Example Problem with Complete Solution

1E-2 : Pressure Gage and Manometer Readings 6 pts
A cylindrical tank contains pressurized nitrogen gas. The gage on the tank reads 88 kPa. A manometer is attached to the tank to verify its pressure. Determine the manometer reading in cm if the manometer fluid is
a.) ρmercury = 13,600 kg/m3, b.) ρwater = 1000 kg/m3
 
Read: Remember that gage pressure is the difference between the absolute pressure and atmospheric pressure.
Apply the Barometer Equation with a known gage pressure to determine the manometer reading, h.
Given: Pgage 88 kPa
rw 1000 kg/m3
rHg 13600 kg/m3
Find: h ??? m
Assumptions: 1- The nitrogen and water in the system are completely static.
2- The densities of the nitrogen and water are uniform and constant.
3- The acceleration of gravity is: g 9.8066 m/s2
gC 1 kg-m/N-s2
Equations / Data / Solve:
Gage pressure is defined by :
Eqn 1
The Manometer Equation tells us that :
Eqn 2
Combining Eqns 1 & 2 gives us :
Eqn 3
Now, we can solve Eqn 3 for h :
Eqn 4
Now, we can plug values into Eqn 4 : a.) h 0.660 m
b.) h 8.974 m
Answers: a.) h 0.66 m
b.) h 8.97 m