Atmospheric pressure and gauge pressure

The air presses too

We live at the bottom of an ocean of air. Its weight presses on every square metre of the ground with about

We do not feel it, because the fluids inside our bodies press back just as hard.

The barometer

Torricelli filled a long glass tube with mercury and turned it upside down in a dish of mercury. The mercury fell until the column was about $76\ \text{cm}$ tall, leaving almost nothing above it. The air pressing on the dish holds up the column:

So pressure is often given in millimetres of mercury: $1\ \text{atm} = 760\ \text{mm}$ of mercury. Higher up a mountain there is less air above, and the barometer reads less.

Gauge and absolute pressure

Absolute pressure is the whole pressure. Gauge pressure is the part above the air's:

A tyre gauge, a blood-pressure cuff and an open manometer all read gauge pressure. A flat tyre reads zero, though its air is at one atmosphere.

The open-tube manometer

A U-tube holds a liquid; one arm is joined to the gas, the other is open to the air. If the gas pressure is higher, it pushes the liquid down on its side, and the difference in levels $h$ gives

You should find that $8\ \text{kPa}$ moves mercury only $6\ \text{cm}$, but water more than thirteen times as far, so water is used only for small pressures.

Watch out. If the liquid stands lower in the open arm, the gas is below air pressure, and the gauge pressure is negative.

A worked example

A barometer in a hill town reads $70.0\ \text{cm}$ of mercury. Find the air pressure.

1. Pressure. $p = 13\,600\ \text{kg/m}^3 \times 9.8\ \text{m/s}^2 \times 0.700\ \text{m} = 9.33 \times 10^{4}\ \text{Pa}$.
2. In atmospheres. $\dfrac{9.33 \times 10^{4}\ \text{Pa}}{1.013 \times 10^{5}\ \text{Pa}} = 0.92\ \text{atm}$.

Think first. Less air above means less pressure, so the answer must be below one atmosphere.

Practise with new numbers

Try it in Python

The program turns barometer readings into pressures.

Remember these

• $p_0 = 1.013 \times 10^{5}\ \text{Pa} = 76\ \text{cm}$ of mercury.
• Barometer: $p_0 = \rho gh$.
• Gauge pressure $= p - p_0$; manometer: $p - p_0 = \rho gh$.

Check yourself

Try each one on your own first. If you are stuck, open a hint. Then check with Show the answer.

1. A tyre gauge reads $1.8 \times 10^{5}\ \text{Pa}$ at sea level. What is the absolute pressure in the tyre?

2. Why is mercury, not water, used in barometers?

3. The mercury in a manometer stands $3\ \text{cm}$ lower in the open arm. Is the gas above or below air pressure?

4. Why does a sealed packet of chips puff up on a flight?