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URLhttps://www.miniphysics.com/hydrostatic-pressure.html
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Meta TitleHydrostatic Pressure (p=ρgh): Notes + Examples (O Level)
Meta DescriptionMaster hydrostatic pressure in liquids (p=ρgh): depth vs pressure, total pressure with atmosphere, common traps, and worked examples for O Level Physics.
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On this page 1. Definition A. Hydrostatic pressure B. Pressure due to a liquid column 2. Key Ideas 3. Detailed Explanations A. Why pressure increases with depth B. Using (what is ?) C. Same depth means same pressure (shape does not matter) D. Pressure acts in all directions 4. Common Mistakes 5. Exam Tips 6. Worked Examples Example 1: Diver underwater (column pressure and total pressure) Example 2: Pressure difference between two depths Example 3: Find depth from pressure Example 4: Different liquids, same depth Example 5: Find density using 7. Mind Stretchers Example 1: Same depth, different shapes Example 2: Pressure on a different planet 8. Practice 1. Definition A. Hydrostatic pressure Hydrostatic pressure is the pressure in a fluid at rest , caused by the weight of the fluid above a point. It increases with depth. B. Pressure due to a liquid column The pressure difference between two points in the same fluid separated vertically by is: If the fluid surface is at pressure , then at depth : In many O Level questions, refers to the pressure due to the liquid column (i.e. the extra pressure compared to the surface). = pressure (Pa) = density (kg m ) = gravitational field strength (N kg ) = vertical depth below the liquid surface (m) 2. Key Ideas Hydrostatic pressure depends on: depth , fluid density , gravitational field strength . For the same liquid and same : deeper point → larger pressure (because ), same depth → same pressure (even if the container shape is different). Hydrostatic pressure does not depend on the shape or cross-sectional area of the container. Use the vertical depth from the surface: If asked for total pressure at depth in an open tank: 3. Detailed Explanations A. Why pressure increases with depth Deeper water produces higher pressure, so water squirts out faster. The deeper you go in a liquid, the more liquid there is above you. more water above → larger weight pressing down larger weight over the same area → larger pressure B. Using (what is ?) Depth h is measured vertically from the liquid surface to the point. For a point at depth below the surface in a uniform liquid: If the surface is open to the air, the total pressure is: Read the question carefully: “pressure due to the water (liquid) column” → use “total pressure at that depth” → add atmospheric pressure Column pressure vs total pressure (open tank) Two straight lines versus depth: one shows pressure due to the water column only; the other includes atmospheric pressure as a constant offset. Column pressure vs total pressure (open tank) Depth below surface (m) Pressure (kPa) Key Column pressure (ρgh) in water Column pressure (ρgh) in water Total pressure (patm + ρgh) Total pressure (patm + ρgh) For water with g≈10, the pressure due to the liquid column increases by about 10 kPa per metre. Total pressure starts at about 100 kPa at the surface and rises with the same gradient. Data table Column pressure (ρgh) in water Depth below surface (m) Pressure (kPa) 0 0 6 60 Total pressure (patm + ρgh) Depth below surface (m) Pressure (kPa) 0 100 6 160 C. Same depth means same pressure (shape does not matter) In the same connected liquid, pressure depends on depth, not container shape. In a liquid at rest: all points at the same depth have the same pressure the pressure at the bottom depends on depth , not on the container’s shape or width D. Pressure acts in all directions Pressure increases with depth: deeper points have larger pressure. Pressure at a point in a fluid acts in all directions (not just downward). This is why water pushes: downward on the bottom of a tank, sideways on the walls of a tank. Upthrust (buoyancy) and Archimedes’ principle are useful extensions, but not required for the O Level Physics (6091) Pressure learning outcomes. See: Upthrust & Archimedes’ Principle . 4. Common Mistakes Using the wrong (it must be the vertical depth below the surface, not the slanted distance). Forgetting to convert cm to m (e.g. ). Mixing density units (use kg m when using SI units in the formula). Forgetting to add atmospheric pressure when the question asks for total pressure . 