Conceptual question, fluid pressure in a barometer

[Addem]

Homework Statement

I took a stab at the following question in a book:

"In one observation, the column in a mercury barometer has a
measured height h of 740.35 mm.The tem-
perature is -5.0 C, at which temperature the density of mercury r is
1.3608 10^4 kg/m^3 .The free-fall acceleration g at the site of the barom-
eter is 9.7835 m/s^2 .What is the atmospheric pressure at that site in pas-
cals and in torr (which is the common unit for barometer readings)?"

And I got the right answer, but it left me wondering why it was the right answer.

Homework Equations

$$p = p_0 + \rho g h$$

The Attempt at a Solution

I used the equation above with the obvious inputs except that I assumed p₀ was 0 because I basically couldn't think of anything else to do. To within a very small error I got the same answer as the back of the book so I'm guessing I did this correctly, but is this correct or is there something I'm missing?

 

[SteamKing]

Homework Statement

I took a stab at the following question in a book:

"In one observation, the column in a mercury barometer has a
measured height h of 740.35 mm.The tem-
perature is -5.0 C, at which temperature the density of mercury r is
1.3608 10^4 kg/m^3 .The free-fall acceleration g at the site of the barom-
eter is 9.7835 m/s^2 .What is the atmospheric pressure at that site in pas-
cals and in torr (which is the common unit for barometer readings)?"

And I got the right answer, but it left me wondering why it was the right answer.

Homework Equations

$$p = p_0 + \rho g h$$

The Attempt at a Solution

I used the equation above with the obvious inputs except that I assumed p₀ was 0 because I basically couldn't think of anything else to do. To within a very small error I got the same answer as the back of the book so I'm guessing I did this correctly, but is this correct or is there something I'm missing?

In a mercury barometer, what is p₀ over the mercury column inside the barometer itself?

 

[Addem]

In some odd coincidence I just finished watching a YouTube video in which the presenter says the pressure at the top is 0. I wasn't actually aware of that but I guess that makes good sense and answers the question! Thanks. :)