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Raw Queries and Responses

1. Shard Calculation

Query:

Response:

Calculated Shard: 166 (from laksa118)

2. Crawled Status Check

Query:

curl -X POST \
  'http://laksa166.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://quartz-akz.pages.dev/Hydrostatic-Pressure\')), getAhrefsUnparsedNoserviceFromURL(\'https://quartz-akz.pages.dev/Hydrostatic-Pressure\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure","crawl_time":1773500332,"first_indexed_time":1730390437,"http_code":200,"src_unparsed":"dev,pages!quartz-akz,\/Hydrostatic-Pressure s443","src_root_hash":"10679949288068471566","history_drop_reason":null,"meta_title":"Hydrostatic Pressure","meta_descriptions":["When Fluids are defined to be ‘at rest’ (that is, all forces are balanced) they are called hydrostatic. In hydrostatic fluids, the pressure increases the ‘deeper’ we go."],"attrs_boilerpipe_text":"When\nFluid\ns are defined to be ‘at rest’ (that is, all forces are balanced) they are called\nhydrostatic\n. In hydrostatic fluids, the pressure increases the ‘deeper’ we go.\nDefinition\nFormula - 1\nHydrostatic pressure\nFormula - 2\nHydrostatic Pressure of Water at a Depth\nFormula - 3\nHydrostatic Pressure of Air at an altitude\nNote\n=\nPressure\n(in\n)\n*\n= Pressure at depth\/altitude\n. This is also referred to as the\nabsolute pressure\n*\n=\nAtmospheric Pressure\n=\nDensity (Physics)\n(in\n)\n= Acceleration due to gravity\n= Height relative to sea level. (in\n)\n= Depth (negative height relative to sea level)\n=\n= Change in y position.\n= Change in height from sea level (always positive!)\n#tosee\n#todo\nis it?\nGauge pressure\nPressure gauges (devices that measure pressure) don’t actually measure\n, the absolute pressure. They measure the\ngauge pressure\n:\nDerivation\nThe formula for hydrostatic pressure is derived by using\nNewton’s first law of motion\nand\nPascal’s Law\n.\nRecall that for a body at rest, the sum of all forces must be zero:\nLet’s start by looking at an\nincompressible fluid\nthat starts from sea level, and extends downwards. We know that for the forces to balance out, the force from the water must balance that from the atmosphere.\nFurthermore, the atmospheric force is from the weight of all the air molecules:\nThen the force from the fluid comes from the molecules inside the fluid.\nAgain, we tend to talk about things in terms of pressure, so for the\nrectangular\narea that is contact with the air, the pressures are equal:\nNow, since we defined the fluid to be incompressible and it is confined, we can apply Pascal’s Law, which says the pressure is equal in a fluid\nwithout gravity\n.\nIf we take a circular disc of area,\nat height\ninside the fluid, due to Pascal’s Law, it must have the same pressure, meaning for each side of the disc (top and bottom), the forces must be equal:\nHydrostatic Pressure _1.excalidraw\nMakes sense so far?\nNow let’s introduce\nGravitational Forces\ninto the system. Pascal’s Law, unfortunately, doesn’t quite behave the same anymore.\nAt\n, we have the top surface experiencing a force due to the weight of air:\nOn the disk,\nwith area\nwe have cylindrical column of water above it, which adds extra force\non top of the pressure force!