Example Problem with Complete Solution

1E-2: Pressure Gage and Manometer Readings 6 pts
Both a gage and a manometer are attached to a gas tank to measure its pressure. If the reading on the pressure gage is 80 kPa, determine the distance between the two fluid levels of the manometer if the fluid is ...
               
a.) mercury (ρ = 13,600 kg/m3)      
b.) water (ρ = 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 80 kPa
rw 1000 kg/m3
rHg 13600 kg/m3
Find : h ??? m
eqn-1
Solution : Gage pressure is defined by : Eqn 1
The Manometer Equation tells us that : eqn-2
Eqn 2
eqn-3
Combining Eqns 1 & 2 gives us : Eqn 3
eqn-4
Now, we can solve Eqn 3 for h : Eqn 4
Now, we can plug values into Eqn 4 :
g 9.8066 m/s2
gC 1 kg-m/N-s2
a.) h 0.600 m
b.) h 8.158 m
Answers : a.) h 0.60 m
b.) h 8.16 m