Finding change in pressure when mercury level drops

[confusedperson]

I don't know what I did wrong for this question, but I assume something is wrong as my solution is extremely simple and this is a 20 marks question...
1. Homework Statement
Refer to uploaded image.

Homework Equations

Pressure = h ( density in kg/m^3 ) ( gravitational acceleration)

The Attempt at a Solution

Pressure change at A = -0.04 ( 13600 ) ( 9.81 )[/B]
Final gauge pressure = 150.3kPa - 0.04 (13600) (9.81) - 1.025 * 10^5 Pa

 

[BvU]

Hi conf,

You want to make a real balance equation and take the density of water into account as well...

 

[confusedperson]

Sorry I do not understand what is the real balance equation...

 

[BvU]

4 cm of Hg took the place of 4 cm of water. That 4 cm of water exercised a pressure as well

 

[confusedperson]

Thank you. I'm not entirely sure how that works but I assume I have to add 4cm of water back into the final gauge pressure?

 

[mfb]

And don't forget the 4 cm of mercury that were there. The mercury level changes on both sides, the water level changes on one side.

 

[confusedperson]

Huh. That was not expected...I simply have not come across a problem of this type before. There goes at least 10 marks for my final exam. However, lesson learnt. Thank you guys for enlightening me on this new knowledge.

 

[BvU]

That's the idea.

And don't forget the 4 cm of mercury that were there. The mercury level changes on both sides, the water level changes on one side.

I thought he/she did take the Hg, but only forgot the water ? So with (13600 - 1000) instead of just 13600 kg/m3 it would have been alright ?

 

[haruspex]

I thought he/she did take the Hg, but only forgot the water ? So with (13600 - 1000) instead of just 13600 kg/m3 it would have been alright ?

@mfb is pointing out that if the level of Hg on the right drops by x then the level on the left rises by x, so the difference in heights drops by 2x. The pressure exerted comes from the height difference.

 

[BvU]

Oh boy, have I been sleeping ! Fixed on the water Thanks for the wake-up call ! But nevertheless I'm off to bed.