Manometers and Barometers

Manometers and barometers are instruments that use liquid columns to measure pressure.

Mercury barometer

A mercury barometer measures atmospheric pressure. It consists of a glass tube, closed at one end, filled with mercury and inverted into a dish of mercury.

The height of the mercury column is supported by atmospheric pressure pushing on the surface of the mercury in the dish.

Standard atmospheric pressure supports a column of approximately 760 mm of mercury.

$p_{\text{atm}} = \rho g h = 13{,}600 \times 9.8 \times 0.76 \approx 101{,}300 \text{ Pa}$

U-tube manometer

A U-tube manometer compares gas pressure with atmospheric pressure.

• If the gas pressure equals atmospheric pressure, the liquid levels are equal.
• If the gas pressure is greater than atmospheric, the liquid is pushed down on the gas side and up on the open side. The difference in heights gives the excess pressure: $\Delta p = \rho g \Delta h$.
• If the gas pressure is less than atmospheric, the liquid rises on the gas side.

Reading a manometer

Gas pressure $= p_{\text{atm}} + \rho g \Delta h$ (if gas side is lower)

Gas pressure $= p_{\text{atm}} - \rho g \Delta h$ (if gas side is higher)

Common errors and how to correct them

• Using the total height of the liquid instead of the height difference between the two sides.
• Forgetting to add or subtract atmospheric pressure.

How to apply this in an exam

Identify which side is higher and which is lower. Calculate $\rho g \Delta h$ for the height difference. Add to or subtract from atmospheric pressure to find the gas pressure.