# Pressure Question using 'mm-Hg'

1. Apr 7, 2013

### FollowTheFez

1. The problem statement, all variables and given/known data

Intravenous infusions are often made under gravity. Assuming the fluid has a density of 1.00g/cm^3, at what height h should the bottle be placed so the liquid pressure is 55mm-Hg?

2. Relevant equations

Atmospheric pressure, Po, = 101kPa = 101000Pa
density of fluid, ρ, = 1g/cm^3 = 1000kg/m^3
density of Hg, ρ, = 13.6x10^3

P=ρgh
P=Po + pgh

3. The attempt at a solution

Pressure of Hg, P= ρgh
= (13.6x10^3) x 9.8 x (5.5x10^-3)
= 733.04 Pa

P=Po + pgh

h= $\frac{P - Po}{ρg}$
h= $\frac{733.04 - 101000}{1000 x 9.8}$
h= -10.23

Therefore, the bag must be 10.23m below whatever the reference point is. Which is obviously wrong!

The answer gives nearly what I've got but I don't understand one aspect of it.
It says...

h= $\frac{ΔP}{ρg}$
h= $\frac{(55mm-Hg)(\frac{133Pa}{1mm-Hg})}{1000 x 9.8}$
h= 0.75m

I don't understand where the 133Pa came from and why they are doing this calculation.
Can someone please explain?

2. Apr 7, 2013

### SteamKing

Staff Emeritus
5.5*10^-3 m is 5.5 mm, not 55 mm.

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