# Pressure in a tube - principles of engineering

I'm a student studying on engineering (typically chemical), I came across this question which I do not understand -

Suppose the pressure at a point within a column of mercury in a tube is $74$ mm Hg . What is the pressure $5$ mm Hg below this point .

This is talking about pressure as the head of fluid . I understand that. But I don't understand what does the 2 statement mean ?

Assume a tube closed at the top (a Torricelli tube) and neglect the vapour pressure of the mercury. Now apply Pascal's Law on hydrostatic pressure:

$$P=P_0+\rho gh$$

With $P_0\approx 0$ (the pressure for $h=0$), $\rho$ the density of the mercury and $h$ the height of the measuring point, measured from the top.

The question has been made really easy by expressing the hydrostatic pressure in mm Hg:

What is the pressure 5 mm Hg below this point?

Well, this means that $h$ has been increased by 5 mm, so that the pressure at that point is simply $74+5=79$ mm Hg.

Of course this also holds if $P_0>0$. E.g. if the tube was closed at the bottom (thus forming a vessel) and open at the top, with the mercury surface exposed to some constant pressure $P_0$, the above would also hold: the pressure would be 79 mm Hg, 5 mm below the point where it was 74 mm Hg.

We can show this as follows, with Pascal:

Pressure at the 1st point (74 mm Hg):

$P_1=P_0+\rho gh_1$

Pressure at the 2nd point:

$P_2=P_0+\rho gh_2$

Because $h_2=h_1+5$, then in mm Hg,

$P_2=P_1+5=$79 mm Hg.

• Why is it 79 instead of 69 ? – user307640 Oct 31 '17 at 14:46
• @user307640: because the new measuring point is 5 mm below the first one. Pascal shows that pressure increases at greater depth, as is intuitive. So it is $74+5=79$ mm Hg. – Gert Oct 31 '17 at 14:48