Thermodynamics: Determine pressure in the tank of a manometer

[mhrob24]

Homework Statement

Find the pressure (Pt) in the tank of the manometer

Relevant Equations

P= W/A = density x gravity x height

I was watching a YT video getting prepared for class this coming semester, and in the video, this diagram of a manometer was drawn (see image at end of message). The professor stated that the pressure in the tank (Pt) is = to the pressure at point A. Following this, he said that technically speaking, it wasn’t EXACTLY equal because of the weight of the gas in the portion of the tube connected to the tank, but because the density of the gas is much smaller than the density of the liquid, it would make a trivial difference.

I THINK I get what he’s saying but I want to be sure. So basically, the “tank” here is considered to be just the square tank…..not including the connection tube (even though that tube is exposed to the gas in the tank). So in all reality, if you wanted to truly calculate the EXACT pressure at point A, you would have to include the weight of the gas in that portion of the tube above point A. Is this correct? That’s the only way I can make sense out of what was said in the video…

 

[Lnewqban]

I believe that you are both correct.
Just like it happens in the ocean, the pressure inside the tank will vary with the "depth" at which the point we want to measure is sumerged in the mass of gas, plus the static pressure inside the tank.

 

[Baluncore]

You may need to analyse the hydrostatic pressure change with height in both the liquid and the gas. The gas has variable density which will make it interesting.