calculation

#### Niles

Hi

In my lecture notes we making some calculations and all terms $\mathcal O(M^3)$ are to be thrown away. Here M is the Mach number. Now, there is the expression (u denotes the velocity):
$$uu\partial_t \rho \approx \rho_0 uu\nabla u$$
which in my notes are thrown away because they claim it is $\mathcal O(M^3)$. But is it really true, I mean the derivative of u will not necessarily be on the same order as Ma, right?

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