At the same vertical depth below an open liquid surface, a denser liquid produces a greater pressure increase above atmospheric pressure. Use Δp = ρgh, where h is measured vertically down from the liquid surface.
The 2027 SEC G3 Physics K323 syllabus covers density and fluid pressure. This guide compares two open containers at the same depth, then reverses the question to find the depth that gives equal pressure.
- Measure depth vertically from the surface.
- Use density in kg/m³ and depth in metres.
- Calculate the pressure due to the liquid.
- Add atmospheric pressure if the question asks for total pressure.
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Identify the pressure being compared
At the free surface of an open container, the pressure is atmospheric. As you move down, the liquid adds pressure. If both containers are open to the same atmosphere, the atmospheric contribution is the same. A comparison can therefore focus on the liquid contributions.
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Worked example | Water and oil at 30 cm
Suppose the density of water is 1,000 kg/m³ and the density of oil is 800 kg/m³. Use g = 10 N/kg for this question. Convert 30 cm to 0.30 m. The water gives 1,000 × 10 × 0.30 = 3,000 Pa above atmospheric pressure. The oil gives 800 × 10 × 0.30 = 2,400 Pa.
The difference is 600 Pa. It is also the difference between the total pressures if the air above both surfaces is at the same pressure.
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Find the oil depth for an equal reading
To match the pressure due to 0.30 m of water, the oil must also contribute 3,000 Pa. Solve 800 × 10 × h = 3,000 to obtain h = 0.375 m, or 37.5 cm. The lower-density liquid needs more depth to make the same contribution.
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Frequently asked questions
Do I measure the distance along a sloping wall?
Measure vertical depth. A sloping wall can be longer than the vertical drop.
Does a wider container give greater pressure at the same depth?
For the same liquid at rest and the same surface pressure, changing the width does not change the pressure at that depth.