\nHydrostatic Pressure _2.excalidraw\nIn terms of pressure and density:\nSince\n, where h is the difference in y, we have:\ndividing by\n:\nNow express everything in terms of y level:","attrs_markdown":"# [Questionably Accurate Notes](https:\/\/quartz-akz.pages.dev\/)\nPress\n\nto search\n\nSearch\n\n# Explorer\n- - [0-1 Knapsack Problem](https:\/\/quartz-akz.pages.dev\/0-1-Knapsack-Problem)\n  - [3D Real Space](https:\/\/quartz-akz.pages.dev\/3D-Real-Space)\n  - [A-star Algorithm](https:\/\/quartz-akz.pages.dev\/A-star-Algorithm)\n  - [Abstract Class](https:\/\/quartz-akz.pages.dev\/Abstract-Class)\n  - [Abstract Data Type](https:\/\/quartz-akz.pages.dev\/Abstract-Data-Type)\n  - [Abstract Methods](https:\/\/quartz-akz.pages.dev\/Abstract-Methods)\n  - 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[Charge](https:\/\/quartz-akz.pages.dev\/Charge)\n  - [Charge Conductivity](https:\/\/quartz-akz.pages.dev\/Charge-Conductivity)\n  - [Charge Density](https:\/\/quartz-akz.pages.dev\/Charge-Density)\n  - [Charge Distribution](https:\/\/quartz-akz.pages.dev\/Charge-Distribution)\n  - [Charge Transfer](https:\/\/quartz-akz.pages.dev\/Charge-Transfer)\n  - [Charged Conducting Sphere](https:\/\/quartz-akz.pages.dev\/Charged-Conducting-Sphere)\n  - [Charged Cylinder with Infinite Length](https:\/\/quartz-akz.pages.dev\/Charged-Cylinder-with-Infinite-Length)\n  - [Charged Particles in Magnetic Fields](https:\/\/quartz-akz.pages.dev\/Charged-Particles-in-Magnetic-Fields)\n  - [Chinese Room Argument](https:\/\/quartz-akz.pages.dev\/Chinese-Room-Argument)\n  - [Church-Turing Thesis](https:\/\/quartz-akz.pages.dev\/Church-Turing-Thesis)\n  - [Class](https:\/\/quartz-akz.pages.dev\/Class)\n  - [Class Relationship](https:\/\/quartz-akz.pages.dev\/Class-Relationship)\n  - [Classical Physics](https:\/\/quartz-akz.pages.dev\/Classical-Physics)\n  - 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[Exception](https:\/\/quartz-akz.pages.dev\/Exception)\n  - [Exception Handling in Java](https:\/\/quartz-akz.pages.dev\/Exception-Handling-in-Java)\n  - [Existential Quantifier](https:\/\/quartz-akz.pages.dev\/Existential-Quantifier)\n  - [Extended Transition Function](https:\/\/quartz-akz.pages.dev\/Extended-Transition-Function)\n  - [Extracting a Basis from a Spanning Set](https:\/\/quartz-akz.pages.dev\/Extracting-a-Basis-from-a-Spanning-Set)\n  - [Factorial](https:\/\/quartz-akz.pages.dev\/Factorial)\n  - [Factoring (Logic)](https:\/\/quartz-akz.pages.dev\/Factoring-\\(Logic\\))\n  - [Factory Pattern](https:\/\/quartz-akz.pages.dev\/Factory-Pattern)\n  - [Famous Physics Experiments](https:\/\/quartz-akz.pages.dev\/Famous-Physics-Experiments)\n  - [Faraday's Law of Induction](https:\/\/quartz-akz.pages.dev\/Faraday's-Law-of-Induction)\n  - [Fibonacci Algorithm](https:\/\/quartz-akz.pages.dev\/Fibonacci-Algorithm)\n  - [Field](https:\/\/quartz-akz.pages.dev\/Field)\n  - [Field Axioms](https:\/\/quartz-akz.pages.dev\/Field-Axioms)\n  - [Finite State Automaton](https:\/\/quartz-akz.pages.dev\/Finite-State-Automaton)\n  - [Flow Line](https:\/\/quartz-akz.pages.dev\/Flow-Line)\n  - [Floyd-Warshall's Algorithm](https:\/\/quartz-akz.pages.dev\/Floyd-Warshall's-Algorithm)\n  - [Fluid](https:\/\/quartz-akz.pages.dev\/Fluid)\n  - [Fluid Flow](https:\/\/quartz-akz.pages.dev\/Fluid-Flow)\n  - [Fluid Particle](https:\/\/quartz-akz.pages.dev\/Fluid-Particle)\n  - [Flux](https:\/\/quartz-akz.pages.dev\/Flux)\n  - [Fooling Set](https:\/\/quartz-akz.pages.dev\/Fooling-Set)\n  - [Force](https:\/\/quartz-akz.pages.dev\/Force)\n  - [Formal Language](https:\/\/quartz-akz.pages.dev\/Formal-Language)\n  - [Formula](https:\/\/quartz-akz.pages.dev\/Formula)\n  - [Formula Parsing](https:\/\/quartz-akz.pages.dev\/Formula-Parsing)\n  - [Frame of Reference](https:\/\/quartz-akz.pages.dev\/Frame-of-Reference)\n  - [Fubini's Theorem](https:\/\/quartz-akz.pages.dev\/Fubini's-Theorem)\n  - [Function (Maths)](https:\/\/quartz-akz.pages.dev\/Function-\\(Maths\\))\n  - 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[Green's Theorem](https:\/\/quartz-akz.pages.dev\/Green's-Theorem)\n  - [Hall Effect](https:\/\/quartz-akz.pages.dev\/Hall-Effect)\n  - [Halting Problem](https:\/\/quartz-akz.pages.dev\/Halting-Problem)\n  - [Hessian Matrix](https:\/\/quartz-akz.pages.dev\/Hessian-Matrix)\n  - [Heuristic](https:\/\/quartz-akz.pages.dev\/Heuristic)\n  - [Hilbert's Program](https:\/\/quartz-akz.pages.dev\/Hilbert's-Program)\n  - [Hill Climbing](https:\/\/quartz-akz.pages.dev\/Hill-Climbing)\n  - [Horn Clause](https:\/\/quartz-akz.pages.dev\/Horn-Clause)\n  - [Hydraulics & Pneumatics](https:\/\/quartz-akz.pages.dev\/Hydraulics-&-Pneumatics)\n  - [Hydrostatic Pressure](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure)\n  - [Hyperbolic Function](https:\/\/quartz-akz.pages.dev\/Hyperbolic-Function)\n  - [Identity & Equality](https:\/\/quartz-akz.pages.dev\/Identity-&-Equality)\n  - [Image (Maths)](https:\/\/quartz-akz.pages.dev\/Image-\\(Maths\\))\n  - [Inclined Plane](https:\/\/quartz-akz.pages.dev\/Inclined-Plane)\n  - [Induced Current](https:\/\/quartz-akz.pages.dev\/Induced-Current)\n  - [Induced Electric Field](https:\/\/quartz-akz.pages.dev\/Induced-Electric-Field)\n  - [Induced EMF](https:\/\/quartz-akz.pages.dev\/Induced-EMF)\n  - [Inductance](https:\/\/quartz-akz.pages.dev\/Inductance)\n  - [Inductor (Physics)](https:\/\/quartz-akz.pages.dev\/Inductor-\\(Physics\\))\n  - [Infinite Conducting Charged Slab](https:\/\/quartz-akz.pages.dev\/Infinite-Conducting-Charged-Slab)\n  - [Infinite Line of Charge](https:\/\/quartz-akz.pages.dev\/Infinite-Line-of-Charge)\n  - [Infinite Line of Current](https:\/\/quartz-akz.pages.dev\/Infinite-Line-of-Current)\n  - [Infinite Parallel Planes Of Charge](https:\/\/quartz-akz.pages.dev\/Infinite-Parallel-Planes-Of-Charge)\n  - [Infinite Plane Of Charge](https:\/\/quartz-akz.pages.dev\/Infinite-Plane-Of-Charge)\n  - [Inheritance](https:\/\/quartz-akz.pages.dev\/Inheritance)\n  - [Inner Product](https:\/\/quartz-akz.pages.dev\/Inner-Product)\n  - [Input in Java](https:\/\/quartz-akz.pages.dev\/Input-in-Java)\n  - [Insertion Sort](https:\/\/quartz-akz.pages.dev\/Insertion-Sort)\n  - [Insulator](https:\/\/quartz-akz.pages.dev\/Insulator)\n  - [Integration By Parts](https:\/\/quartz-akz.pages.dev\/Integration-By-Parts)\n  - [Integration By Substitution](https:\/\/quartz-akz.pages.dev\/Integration-By-Substitution)\n  - [Integration By Substitution In Higher Dimensions](https:\/\/quartz-akz.pages.dev\/Integration-By-Substitution-In-Higher-Dimensions)\n  - [Interface](https:\/\/quartz-akz.pages.dev\/Interface)\n  - [Interpretation](https:\/\/quartz-akz.pages.dev\/Interpretation)\n  - [Inverse Matrix](https:\/\/quartz-akz.pages.dev\/Inverse-Matrix)\n  - [Invertible Linear Transformation](https:\/\/quartz-akz.pages.dev\/Invertible-Linear-Transformation)\n  - [Jacobi Matrix](https:\/\/quartz-akz.pages.dev\/Jacobi-Matrix)\n  - [Java Collections](https:\/\/quartz-akz.pages.dev\/Java-Collections)\n  - [Java Keywords](https:\/\/quartz-akz.pages.dev\/Java-Keywords)\n  - [Java Maps](https:\/\/quartz-akz.pages.dev\/Java-Maps)\n  - 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[Least Squared Error Fitting](https:\/\/quartz-akz.pages.dev\/Least-Squared-Error-Fitting)\n  - [Level Set](https:\/\/quartz-akz.pages.dev\/Level-Set)\n  - [Lever](https:\/\/quartz-akz.pages.dev\/Lever)\n  - [Light](https:\/\/quartz-akz.pages.dev\/Light)\n  - [Lightning](https:\/\/quartz-akz.pages.dev\/Lightning)\n  - [Limit (Calculus)](https:\/\/quartz-akz.pages.dev\/Limit-\\(Calculus\\))\n  - [Limit (Real Analysis)](https:\/\/quartz-akz.pages.dev\/Limit-\\(Real-Analysis\\))\n  - [Limit Laws](https:\/\/quartz-akz.pages.dev\/Limit-Laws)\n  - [Limits Of 2-Variable Functions](https:\/\/quartz-akz.pages.dev\/Limits-Of-2-Variable-Functions)\n  - [Linear Algebra](https:\/\/quartz-akz.pages.dev\/Linear-Algebra)\n  - [Linear Dependence](https:\/\/quartz-akz.pages.dev\/Linear-Dependence)\n  - [Linear Equation](https:\/\/quartz-akz.pages.dev\/Linear-Equation)\n  - [Linear First Order ODE](https:\/\/quartz-akz.pages.dev\/Linear-First-Order-ODE)\n  - [Linear Span](https:\/\/quartz-akz.pages.dev\/Linear-Span)\n  - [Linear System](https:\/\/quartz-akz.pages.dev\/Linear-System)\n  - [Linear Transformation](https:\/\/quartz-akz.pages.dev\/Linear-Transformation)\n  - [Linkage](https:\/\/quartz-akz.pages.dev\/Linkage)\n  - [List](https:\/\/quartz-akz.pages.dev\/List)\n  - [Logic](https:\/\/quartz-akz.pages.dev\/Logic)\n  - [Logical Connective](https:\/\/quartz-akz.pages.dev\/Logical-Connective)\n  - [Logical Database Design](https:\/\/quartz-akz.pages.dev\/Logical-Database-Design)\n  - [Logical Encoding](https:\/\/quartz-akz.pages.dev\/Logical-Encoding)\n  - [Logical Equivalence](https:\/\/quartz-akz.pages.dev\/Logical-Equivalence)\n  - [Logical Quantifier](https:\/\/quartz-akz.pages.dev\/Logical-Quantifier)\n  - [Logical Substitution](https:\/\/quartz-akz.pages.dev\/Logical-Substitution)\n  - [Lorentz Force](https:\/\/quartz-akz.pages.dev\/Lorentz-Force)\n  - [Magnet](https:\/\/quartz-akz.pages.dev\/Magnet)\n  - [Magnetic](https:\/\/quartz-akz.pages.dev\/Magnetic)\n  - [Magnetic Bottles](https:\/\/quartz-akz.pages.dev\/Magnetic-Bottles)\n  - 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[Memorylessness Lemma](https:\/\/quartz-akz.pages.dev\/Memorylessness-Lemma)\n  - [Merge Sort](https:\/\/quartz-akz.pages.dev\/Merge-Sort)\n  - [Method](https:\/\/quartz-akz.pages.dev\/Method)\n  - [Method Overloading](https:\/\/quartz-akz.pages.dev\/Method-Overloading)\n  - [Method Overriding](https:\/\/quartz-akz.pages.dev\/Method-Overriding)\n  - [Method Reference](https:\/\/quartz-akz.pages.dev\/Method-Reference)\n  - [Minimally Equivalent