5. Exam Tips Write the formula first ( or ), then substitute with units. Quote the correct unit at the end: Pa (or kPa). For water, a common value is . If two points are at the same depth in the same connected liquid, state: “same → same pressure”. 6. Worked Examples Example 1: Diver underwater (column pressure and total pressure) A diver is below the surface of fresh water. Calculate: the pressure due to the water column the total pressure if atmospheric pressure is Take and . Show Answer Pressure due to water column: Total pressure: Example 2: Pressure difference between two depths Two points in the same liquid are separated vertically by . Find the pressure difference between them. Take and . Example 3: Find depth from pressure In water, the pressure due to the liquid column is . Find the depth. Take and . Example 4: Different liquids, same depth A point is below the surface of: water ( ) oil ( ) Compare the pressure due to the liquid column in each case. Take . Show Answer Water: Oil: At the same depth, the denser liquid produces a larger pressure. Example 5: Find density using In a liquid, pressure increases by when the depth increases by . Find the density of the liquid. Take . 7. Mind Stretchers Example 1: Same depth, different shapes Two tanks have different shapes but both contain water to the same depth. One tank is very wide and the other is narrow. Which tank has the larger pressure at the bottom? Explain. Show Answer They have the same pressure at the bottom. Hydrostatic pressure depends on depth only: Same liquid (same ) and same depth gives the same pressure, regardless of tank shape. Example 2: Pressure on a different planet A lake of the same depth exists on a planet where is half of Earth’s value. How does the hydrostatic pressure due to the water column at a given depth compare with Earth? Explain. Show Answer It is half of Earth’s value. Hydrostatic pressure due to the liquid column is: If is halved while and are the same, then is halved. 8. Practice Categories Tags O Level Physics Pressure
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[Skip to main content](https://www.miniphysics.com/hydrostatic-pressure.html#main-content) [Mini Physics](https://www.miniphysics.com/) - [O Level](https://www.miniphysics.com/o-level-secondary-school-physics-notes.html) - [A Level](https://www.miniphysics.com/a-level-physics-notes.html) - [Practice](https://www.miniphysics.com/structured.html) - [O Level MCQ Practice](https://www.miniphysics.com/o-level-physics-quiz.html) - [A Level MCQ Practice](https://www.miniphysics.com/a-level-physics-quiz.html) - [Structured Practice](https://www.miniphysics.com/structured.html) - [IPhO Problem Sets (Extension)](https://www.miniphysics.com/ipho-problem-sets.html) - [Advanced](https://www.miniphysics.com/advanced.html) - [H3 Physics (Extension)](https://www.miniphysics.com/h3-physics-junior-college.html) - [IPhO Prep (Extension)](https://www.miniphysics.com/international-physics-olympiad-prep.html) - [University Year 1 Guided Modules](https://www.miniphysics.com/university-physics-year-1-notes.html) - [University Year 2 Bridge (Support, Noindex)](https://www.miniphysics.com/university-year-2.html "Support route (noindex)") - [About](https://www.miniphysics.com/about-mini-physics.html) - [About Mini Physics](https://www.miniphysics.com/about-mini-physics.html) - [Editorial Policy](https://www.miniphysics.com/editorial-policy.html) - [Blog](https://www.miniphysics.com/category/blog.html) - [Contact](https://www.miniphysics.com/contact-us.html) [Practice browser](https://www.miniphysics.com/practice-browser.html) lesson o-level students core 1. [Home](https://www.miniphysics.com/) 2. / [O Level](https://www.miniphysics.com/o-level-secondary-school-physics-notes.html) 3. / [Pressure Hub](https://www.miniphysics.com/pressure-2.html) 4. / Hydrostatic Pressure # Hydrostatic Pressure **Show/Hide Sub-topics (Pressure \| O Level Physics)** 1. [Density](https://www.miniphysics.com/density.html) 2. [What Is Pressure?](https://www.miniphysics.com/what-is-pressure.html) 3. [Hydrostatic Pressure](https://www.miniphysics.com/hydrostatic-pressure.html) 4. [Hydraulic Systems](https://www.miniphysics.com/ss-hydraulic-systems.html) 5. [Barometer & Atmospheric Pressure](https://www.miniphysics.com/barometer.html) 6. [Manometer](https://www.miniphysics.com/manometer.html) **On this page** - [1\. Definition](https://www.miniphysics.com/hydrostatic-pressure.html#1-definition) - [A. Hydrostatic pressure](https://www.miniphysics.com/hydrostatic-pressure.html#a-hydrostatic-pressure) - [B. Pressure