Experiment: Measuring gas pressure with a liquid manometer

Aim

To determine the pressure of a gas supply using a liquid column manometer.

Variables

• Manipulated: Setting of the gas supply (flow rate)
• Responding: Height difference of the liquid columns, h
• Constant: Atmospheric pressure and the density of the manometer liquid

Apparatus & materials

• U-tube manometer containing water
• Rubber tubing
• Gas supply tap
• Ruler
• Barometer (for atmospheric pressure)

Procedure

1. Half-fill the U-tube with water; with both arms open, check that the two water levels are equal.
2. Connect one arm of the manometer to the gas supply with rubber tubing.
3. Turn on the gas supply; the water level in the connected arm falls while the other arm rises.
4. Measure the vertical height difference h between the two water levels with the ruler.
5. Read the atmospheric pressure from the barometer.
6. Repeat at a few different supply settings and record h each time.

Tabulating results

Record the height difference h in cm (or m) for each setting, along with the density of the liquid and the atmospheric pressure read from the barometer.

The graph

A graph is optional. If several settings are used, the gas pressure can be compared with the height difference h to show that a greater h means a greater gas pressure.

Analysis

When the gas pushes the liquid down on its side, the gas pressure P(gas) = P(atmospheric) + hρg. Convert h to a pressure using hρg and add the atmospheric pressure to obtain the gas pressure.

Pressure · Graph skills

Sample results and what they show

Example data using a water manometer, with the atmospheric pressure read from a barometer as 101 kPa and the water density taken as 1000 kg m⁻³ (g = 9.81 m s⁻²):

• Setting 1: height difference h = 12.0 cm
• Setting 2: h = 20.0 cm
• Setting 3: h = 28.0 cm

The connected arm falls and the open arm rises, so the gas pressure is greater than atmospheric. A larger flow setting gives a larger height difference h, which means a larger gas pressure.

Work out one value: for setting 2, the column pressure is hρg = 0.200 m × 1000 kg m⁻³ × 9.81 m s⁻² = 1962 Pa ≈ 1.96 kPa, so the gas pressure is P(gas) = P(atm) + hρg = 101 kPa + 1.96 kPa = 103 kPa. The height difference on its own is only the amount by which the gas pressure exceeds atmospheric pressure.

Reading the graph and finding the answer

A graph is optional here, but plotting the gas pressure P(gas) (y-axis) against the height difference h in metres (x-axis) is instructive: it gives a straight line that does not pass through the origin.

The y-intercept is the atmospheric pressure, because when h = 0 the two levels are equal and P(gas) = P(atm). The gradient is ρg.

Using a large triangle:

gradient = ΔP ÷ Δh = ρg = 1000 kg m⁻³ × 9.81 m s⁻² = 9810 Pa m⁻¹

So every extra 1 m of height difference corresponds to 9810 Pa (about 9.81 kPa) of extra gas pressure. The single most important reading, though, is a direct one: measure h, convert it to a pressure with hρg, and add the atmospheric pressure.

Marks examiners look for

For the practical marks: check that the two water levels are equal when both arms are open (no zero error), read both levels at eye level to avoid parallax error, make sure the tubing has no leaks, and use a manometer liquid of known density.

For the Paper 3 science-process-skill marks, state clearly that the manipulated variable is the gas supply setting, the responding variable is the height difference h, and the fixed variables are the atmospheric pressure and the density of the manometer liquid. Record h with a unit and show the conversion hρg fully, keeping SI units so the answer comes out in pascals.

A common error is to quote the height difference as the gas pressure; the correct gas pressure is atmospheric pressure plus hρg. State the final gas pressure with a unit, for example 103 kPa, and mention that the connected arm being lower confirms the gas pressure exceeds atmospheric.

Source: DSKP KSSM Physics Form 4 and 5 (Versi English) (Bahagian Pembangunan Kurikulum (BPK), KPM)