1E-3 : | Pressure in a Tank Using a Complex Manometer | 5 pts | |||||||
The gauge pressure of the air in the tank shown in the figure is measured to be 65 kPa. Determine the differential height, h, of the mercury column. | |||||||||
Read : | The density of the air is so much lover than the density of the liquids in this problem that the weight of the air can be considered negligible in the force balances we will write in this problem. | ||||||||
Given : | Pgauge | 65 |
kPa | ||||||
hoil | 0.75 |
m | SGoil | 0.72 |
|||||
hwater | 0.3 |
m | SGm | 13.6 |
|||||
Solution : | Begin by writing the manometer equation for each interval between points a and f on the diagram. | ||||||||
Eqn 1 | Eqn 3 | ||||||||
Eqn 2 | Eqn 4 | ||||||||
Eqn 5 | |||||||||
If we add all 5 of these equations together we obtain : | |||||||||
Eqn 6 | |||||||||
The only unknown in this equation is h. So, the next step is to solve the equation for h. | |||||||||
Eqn 7 | |||||||||
We know that : | g | 9.8066 |
m/s2 | ||||||
gc | 1 |
kg-m/N-s2 | |||||||
ρwater | 1000 |
kg/m3 | |||||||
Also, because Pf = Patm and the definition of gauge pressure : | Eqn 8 | ||||||||
Pa-Pf = | 65000 |
N/m2 | |||||||
All we need to do is convert specific gravity into density and we are ready to plug values into Eqn 7. | |||||||||
The definition of specific gravity is : | Eqn 9 | ||||||||
This helps us simplify Eqn 7 to : |
Eqn 10 | ||||||||
Eqn 11 | |||||||||
From Eqn 9 : | Eqn 12 | ||||||||
ρm | 13600 |
kg/m3 | |||||||
Answers : | Plugging values into Eqn 11 yields : | h | 0.487 |
m | |||||
48.7 |
cm |