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## Homework Statement

I must derive Torricelli's law.

## Homework Equations

[tex]P+\rho gh +\frac{\rho v^2}{2} = \text{constant}[/tex].

## The Attempt at a Solution

I chose the origin of the system as being on the surface of the liquid.

I have that [tex]P_0 = P_1+ \frac{\rho v_1^2}{2}[/tex].

But [tex]P_1=P_0+\rho gh[/tex], so the equation is equivalent to [tex]0 = \rho gh +\frac{ \rho v_1^2}{2}[/tex].

Hence [tex]v_1^2=- 2gh[/tex].

I see that I made an error of sign, but I don't know where. The "x-axis"'s positive sense I considered was the one pointing to the ground.

What did I do wrong?

Thanks in advance.