Distinguish liquid depth from container shape and route length
Compare equal-depth points without mistaking volume, vessel width or a sloping path for pressure.
Core and Extended; Physics 0625, 2026–2028, section 1.8. Define and use p = F/A, explain everyday force/area effects, and describe liquid depth and density qualitatively. Numerical liquid-pressure changes belong to the clearly labelled Supplement lessons. Written work is self-checked.
Before you begin
- Explain liquid depth and density effects.
- Distinguish vertical displacement from distance along a route.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which distance describes depth below a liquid surface?
What you will learn
- Use the vertical surface-to-point depth in a stationary liquid.
- Explain equal-depth pressure with matched liquid and surface conditions.
Shape alone does not set a point's pressure
Two stationary containers hold the same uniform liquid with equal surface pressure and equal g. Points at equal vertical depth have equal pressure even if one container is wider or contains more liquid. Greater volume can increase the total liquid mass without changing the pressure at that specified point. Container walls can also support forces, so dividing the whole vessel's liquid weight by its base area is not a reliable replacement for a depth comparison in every shape.
A pressure and a force are different quantities. At the same pressure, a larger horizontal base area can carry a larger pressure force when the pressure over that base is uniform. Equal point pressures do not therefore imply equal forces on differently sized bases. The force-per-area relationship remains consistent with the depth account.
Measure from the surface to the point
The vertical depth begins at the relevant liquid surface. A point low on a tank sketch is not automatically deeper if its surface is also lower. For two points in one uniform stationary liquid, compare their vertical levels: an equal level below the common surface means equal pressure; a lower level means greater pressure.
A 5 m sloping route reaching only 3 m below the surface gives a 3 m vertical depth, not 5 m. Qualitative pressure comparisons do not require a container to have a straight wall above the point. State the liquid, boundary and stationary conditions and leave unsupported differences in flow, density or applied surface pressure explicit.
Pause and explain
Must the wider tank have greater point pressure at the same depth in the same liquid with matching surface conditions?
Worked example
A wide and narrow vessel contain the same stationary uniform liquid with equal surface pressure and g. Their labelled points are both 3 m vertically below their surfaces. Compare point pressures.
Show the worked solution
- The liquid and surface conditions match.
- The vertical depths are equal.
- Point pressures are equal despite different widths and total liquid volumes.
Answer Equal pressure at the two labelled points.
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Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
Compare equal-depth points in a wide and narrow tank holding the same stationary uniform liquid under matching surface pressure and g.
Give me a hint
Keep the point conditions separate from each vessel's volume.
Compare my reasoning
- The density is the same.
- The vertical depths and surface conditions match.
- Point pressures are equal even if total liquid masses differ.
Equal point pressures.
Look for these in your work
- Control liquid and boundary conditions.
- Do not rank by width.
One point is reached by a 5 m sloping route and lies 3 m below the surface. Another lies 3 m vertically below the same surface in the same uniform stationary liquid. Compare pressures.
Give me a hint
Discard the route length and compare the actual vertical levels.
Compare my reasoning
- The first depth is 3 m, not 5 m.
- The second depth is also 3 m.
- The matching depths give equal pressure.
Equal pressure; both depths are 3 m.
Look for these in your work
- Identify the correct depth.
- Use the common liquid and surface.
Two horizontal bases have the same uniform pressure, but the second base has twice the area. Does equal pressure imply equal liquid pressure force?
Give me a hint
Use F = pA while distinguishing point pressure from a total force.
Compare my reasoning
- The pressure is held fixed.
- Force equals that pressure times base area.
- Twice the area gives twice the pressure force, under the stated uniform-base model.
No; the second pressure force is twice as large.
Look for these in your work
- Keep pressure and force distinct.
- Use the uniform pressure and stated areas.
Common mistakes
- Volume and width do not replace vertical depth.
- Equal pressure does not mean equal force on different areas.
- Do not measure depth along a wall or route.
What can you explain now?
Does a 5 m sloping route ending 3 m below the surface give a 5 m pressure depth?
Compare with the explanation
No; the depth is 3 m.
The relevant distance is vertical below the surface.
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Make it stick
Compare shaped vessels and sloping routes, then explain why equal pressure can coexist with unequal base forces.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.