What Is the Largest Pressure Measurable by a 70cm Water Column Manometer?

[Iooz]

Homework Statement

If you have a manometer with a 70cm tall water column, what is the largest pressure
that can be measured? Assume that the densities of water and mercury are 1000 kg/m3
and 13 600 kg/m3 respectively

Homework Equations

P=pgh+Patm

The Attempt at a Solution

I've attempted this question and am getting an answer of 801mmHg however the answer is 51.5mmHg.
My attempt:
P=pgh+Patm
=(1000 x 9.8 x 0.70) + (1 x 10⁵)
=106860Pa
And then to convert it to mmHg since 101325Pa=760mmHg I went (106860 x 760)/101325
=801mmHg

Can someone please help with where I'm going wrong here?

 

[Merlin3189]

Have you tried not adding atmospheric pressure?

 

[gleem]

You have not interpreted the question correctly. A 70 cm column of water is equivalent to a column of mercury.of what height?

 

[Iooz]

Have you tried not adding atmospheric pressure?

I have now tried this and this gives me the right answer of 51.5mmHg however I don't understand why I would not add atmospheric pressure?

 

[Iooz]

You have not interpreted the question correctly. A 70 cm column of water is equivalent to a column of mercury.of what height?

I have worked this out and have gotten an answer of a 0.05m column of Mercury is equivalent to 0.7m of water.
However I'm unsure how to use this in the calculation?

 

[gleem]

I have worked this out and have gotten an answer of a 0.05m column of Mercury is equivalent to 0.7m of water.
However I'm unsure how to use this in the calculation?

You have the answer. Actually the question should have been what is the largest pressure difference you can measure.

 

[Iooz]

You have the answer. Actually the question should have been what is the largest pressure difference you can measure.

Oh I see what you did here! Converting 0.05m to mm will give me mmHg.
Thank you :)

 

[Merlin3189]

I made the comment simply because your maths seemed ok, so the only other possibility was that your method was not the one they wanted.

I only discovered the formula you use when I came to PF. All my life I've used the simple P=ρgh to calculate the pressure of a column of liquid.
I understand why you use the formula and I can't say that it's right or wrong. I just like to know the pressure of the liquid column, then use that as appropriate to the situation.

Here we are told it is a medical manometer, so I think it measures pressures relative to atmospheric. So no addition of atmospheric pressure is required.
Since the pressures the doctor quotes when measuring blood pressure are of the order of 50 - 150 mmHg, your heart would have to be some sort of vacuum pump if that were an absolute pressure.

I don't understand Gleem's comment, as you did give your answer in terms of an equivalent column of Hg, even though that was not asked for in the question.
It did strike me as odd that they told you the density of Hg when it seems completely irrelevant to the question as stated! If someone asked me for a pressure, I would give an answer in N/m² or Pascal.

 

[gleem]

@Merlin3189 In medical physics pressure is usually measured in mmHg because most labs have Mercury Barometers or calibrate an aneroid or other type of barometer against a mercury barometer.