due to a liquid column](https://www.miniphysics.com/hydrostatic-pressure.html#b-pressure-due-to-a-liquid-column) - [2\. Key Ideas](https://www.miniphysics.com/hydrostatic-pressure.html#2-key-ideas) - [3\. Detailed Explanations](https://www.miniphysics.com/hydrostatic-pressure.html#3-detailed-explanations) - [A. Why pressure increases with depth](https://www.miniphysics.com/hydrostatic-pressure.html#a-why-pressure-increases-with-depth) - [B. Using (what is ?)](https://www.miniphysics.com/hydrostatic-pressure.html#b-using--what-is-) - [C. Same depth means same pressure (shape does not matter)](https://www.miniphysics.com/hydrostatic-pressure.html#c-same-depth-means-same-pressure-shape-does-not-matter) - [D. Pressure acts in all directions](https://www.miniphysics.com/hydrostatic-pressure.html#d-pressure-acts-in-all-directions) - [4\. Common Mistakes](https://www.miniphysics.com/hydrostatic-pressure.html#4-common-mistakes) - [5\. Exam Tips](https://www.miniphysics.com/hydrostatic-pressure.html#5-exam-tips) - [6\. Worked Examples](https://www.miniphysics.com/hydrostatic-pressure.html#6-worked-examples) - [Example 1: Diver underwater (column pressure and total pressure)](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-diver-underwater-column-pressure-and-total-pressure) - [Example 2: Pressure difference between two depths](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-difference-between-two-depths) - [Example 3: Find depth from pressure](https://www.miniphysics.com/hydrostatic-pressure.html#example-3-find-depth-from-pressure) - [Example 4: Different liquids, same depth](https://www.miniphysics.com/hydrostatic-pressure.html#example-4-different-liquids-same-depth) - [Example 5: Find density using](https://www.miniphysics.com/hydrostatic-pressure.html#example-5-find-density-using-) - [7\. Mind Stretchers](https://www.miniphysics.com/hydrostatic-pressure.html#7-mind-stretchers) - [Example 1: Same depth, different shapes](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-same-depth-different-shapes) - [Example 2: Pressure on a different planet](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-on-a-different-planet) - [8\. Practice](https://www.miniphysics.com/hydrostatic-pressure.html#8-practice) ## 1\. Definition ### A. Hydrostatic pressure **Hydrostatic pressure** is the pressure in a **fluid at rest**, caused by the **weight of the fluid above** a point. It increases with depth. ### B. Pressure due to a liquid column The **pressure difference** between two points in the same fluid separated vertically by is: If the fluid surface is at pressure , then at depth : In many O Level questions, refers to the **pressure due to the liquid column** (i.e. the *extra* pressure compared to the surface). - \= pressure (Pa) - \= [density](https://www.miniphysics.com/density.html) (kg m ) - \= [gravitational field strength](https://www.miniphysics.com/gravitational-field.html) (N kg ) - \= vertical depth below the liquid surface (m) ## 2\. Key Ideas - Hydrostatic pressure depends on: - depth , - fluid density , - gravitational field strength . - For the same liquid and same : - deeper point → larger pressure (because ), - same depth → same pressure (even if the container shape is different). - Hydrostatic pressure does **not** depend on the shape or cross-sectional area of the container. - Use the vertical depth from the surface: - If asked for **total pressure** at depth in an open tank: ## 3\. Detailed Explanations ### A. Why pressure increases with depth [![Water jets from a deeper hole travel further than jets from a shallow hole](https://www.miniphysics.com/_astro/pressure.D4FiMJi-_1wWm5e.webp)](https://www.miniphysics.com/_astro/pressure.D4FiMJi-.jpg) Deeper water produces higher pressure, so water squirts out faster. The deeper you go in a liquid, the more liquid there is above you. - more water above → larger weight pressing down - larger weight over the same area → larger pressure ### B. Using (what is ?) [![Point A at depth h below the surface of a liquid](https://www.miniphysics.com/_astro/Liquid-pressure-2.C_8w34qF_aL7KP.webp)](https://www.miniphysics.com/_astro/Liquid-pressure-2.C_8w34qF.jpg) Depth h is measured vertically from the liquid surface to the point. For a point at depth below the surface in a uniform liquid: If the surface is open to the air, the total pressure is: Exam Tip: choose the correct pressure Read the question carefully: - “pressure due to the water (liquid) column” → use - “total pressure at that depth” → add atmospheric pressure