SCIENCE · INVESTIGATE AND EXPLAIN

Track gauge pressure across a density interface

A small static fluid element is in force balance. The pressure on its lower face exceeds that on its upper face by the weight of the intervening fluid divided by area. In a uniform-density region this gives Δp=ρgΔh for a downward depth change. Pressure acts normally on each face; it is not a downward vector like the weight.

Learning outcome: Predict the interface and bottom pressures for two layer combinations with equal total depth. Preserve the continuous piecewise graph, gauge and absolute references, and explain why exchanging layer thickness changes the result.

Starting recap

Declare density, pressure reference, flow regime and admissible force constraints. Convert area and volume units before balancing forces, mass or energy.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

Changing oil depth to 0.4 m while retaining water depth 0.3 m gives gauge pressure 6200 Pa. Adding 0.2 m oil adds 1600 Pa, whereas adding 0.2 m water would add 2000 Pa.

Open the experiment

Predict

At a broad oil–water interface with negligible surface-tension pressure, pressure:

Your prediction and reason

Experiment

Predict the interface and bottom pressures for two layer combinations with equal total depth. Preserve the continuous piecewise graph, gauge and absolute references, and explain why exchanging layer thickness changes the result.

Follow pressure across a liquid interface

Worked teaching model · synthetic values · Static immiscible oil density 800 kg/m³ above water density 1000 kg/m³, atmosphere 100000 Pa and g=10 m/s². Neglect surface-tension pressure at the broad interface. No physical pressure apparatus.

Upper oil depth: 0.2 m Lower water depth: 0.3 m

Reset keeps your prediction, captures and practice history.

Continuous pressure with a changed density slope

Unlike graph quantities rescale independently; read units and values, not screen angles. 1: oil then water (solid). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Continuous pressure with a changed density slope

oil then water

depth below top surface (m)	gauge pressure (Pa)
0	0
0.2	1600
0.5	4600

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Interface gauge pressure	1600	Pa
Bottom gauge pressure	4600	Pa
Bottom absolute pressure	104600	Pa
Equivalent water-column depth	0.46	m

Pressure is continuous at the broad interface while pressure increase per depth changes with density.

Add rho g Delta h for each downward segment; subtract for upward segments. Gauge pressure subtracts the atmospheric reference. The equivalent water height is not generally the geometric depth. Shape and total volume do not enter this local static depth relation.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

Pressure is continuous at the broad interface while pressure increase per depth changes with density.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Declare the fluid, reference and evidence

Build the algebraic model

The virtual vessel has an oil layer of density 800 kg/m³ over water of density 1000 kg/m³, with g=10 m/s². At the broad interface pressure is continuous under the stated negligible-curvature assumption. The pressure-versus-depth graph changes slope there: 8000 Pa/m in oil and 10000 Pa/m in water. A discontinuous density does not require a discontinuous pressure.

Check the original numerical packet

For oil depth 0.2 m and water depth 0.3 m, gauge pressure at the bottom is 8000×0.2+10000×0.3=4600 Pa. Adding the supplied atmospheric reference 100000 Pa gives absolute pressure 104600 Pa. The same pressure would occur below 0.46 m of water, not the actual total depth 0.50 m.

Challenge the assumptions and transfer

A manometer compares pressures by walking through connected static fluid: add ρgΔh when moving down and subtract it when moving up. For an original water manometer with one surface 0.12 m lower than the other, the gas above the lower surface exceeds the other gas pressure by 1200 Pa. A 0.06 m difference halves this pressure difference. Container width or total liquid weight alone does not determine pressure at a specified depth; walls can support part of the total liquid weight.

Worked original case

Changing oil depth to 0.4 m while retaining water depth 0.3 m gives gauge pressure 6200 Pa. Adding 0.2 m oil adds 1600 Pa, whereas adding 0.2 m water would add 2000 Pa.

Bounded investigation

Changed-case numerical practice

Try the changed case before feedback

Oil of density 800 kg/m³ lies 0.3 m above 0.2 m water of density 1000 kg/m³. With g=10, find bottom gauge pressure in Pa.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and limits

Original content checked 30 October 2026 against OpenStax College Physics 2e. All records are supplied or generated educational evidence. No pressure rigs, liquid handling, bodily measurements or physical exposure protocols are requested. Virtual admissibility does not certify real equipment safety, practical skill or independent mastery.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

When can pressure be equated at two points of a connected static liquid?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Infer liquid density without confusing it with a balance offset Next: Account for hydraulic force gain without inventing energy

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.