How would i show $H$ is constant

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I was wondering if anyone could help me with the following problem.

If $H=\frac{P}{\rho}+\frac{v^{2}}{2}+gz$, Then $H$ is constant along streamlines

and if $\nabla \times v=0$, then $H$ is constant throughout the flow.

I don't really understand how to do this.