Two straight lines versus depth: one shows pressure due to the water column only; the other includes atmospheric pressure as a constant offset. Column pressure vs total pressure (open tank) 0 2 4 6 0 50 100 150 200 Depth below surface (m) Pressure (kPa) Key Column pressure (ρgh) in water Total pressure (patm + ρgh) For water with g≈10, the pressure due to the liquid column increases by about 10 kPa per metre. Total pressure starts at about 100 kPa at the surface and rises with the same gradient. Data table | Column pressure (ρgh) in water | | |---|---| | Depth below surface (m) | Pressure (kPa) | | 0 | 0 | | 6 | 60 | | Total pressure (patm + ρgh) | | |---|---| | Depth below surface (m) | Pressure (kPa) | | 0 | 100 | | 6 | 160 | ### C. Same depth means same pressure (shape does not matter) [![Different-shaped connected containers show that points at the same depth in a liquid have the same pressure](https://www.miniphysics.com/_astro/pressure-at-same-height.B-qL7Clt_Z2cE7r3.webp)](https://www.miniphysics.com/_astro/pressure-at-same-height.B-qL7Clt.jpg) In the same connected liquid, pressure depends on depth, not container shape. In a liquid at rest: - all points at the same depth have the same pressure - the pressure at the bottom depends on depth , not on the container’s shape or width ### D. Pressure acts in all directions [![Pressure labels increase from P0 near the surface to P3 at the bottom of a liquid](https://www.miniphysics.com/_astro/Liquid-pressure.BoPI1Ki2_Z1nIAuW.webp)](https://www.miniphysics.com/_astro/Liquid-pressure.BoPI1Ki2.jpg) Pressure increases with depth: deeper points have larger pressure. Pressure at a point in a fluid acts **in all directions** (not just downward). This is why water pushes: - downward on the bottom of a tank, - sideways on the walls of a tank. A Level extension Upthrust (buoyancy) and Archimedes’ principle are useful extensions, but not required for the O Level Physics (6091) Pressure learning outcomes. See: [Upthrust & Archimedes’ Principle](https://www.miniphysics.com/upthrust-and-archimedes-principle.html). ## 4\. Common Mistakes - Using the wrong (it must be the **vertical depth** below the surface, not the slanted distance). - Forgetting to convert cm to m (e.g. ). - Mixing density units (use kg m when using SI units in the formula). - Forgetting to add atmospheric pressure when the question asks for **total pressure**. ## 5\. Exam Tips - Write the formula first ( or ), then substitute with units. - Quote the correct unit at the end: Pa (or kPa). - For water, a common value is . - If two points are at the same depth in the same connected liquid, state: “same → same pressure”. ## 6\. Worked Examples ### Example 1: Diver underwater (column pressure and total pressure) A diver is below the surface of fresh water. Calculate: 1. the pressure due to the water column 2. the total pressure if atmospheric pressure is Take and . **Show Answer** 1. Pressure due to water column: 2. Total pressure: ### Example 2: Pressure difference between two depths Two points in the same liquid are separated vertically by . Find the pressure difference between them. Take and . **Show Answer** ### Example 3: Find depth from pressure In water, the pressure due to the liquid column is . Find the depth. Take and . **Show Answer** ### Example 4: Different liquids, same depth A point is below the surface of: 1. water ( ) 2. oil ( ) Compare the pressure due to the liquid column in each case. Take . **Show Answer** Water: Oil: At the same depth, the denser liquid produces a larger pressure. ### Example 5: Find density using In a liquid, pressure increases by when the depth increases by . Find the density of the liquid. Take . **Show Answer** ## 7\. Mind Stretchers ### Example 1: Same depth, different shapes Two tanks have different shapes but both contain water to the same depth. One tank is very wide and the other is narrow. Which tank has the larger pressure at the bottom? Explain. **Show Answer** They have the same pressure at the bottom. Hydrostatic pressure depends on depth only: Same liquid (same ) and same depth gives the same pressure, regardless of tank shape. ### Example 2: Pressure on a different planet A lake of the same depth exists on a planet where is half of Earth’s value. How does the hydrostatic pressure due to the water column at a given depth compare with Earth? Explain. **Show Answer** It is half of Earth’s value. Hydrostatic pressure due to the liquid column is: If is halved while and are the same, then is halved. ## 8\. Practice Practice Time\! Ready to test