Measuring Pressure with a Manometer
A manometer is used to measure the pressure of a gas in a tank. The fluid used has a specific gravity of 0.85, and the manometer column height is 55 cm, as shown in Fig. 3–21. If the local atmospheric pressure is 96 kPa, determine the absolute pressure within the tank.
The reading of a manometer attached to a tank and the atmospheric pressure are given. The absolute pressure in the tank is to be determined.
Assumptions The density of the gas in the tank is much lower than the density of the manometer fluid.
Properties The specific gravity of the manometer fluid is given to be 0.85. We take the standard density of water to be 1000 kg/m³.
Analysis The density of the fluid is obtained by multiplying its specific gravity by the density of water,
\rho= SG \left(\rho_{ H _{2} O }\right)=(0.85)\left(1000 kg / m ^{3}\right)=850 kg / m ^{3}
Then from Eq. 3–13,
P_{2}=P_{ atm }+\rho g h (3-13)
\begin{aligned}P &=P_{ atm }+\rho g h \\&=96 kPa +\left(850 kg / m ^{3}\right)\left(9.81 m / s ^{2}\right)(0.55 m )\left(\frac{1 N }{1 kg \cdot m / s ^{2}}\right)\left(\frac{1 kPa }{1000 N / m ^{2}}\right) \\&=100.6 kPa\end{aligned}
Discussion Note that the gage pressure in the tank is 4.6 kPa.