Measuring Atmospheric Pressure with a Barometer
Determine the atmospheric pressure at a location where the barometric reading is 740 mm Hg and the gravitational acceleration is g = 9.81 m/s². Assume the temperature of mercury to be 10°C, at which its density is 13,570 kg/m³.
The barometric reading at a location in height of mercury column is given. The atmospheric pressure is to be determined.
Assumptions The temperature of mercury is 10°C.
Properties The density of mercury is given to be 13,570 kg/m³.
Analysis From Eq. 1–26, the atmospheric pressure is determined to be
P_{ atm }=\rho g h (1–26)
\begin{aligned}P_{ atm } &=\rho g h \\&=\left(13,570 kg / m ^{3}\right)\left(9.81 m / s ^{2}\right)(0.74 m )\left(\frac{1 N }{1 kg \cdot m / s ^{2}}\right)\left(\frac{1 kPa }{1000 N / m ^{2}}\right) \\&=98.5 kPa\end{aligned}
Discussion Note that density changes with temperature, and thus this effect should be considered in calculations.