= Reduced pressure in a rotating fluid
{title2=$P=p+\rho\Phi-\rho|\boldsymbol\Omega\times\mathbf x|^2/2$}
For constant <density> and a <conservative force> per mass $-\nabla\Phi$, gravity and centrifugal acceleration can be incorporated into the displayed reduced pressure. The resulting <Euler equations> in rotating axes are $\mathbf u_t+(\mathbf u\cdot\nabla)\mathbf u+2\boldsymbol\Omega\times\mathbf u=-\nabla P/\rho$. The sign of the centrifugal contribution follows from $\boldsymbol\Omega\times(\boldsymbol\Omega\times\mathbf x)=-\nabla|\boldsymbol\Omega\times\mathbf x|^2/2$. Constant density is what permits combination into one pressure gradient without extra density-gradient terms.
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