your understanding? [Try the Pressure MCQs](https://www.miniphysics.com/quiz/pressure.html) ### Next Step: Practice This Topic Pressure: take one targeted next step, then escalate difficulty only after the first route stabilizes. - [Best next step: Pressure Quiz](https://www.miniphysics.com/quiz/pressure.html)Fast concept check before deeper follow-up. - [Harder follow-up: Paper 2 Structured Practice — Pressure](https://www.miniphysics.com/structured/pressure.html)Longer-response follow-up with mark-scheme scoring. - [Repair with simulation: Pressure & Hydraulics Explorer](https://www.miniphysics.com/simulations/pressure-hydraulics-explorer.html)Repair step: visualize the concept, then retake a timed route. - [Pressure Hub](https://www.miniphysics.com/pressure-2.html)Quick recap of the full topic before timed practice. [Previous LessonWhat Is Pressure?](https://www.miniphysics.com/what-is-pressure.html) [Next LessonHydraulic Systems](https://www.miniphysics.com/ss-hydraulic-systems.html) Updated Jan 26, 2026 Maintained cluster coverage [Report correction](https://www.miniphysics.com/contact-us.html?kind=correction&reason=correction&subject=Correction&page=%2Fhydrostatic-pressure.html) Show details Hide details **Maintained cluster coverage.** Use the [O Level Pressure hub](https://www.miniphysics.com/pressure-2.html) as the primary route. This coverage signal is separate from per-page review metadata. Hub last reviewed Mar 21, 2026. Maintained pressure hub for solids/fluids setup and gauge/absolute distinctions. Mini Physics is curated by **Mr. Mini Physics** , a Physics tutor since **2010**. Writes and curates Mini Physics under a consistent pen name. [Who runs Mini Physics](https://www.miniphysics.com/about-mini-physics.html). Categories - [O Level](https://www.miniphysics.com/o-level-secondary-school-physics-notes.html) - [Pressure](https://www.miniphysics.com/pressure-2.html) Tags - O Level - Physics - Pressure On this page - [1\. Definition](https://www.miniphysics.com/hydrostatic-pressure.html#1-definition) - [A. Hydrostatic pressure](https://www.miniphysics.com/hydrostatic-pressure.html#a-hydrostatic-pressure) - [B. Pressure due to a liquid column](https://www.miniphysics.com/hydrostatic-pressure.html#b-pressure-due-to-a-liquid-column) - [2\. Key Ideas](https://www.miniphysics.com/hydrostatic-pressure.html#2-key-ideas) - [3\. Detailed Explanations](https://www.miniphysics.com/hydrostatic-pressure.html#3-detailed-explanations) - [A. Why pressure increases with depth](https://www.miniphysics.com/hydrostatic-pressure.html#a-why-pressure-increases-with-depth) - [B. Using (what is ?)](https://www.miniphysics.com/hydrostatic-pressure.html#b-using--what-is-) - [C. Same depth means same pressure (shape does not matter)](https://www.miniphysics.com/hydrostatic-pressure.html#c-same-depth-means-same-pressure-shape-does-not-matter) - [D. Pressure acts in all directions](https://www.miniphysics.com/hydrostatic-pressure.html#d-pressure-acts-in-all-directions) - [4\. Common Mistakes](https://www.miniphysics.com/hydrostatic-pressure.html#4-common-mistakes) - [5\. Exam Tips](https://www.miniphysics.com/hydrostatic-pressure.html#5-exam-tips) - [6\. Worked Examples](https://www.miniphysics.com/hydrostatic-pressure.html#6-worked-examples) - [Example 1: Diver underwater (column pressure and total pressure)](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-diver-underwater-column-pressure-and-total-pressure) - [Example 2: Pressure difference between two depths](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-difference-between-two-depths) - [Example 3: Find depth from pressure](https://www.miniphysics.com/hydrostatic-pressure.html#example-3-find-depth-from-pressure) - [Example 4: Different liquids, same depth](https://www.miniphysics.com/hydrostatic-pressure.html#example-4-different-liquids-same-depth) - [Example 5: Find density using](https://www.miniphysics.com/hydrostatic-pressure.html#example-5-find-density-using-) - [7\. Mind Stretchers](https://www.miniphysics.com/hydrostatic-pressure.html#7-mind-stretchers) - [Example 1: Same depth, different shapes](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-same-depth-different-shapes) - [Example 2: Pressure on a different planet](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-on-a-different-planet) - [8\. 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Readable Markdown
**On this page** - [1\. Definition](https://www.miniphysics.com/hydrostatic-pressure.html#1-definition) - [A. Hydrostatic pressure](https://www.miniphysics.com/hydrostatic-pressure.html#a-hydrostatic-pressure) - [B. Pressure due to a liquid column](https://www.miniphysics.com/hydrostatic-pressure.html#b-pressure-due-to-a-liquid-column) - [2\. Key Ideas](https://www.miniphysics.com/hydrostatic-pressure.html#2-key-ideas) - [3\. Detailed Explanations](https://www.miniphysics.com/hydrostatic-pressure.html#3-detailed-explanations) - [A. Why pressure increases with depth](https://www.miniphysics.com/hydrostatic-pressure.html#a-why-pressure-increases-with-depth) - [B. Using (what is ?)](https://www.miniphysics.com/hydrostatic-pressure.html#b-using--what-is-) - [C. Same depth means same pressure (shape does not matter)](https://www.miniphysics.com/hydrostatic-pressure.html#c-same-depth-means-same-pressure-shape-does-not-matter) - [D. Pressure acts in all directions](https://www.miniphysics.com/hydrostatic-pressure.html#d-pressure-acts-in-all-directions) - [4\. Common Mistakes](https://www.miniphysics.com/hydrostatic-pressure.html#4-common-mistakes) - [5\. Exam Tips](https://www.miniphysics.com/hydrostatic-pressure.html#5-exam-tips) - [6\. Worked Examples](https://www.miniphysics.com/hydrostatic-pressure.html#6-worked-examples) - [Example 1: Diver underwater (column pressure and total pressure)](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-diver-underwater-column-pressure-and-total-pressure) - [Example 2: Pressure difference between two depths](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-difference-between-two-depths) - [Example 3: Find depth from pressure](https://www.miniphysics.com/hydrostatic-pressure.html#example-3-find-depth-from-pressure) - [Example 4: Different liquids, same depth](https://www.miniphysics.com/hydrostatic-pressure.html#example-4-different-liquids-same-depth) - [Example 5: Find density using](https://www.miniphysics.com/hydrostatic-pressure.html#example-5-find-density-using-) - [7\. Mind Stretchers](https://www.miniphysics.com/hydrostatic-pressure.html#7-mind-stretchers) - [Example 1: Same depth, different shapes](https://www.miniphysics.com/hydrostatic-pressure.html#example-1-same-depth-different-shapes) - [Example 2: Pressure on a different planet](https://www.miniphysics.com/hydrostatic-pressure.html#example-2-pressure-on-a-different-planet) - [8\. Practice](https://www.miniphysics.com/hydrostatic-pressure.html#8-practice) ## 1\. Definition ### A. Hydrostatic pressure **Hydrostatic pressure** is the pressure in a **fluid at rest**, caused by the **weight of the fluid above** a point. It increases with depth. ### B. Pressure due to a liquid column The **pressure difference** between two points in the same fluid separated vertically by is: If the fluid surface is at pressure , then at depth : In many O Level questions, refers to the **pressure due to the liquid column** (i.e. the *extra* pressure compared to the surface). - \= pressure (Pa) - \= [density](https://www.miniphysics.com/density.html) (kg m ) - \= [gravitational field strength](https://www.miniphysics.com/gravitational-field.html) (N kg ) - \= vertical depth below the liquid surface (m) ## 2\. Key Ideas - Hydrostatic pressure depends on: - depth , - fluid density , - gravitational field strength . - For the same liquid and same : - deeper point → larger pressure (because ), - same depth → same pressure (even if the container shape is different). - Hydrostatic pressure does **not** depend on the shape or cross-sectional area of the container. - Use the vertical depth from the surface: - If asked for **total pressure** at depth in an open tank: ## 3\. Detailed Explanations ### A. Why pressure increases with depth [![Water jets from a deeper hole travel further than jets from a shallow hole](https://www.miniphysics.com/_astro/pressure.D4FiMJi-_1wWm5e.webp)](https://www.miniphysics.com/_astro/pressure.D4FiMJi-.jpg) Deeper water produces higher pressure, so water squirts out faster. The deeper you go in a liquid, the more liquid there is above you. - more water above → larger weight pressing down - larger weight over the same area → larger pressure ### B. Using (what is ?) [![Point A at depth h below the surface of a liquid](https://www.miniphysics.com/_astro/Liquid-pressure-2.C_8w34qF_aL7KP.webp)](https://www.miniphysics.com/_astro/Liquid-pressure-2.C_8w34qF.jpg) Depth h is measured vertically from the liquid surface to the point. For a point at depth below the surface in a uniform liquid: If the surface is open to the air, the total pressure is: Read the question carefully: - “pressure due to the water (liquid) column” → use - “total pressure at that depth” → add