2.3 - Gas Pressure

Measuring Gas Pressure with a Manometer

• A manometer is a glass U-tube containing a liquid, such as coloured water, used to measure gas pressure.
• Before connection to a gas supply, both arms experience atmospheric pressure and have equal liquid levels.
• In the illustrated compressed-gas arrangement, the gas-side level is lower than the open-arm level. The vertical difference $h$ represents the pressure difference.
• At a common horizontal level in the static manometer liquid, pressures are equal:

• Here $\rho$ is the density of the manometer liquid. In liquid-column units, add the column-height difference directly to atmospheric pressure expressed in the same units.
• A larger tube diameter does not change the calculated pressure: liquid pressure does not depend on surface area.
• Mercury is very toxic, so mercury manometers are now less common. Portable digital manometers use pressure transducers and provide more accurate readings.

Worked Examples

• Compressed gas: A mercury manometer shows $h=40\mathrm{cm}$ with $P_{\mathrm{atm}}=76\mathrm{cm}\mathrm{Hg}$:

• With ${\rho }_{\mathrm{Hg}}=13600\mathrm{kg}{\mathrm{m}}^{-3}$ and $g=9.81\mathrm{m}{\mathrm{s}}^{-2}$:

• Air-flow pipe: A mercury level difference of $25\mathrm{cm}$ gives a pressure difference of $25\mathrm{cm}\mathrm{Hg}$. For atmospheric pressure $75\mathrm{cm}\mathrm{Hg}$, the illustrated pipe pressure is: