My text was able to show that for an ideal (incompressible and inviscid) and steady fluid in a gravitational field, the energy density [itex]E=\frac{1}{2}\rho u^2 + \rho\chi+P[/itex] is constant for any fluid element, where [itex]\chi[/itex] is the gravitational potential. That is(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{DE}{Dt}=\frac{\partial E}{\partial t} + \mathbf{u}\cdot\nabla E=0[/tex].Does this hold for an unsteady ideal fluid? If not, what causes the change in the mechanical energy of the fluid element?

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# Does conservation of energy for unsteady ideal fluid hold?

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