atmospheric pressure Two straight lines versus depth: one shows pressure due to the water column only; the other includes atmospheric pressure as a constant offset. Column pressure vs total pressure (open tank) Depth below surface (m) Pressure (kPa) Key Column pressure (ρgh) in water Total pressure (patm + ρgh) For water with g≈10, the pressure due to the liquid column increases by about 10 kPa per metre. Total pressure starts at about 100 kPa at the surface and rises with the same gradient. Data table | Column pressure (ρgh) in water | | |---|---| | Depth below surface (m) | Pressure (kPa) | | 0 | 0 | | 6 | 60 | | Total pressure (patm + ρgh) | | |---|---| | Depth below surface (m) | Pressure (kPa) | | 0 | 100 | | 6 | 160 | ### C. Same depth means same pressure (shape does not matter) [![Different-shaped connected containers show that points at the same depth in a liquid have the same pressure](https://www.miniphysics.com/_astro/pressure-at-same-height.B-qL7Clt_Z2cE7r3.webp)](https://www.miniphysics.com/_astro/pressure-at-same-height.B-qL7Clt.jpg) In the same connected liquid, pressure depends on depth, not container shape. In a liquid at rest: - all points at the same depth have the same pressure - the pressure at the bottom depends on depth , not on the container’s shape or width ### D. Pressure acts in all directions [![Pressure labels increase from P0 near the surface to P3 at the bottom of a liquid](https://www.miniphysics.com/_astro/Liquid-pressure.BoPI1Ki2_Z1nIAuW.webp)](https://www.miniphysics.com/_astro/Liquid-pressure.BoPI1Ki2.jpg) Pressure increases with depth: deeper points have larger pressure. Pressure at a point in a fluid acts **in all directions** (not just downward). This is why water pushes: - downward on the bottom of a tank, - sideways on the walls of a tank. Upthrust (buoyancy) and Archimedes’ principle are useful extensions, but not required for the O Level Physics (6091) Pressure learning outcomes. See: [Upthrust & Archimedes’ Principle](https://www.miniphysics.com/upthrust-and-archimedes-principle.html). ## 4\. Common Mistakes - Using the wrong (it must be the **vertical depth** below the surface, not the slanted distance). - Forgetting to convert cm to m (e.g. ). - Mixing density units (use kg m when using SI units in the formula). - Forgetting to add atmospheric pressure when the question asks for **total pressure**. ## 5\. Exam Tips - Write the formula first ( or ), then substitute with units. - Quote the correct unit at the end: Pa (or kPa). - For water, a common value is . - If two points are at the same depth in the same connected liquid, state: “same → same pressure”. ## 6\. Worked Examples ### Example 1: Diver underwater (column pressure and total pressure) A diver is below the surface of fresh water. Calculate: 1. the pressure due to the water column 2. the total pressure if atmospheric pressure is Take and . **Show Answer** 1. Pressure due to water column: 2. Total pressure: ### Example 2: Pressure difference between two depths Two points in the same liquid are separated vertically by . Find the pressure difference between them. Take and . ### Example 3: Find depth from pressure In water, the pressure due to the liquid column is . Find the depth. Take and . ### Example 4: Different liquids, same depth A point is below the surface of: 1. water ( ) 2. oil ( ) Compare the pressure due to the liquid column in each case. Take . **Show Answer** Water: Oil: At the same depth, the denser liquid produces a larger pressure. ### Example 5: Find density using In a liquid, pressure increases by when the depth increases by . Find the density of the liquid. Take . ## 7\. Mind Stretchers ### Example 1: Same depth, different shapes Two tanks have different shapes but both contain water to the same depth. One tank is very wide and the other is narrow. Which tank has the larger pressure at the bottom? Explain. **Show Answer** They have the same pressure at the bottom. Hydrostatic pressure depends on depth only: Same liquid (same ) and same depth gives the same pressure, regardless of tank shape. ### Example 2: Pressure on a different planet A lake of the same depth exists on a planet where is half of Earth’s value. How does the hydrostatic pressure due to the water column at a given depth compare with Earth? Explain. **Show Answer** It is half of Earth’s value. Hydrostatic pressure due to the liquid column is: If is halved while and are the same, then is halved. ## 8\. Practice Categories Tags - O Level - Physics - Pressure
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