Measuring pressure using a manometer.

[baddin]

Problem:
1. The pressure of a gas cell is measured with a mercurcy manometer. The mercury is 32.6 cm higher in the outside arm than in the arm connected to the gas cell. Calculate the gas pressure.


Relevant equations/given data
2. p(Pressure at depth h) = p(Pressure of atmosphere) + ρ(Density of liquid)*g(Gravitionational acceleration)*h
Pressure of atmosphere = 1atm = 101,300Pa. Density of mercury = 13,600kg/m^3


Attempted solution
3. p(gas) = p(Pressure of atmosphere) + ρ(Density of liquid)*g(Gravitionational acceleration)*h
p(gas) = 101,300 + (13600*9.8*0.326) = 144749.28Pa = 144.75kPa. I have the solution and it says the answer should be 149.5kPa. Have I done something wrong, or is the solution incorrect?

 

[sonnyfab]

Your calculation is exactly correct. The answer is the book is for a mercury height of 36.2cm. Is there any chance that you misread the problem and got the 6 and 2 backwards? If not, don't spend any more time thinking about it, you know what you are doing and the answer key had a typo.

Dr Peter Vaughan
BASIS Peoria Physics

 

[baddin]

Oh my! Stupid me! You are right, I misread the 6 and the 2 backwards. That clears it up, thanks for the help! =D

 

[sonnyfab]

Those are absolutely the most difficult mistakes to find. Fortunately, they are also by far the least important mistakes.

 

[Nickie]

I would first check my calculations to ensure I did not make any errors. I would also double-check the given data and equations to make sure they are correct. If everything appears to be correct, I would then consider the possibility of experimental error or uncertainty in the measurements. It is also possible that the solution provided is incorrect and I would suggest rechecking the calculations or seeking a second opinion from another scientist. Ultimately, it is important to carefully analyze and evaluate all aspects of the experiment and data to ensure accurate and reliable results.