[cherryblossom]

The question reads:

How high in meters must a column of water be to exert a pressure equal to that of a 760-mm column of mercury? The density of water is 1.0g/mL, whereas that of mercury is 13.6g/mL.

I know we have to show our attempts to solve the problem, but to be honest, I don't even know where to start on this one. Any hints would be appreciated!

[cherryblossom]

Wait! I missed something very simple in my textbook! Will repost if I can't figure it out in 5 minutes!

[cherryblossom]

OK, I still can't quite figure out where the density comes into it. Once again, any help would be appreciated.

[Dan]

OK, I still can't quite figure out where the density comes into it.

This implies you have figured out some other aspects of the problem - please post what you've done so far.

Hint: A measure of pressure is N/m² (Newtons per square metre)

[cherryblossom]

I wouldn't say I figured much out, I just read a bit more carefully and realized that 760 mm Hg is equal to 1atm.

Pressure =  force/area

Force = mass x acceleration, in which acceleration is equal to gravity.

Mass= density x volume

So, if I'm on the right track, what I seem to be missing is volume. Unless I misread the question and 760mm doesn't refer to pressure, but instead refers to the volume of the column?

[Dan]

Unless I misread the question and 760mm doesn't refer to pressure, but instead refers to the volume of the column?

You are almost there.

760 mm refers to the height of the column, not the volume.

What relates the height of the column to its volume?

[cherryblossom]

Errr.. volume= height x radius x pi?

So I have the height, and pi, but the radius is eluding me.

[Dan]

Errr.. volume= height x radius x pi?

No. The volume = height x radius² x pi; or more conveniently:

volume = height x area, since area is given by pi x radius².

You don't need to know the value for the area.

Since: pressure = force/area (P = F/A)
 and    force = mass x standard gravity (F = mg₀)
 and    mass = density x volume (m = dV)
 and    volume = height x area (V = hA)

You can can you combine these equations to give a new expression that is independent of area.