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I have a crucible with molten metal flowing under its own head. As per torricelli's law the velocity of the fluid would be $\sqrt{2gh}$.

Is there any mechanism with which I can maintain a constant flow rate of my choice?

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    $\begingroup$ I don't know much about the fluid properties of molten metals, but note that Toricelli's Law assumes an inviscid fluid. Water is fairly close to inviscid for common applications of Toricellis - metal may not be. ... For water, the way to maintain a constant flow rate would be to maintain a constant head, either by replacement, or by having a large enough US reservoir that loss through flow doesn't matter. Again, I don't know if those are practical solutions to your molten metal quandary. $\endgroup$ – Adam Mar 28 '17 at 19:23
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To maintain flow rate (Q), velocity (v) must be constant. To keep velocity constant, potential head(h) must be constant. To keep potential head constant either a large crucible (like a reservoir) can be used OR flow rate OUT of crucible must be equal to flow rate IN to the crucible.

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