Finding the pressure in vacuum

Question

I have the following question

And I have the formula for finding the pressure difference which is as follows:
P(below) = P(above) + ρgh
And since they provide the information that it is vacuum, then Patm > Pabs.

Here is the solution:

I don't really understand why it is minus ρgh and I'm confused how to use the fact that it is vacuum. Also, what can we usually consider P(below) and P(above)?

sammy gerbil · Answer

You're right, the question is confusing because there is no vacuum here.

The minus sign is because the pressure in the pipe + the pressure due to 3cm of liquid = atmospheric pressure. The pressure in the pipe is below atmospheric pressure.

The pressure relative to atmospheric pressure is called gauge pressure. So the gauge pressure is $-rho g h$. Pressure relative to zero is absolute pressure, $P_0-rho gh$.

In this case $P(below)$ is the pressure at the lower side of the manometer, ie atmopheric pressure $P_0$. $P(above)$ is the pressure on the higher side of the manometer, ie the pressure in the pipe.

Finding the pressure in vacuum

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