DFA](https:\/\/quartz-akz.pages.dev\/Minimally-Equivalent-DFA)\n  - [Mixing Problem](https:\/\/quartz-akz.pages.dev\/Mixing-Problem)\n  - [Model (Logic)](https:\/\/quartz-akz.pages.dev\/Model-\\(Logic\\))\n  - [Modelling Springs with Differential Equations](https:\/\/quartz-akz.pages.dev\/Modelling-Springs-with-Differential-Equations)\n  - [Models of Computation](https:\/\/quartz-akz.pages.dev\/Models-of-Computation)\n  - [Moment](https:\/\/quartz-akz.pages.dev\/Moment)\n  - [Motion](https:\/\/quartz-akz.pages.dev\/Motion)\n  - [Motional EMF](https:\/\/quartz-akz.pages.dev\/Motional-EMF)\n  - [Motor](https:\/\/quartz-akz.pages.dev\/Motor)\n  - [Multi-tape Turing Machine](https:\/\/quartz-akz.pages.dev\/Multi-tape-Turing-Machine)\n  - [Multivariate Chain Rule](https:\/\/quartz-akz.pages.dev\/Multivariate-Chain-Rule)\n  - [N-Queens Problem](https:\/\/quartz-akz.pages.dev\/N-Queens-Problem)\n  - [Navier-Stokes Equation](https:\/\/quartz-akz.pages.dev\/Navier-Stokes-Equation)\n  - [Negative Normal Form](https:\/\/quartz-akz.pages.dev\/Negative-Normal-Form)\n  - [Neural Network](https:\/\/quartz-akz.pages.dev\/Neural-Network)\n  - [Newton's Laws of Motion](https:\/\/quartz-akz.pages.dev\/Newton's-Laws-of-Motion)\n  - [Non-Deterministic Finite Automaton](https:\/\/quartz-akz.pages.dev\/Non-Deterministic-Finite-Automaton)\n  - [Non-Regular Language](https:\/\/quartz-akz.pages.dev\/Non-Regular-Language)\n  - [Normalization](https:\/\/quartz-akz.pages.dev\/Normalization)\n  - [NP-Class](https:\/\/quartz-akz.pages.dev\/NP-Class)\n  - [NP-Complete](https:\/\/quartz-akz.pages.dev\/NP-Complete)\n  - [NP-Hard](https:\/\/quartz-akz.pages.dev\/NP-Hard)\n  - [Nullity](https:\/\/quartz-akz.pages.dev\/Nullity)\n  - [Object](https:\/\/quartz-akz.pages.dev\/Object)\n  - [Object Orientated Software Development](https:\/\/quartz-akz.pages.dev\/Object-Orientated-Software-Development)\n  - [Object Oriented Programming](https:\/\/quartz-akz.pages.dev\/Object-Oriented-Programming)\n  - [Object Oriented Programming Language](https:\/\/quartz-akz.pages.dev\/Object-Oriented-Programming-Language)\n  - [Observer Pattern](https:\/\/quartz-akz.pages.dev\/Observer-Pattern)\n  - [Obtaining the Eigenvectors from a Matrix](https:\/\/quartz-akz.pages.dev\/Obtaining-the-Eigenvectors-from-a-Matrix)\n  - [Ohm's Law](https:\/\/quartz-akz.pages.dev\/Ohm's-Law)\n  - [OOP Design Pattern](https:\/\/quartz-akz.pages.dev\/OOP-Design-Pattern)\n  - [Ordinary Differential Equation](https:\/\/quartz-akz.pages.dev\/Ordinary-Differential-Equation)\n  - [Orthogonal Matrix](https:\/\/quartz-akz.pages.dev\/Orthogonal-Matrix)\n  - 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[Physical Database Design](https:\/\/quartz-akz.pages.dev\/Physical-Database-Design)\n  - [Physics 2 (Advanced)](https:\/\/quartz-akz.pages.dev\/Physics-2-\\(Advanced\\))\n  - [Planck-Einstein Equation](https:\/\/quartz-akz.pages.dev\/Planck-Einstein-Equation)\n  - [Plane](https:\/\/quartz-akz.pages.dev\/Plane)\n  - [Plane of Charge](https:\/\/quartz-akz.pages.dev\/Plane-of-Charge)\n  - [Point Charge](https:\/\/quartz-akz.pages.dev\/Point-Charge)\n  - [Polar Coordinates](https:\/\/quartz-akz.pages.dev\/Polar-Coordinates)\n  - [Population Models](https:\/\/quartz-akz.pages.dev\/Population-Models)\n  - [Potential Energy](https:\/\/quartz-akz.pages.dev\/Potential-Energy)\n  - [Potential Energy for Point Charge Pair System](https:\/\/quartz-akz.pages.dev\/Potential-Energy-for-Point-Charge-Pair-System)\n  - [Poynting Vector](https:\/\/quartz-akz.pages.dev\/Poynting-Vector)\n  - [Predicate](https:\/\/quartz-akz.pages.dev\/Predicate)\n  - [Predicate Logic](https:\/\/quartz-akz.pages.dev\/Predicate-Logic)\n  - 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[Quantifier Equivalences](https:\/\/quartz-akz.pages.dev\/Quantifier-Equivalences)\n  - [Quantifier Scope](https:\/\/quartz-akz.pages.dev\/Quantifier-Scope)\n  - [Query Optimisation](https:\/\/quartz-akz.pages.dev\/Query-Optimisation)\n  - [Query Plan](https:\/\/quartz-akz.pages.dev\/Query-Plan)\n  - [Query Processing](https:\/\/quartz-akz.pages.dev\/Query-Processing)\n  - [Queue](https:\/\/quartz-akz.pages.dev\/Queue)\n  - [Quick Sort](https:\/\/quartz-akz.pages.dev\/Quick-Sort)\n  - [Rank](https:\/\/quartz-akz.pages.dev\/Rank)\n  - [Ratchet & Pawl](https:\/\/quartz-akz.pages.dev\/Ratchet-&-Pawl)\n  - [Ratio Test](https:\/\/quartz-akz.pages.dev\/Ratio-Test)\n  - [Real Space](https:\/\/quartz-akz.pages.dev\/Real-Space)\n  - [Recognisability](https:\/\/quartz-akz.pages.dev\/Recognisability)\n  - [Recurrence Relation](https:\/\/quartz-akz.pages.dev\/Recurrence-Relation)\n  - [Recursion (Computer Science)](https:\/\/quartz-akz.pages.dev\/Recursion-\\(Computer-Science\\))\n  - [Reduced Row Echelon Form](https:\/\/quartz-akz.pages.dev\/Reduced-Row-Echelon-Form)\n  - 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In hydrostatic fluids, the pressure increases the ‘deeper’ we go.\n\n### Definition [§](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#definition)\n##### Formula - 1 [§](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---1)\n> Hydrostatic pressure\n> \n> ΔP\\=−ρfluidgΔy\\=ρfluidgd\n> \n> Py2\\=Py1\\+ρfluid⋅g(y2−y1)\n##### Formula - 2 [§](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---2)\n> Hydrostatic Pressure of Water at a Depth\n> \n> Ph\\=P0\\+ρwatergh\n##### Formula - 3 [§](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---3)\n> Hydrostatic Pressure of Air at an altitude\n> \n> Ph\\=P0−ρairgh\n> \n> > Note\n> > \n> > - P = [Pressure](https:\/\/quartz-akz.pages.dev\/Pressure) (in Pa) \\* Ph = Pressure at depth\/altitude h. This is also referred to as the **absolute pressure** \\* P0 =[Atmospheric Pressure](https:\/\/quartz-akz.pages.dev\/Pressure#atmospheric-pressure) ≈100 kPa\n\n- ρ = [Density (Physics)](https:\/\/quartz-akz.pages.dev\/Density-\\(Physics\\)) (in kg\/m3)\n- g = Acceleration due to gravity ≈9\\.8 m\/s2\n- y = Height relative to sea level. (in m)\n  - d = Depth (negative height relative to sea level)\n  - Δy = y2−y1 = Change in y position.\n- h = Change in height from sea level (always positive!)[\\#tosee](https:\/\/quartz-akz.pages.dev\/tags\/tosee)[\\#todo](https:\/\/quartz-akz.pages.dev\/tags\/todo) is it?\n\n> Gauge pressure\n> \n> Pressure gauges (devices that measure pressure) don’t actually measure Ph, the absolute pressure. They measure the **gauge pressure**: ρfluid⋅gh\n### Derivation [§](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#derivation)\nThe formula for hydrostatic pressure is derived by using [Newton’s first law of motion](https:\/\/quartz-akz.pages.dev\/Newton's-Laws-of-Motion#first-law-law-of-inertia) and [Pascal’s Law](https:\/\/quartz-akz.pages.dev\/Pascal's-Law).\n\nRecall that for a body at rest, the sum of all forces must be zero:\n\n∑\n\nF\n\n\\=\n\n0\n\nLet’s start by looking at an [incompressible fluid](https:\/\/quartz-akz.pages.dev\/Fluid#compressibility) that starts from sea level, and extends downwards. We know that for the forces to balance out, the force from the water must balance that from the atmosphere.\n\nFurthermore, the atmospheric force is from the weight of all the air molecules:\n\nFatmosphere\\=matmos⋅g\n\nThen the force from the fluid comes from the molecules inside the fluid.\n\nFfluid\\=Fatmosphere\n\n![700](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure-.excalidraw)\n\nAgain, we tend to talk about things in terms of pressure, so for the *rectangular* area that is contact with the air, the pressures are equal: ![](https:\/\/quartz-akz.pages.dev\/Pressure#formula)\n\nPatmosphere\\=AFatmos\n\nPy\\=0\\=AFfluid\n\nPatmosphere\\=Pfluid at y\\=0\n\nNow, since we defined the fluid to be incompressible and it is confined, we can apply Pascal’s Law, which says the pressure is equal in a fluid **without gravity**.\n\nIf we take a circular disc of area, C at height y\\=−h inside the fluid, due to Pascal’s Law, it must have the same pressure, meaning for each side of the disc (top and bottom), the forces must be equal:\n\n[Hydrostatic Pressure \\_1.excalidraw](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure-_1.excalidraw)\n\nMakes sense so far?\n\nNow let’s introduce [Gravitational Forces](https:\/\/quartz-akz.pages.dev\/Gravitational-Force) into the system. Pascal’s Law, unfortunately, doesn’t quite behave the same anymore.\n\nAt y\\=0, we have the top surface experiencing a force due to the weight of air:\n\nPfluid\\=Pair\\=Py\\=0\n\nOn the disk, C with area A we have cylindrical column of water above it, which adds extra force *on top of the pressure force\\!*\n\n∑FC\\=Ffluid\\+Fweight of column\n\n[Hydrostatic Pressure \\_2.excalidraw](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure-_2.excalidraw)\n\nIn terms of pressure and density:\n\nFweight of column\\=mcolumng\\=ρfluidVcolumn⋅g\n\nPC⋅A\\=Pfluid⋅A\\+ρVcolumn⋅g\n\nSince Vcolumn\\=A⋅h, where h is the difference in y, we have:\n\nPC⋅A\\=Pfluid⋅A\\+ρAhg\n\ndividing by A:\n\nPC\\=Pfluid\\+ρhg\n\nNow express everything in terms of y level:\n\nP−h\\=P0\\+ρhg\n\n### Table of Contents\n- [Definition](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#definition)\n- [Formula - 1](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---1)\n- [Formula - 2](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---2)\n- [Formula - 3](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#formula---3)\n- [Derivation](https:\/\/quartz-akz.pages.dev\/Hydrostatic-Pressure#derivation)\n### Related Concepts\nPress\n\nto search\n\nSearch\n\n### See Also:\n- [Archimedes' Principle](https:\/\/quartz-akz.pages.dev\/Archimedes'-Principle)\n- [Physics 2 (Advanced)](https:\/\/quartz-akz.pages.dev\/Physics-2-\\(Advanced\\))\n\nSite made by [Sujay Lobo](https:\/\/github.com\/slimeborger)  \nCreated using [Quartz v4.1.1](https:\/\/quartz.jzhao.xyz\/) by [Jacky Zhao](https:\/\/github.com\/jackyzha0)   \nFavicon by [juicy\\_fish](https:\/\/www.freepik.com\/free-vector\/set-network-lines-circles-flat_41681654.htm#query=network%20icon&position=5&from_view=search&track=ais&uuid=f427ea34-d92d-4b6e-838a-cc096cdee92c) on Freepik  \nThis work is licensed under [CC BY-SA 4.0](http:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/?ref=chooser-v1)   \n![](https:\/\/mirrors.creativecommons.org\/presskit\/icons\/cc.svg?ref=chooser-v1)![](https:\/\/mirrors.creativecommons.org\/presskit\/icons\/by.svg?ref=chooser-v1)![](https:\/\/mirrors.creativecommons.org\/presskit\/icons\/sa.svg?ref=chooser-v1)","attrs_readable_markdown":null,"meta_canonical":null}

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Boilerpipe Text	When Fluid s are defined to be ‘at rest’ (that is, all forces are balanced) they are called hydrostatic . In hydrostatic fluids, the pressure increases the ‘deeper’ we go. Definition Formula - 1 Hydrostatic pressure Formula - 2 Hydrostatic Pressure of Water at a Depth Formula - 3 Hydrostatic Pressure of Air at an altitude Note = Pressure (in ) * = Pressure at depth/altitude . This is also referred to as the absolute pressure * = Atmospheric Pressure = Density (Physics) (in ) = Acceleration due to gravity = Height relative to sea level. (in ) = Depth (negative height relative to sea level) = = Change in y position. = Change in height from sea level (always positive!) #tosee #todo is it? Gauge pressure Pressure gauges (devices that measure pressure) don’t actually measure , the absolute pressure. They measure the gauge pressure : Derivation The formula for hydrostatic pressure is derived by using Newton’s first law of motion and Pascal’s Law . Recall that for a body at rest, the sum of all forces must be zero: Let’s start by looking at an incompressible fluid that starts from sea level, and extends downwards. We know that for the forces to balance out, the force from the water must balance that from the atmosphere. Furthermore, the atmospheric force is from the weight of all the air molecules: Then the force from the fluid comes from the molecules inside the fluid. Again, we tend to talk about things in terms of pressure, so for the rectangular area that is contact with the air, the pressures are equal: Now, since we defined the fluid to be incompressible and it is confined, we can apply Pascal’s Law, which says the pressure is equal in a fluid without gravity . If we take a circular disc of area, at height inside the fluid, due to Pascal’s Law, it must have the same pressure, meaning for each side of the disc (top and bottom), the forces must be equal: Hydrostatic Pressure _1.excalidraw Makes sense so far? Now let’s introduce Gravitational Forces into the system. Pascal’s Law, unfortunately, doesn’t quite behave the same anymore. At , we have the top surface experiencing a force due to the weight of air: On the disk, with area we have cylindrical column of water above it, which adds extra force on top of the pressure force! Hydrostatic Pressure _2.excalidraw In terms of pressure and density: Since , where h is the difference in y, we have: dividing by : Now express everything in terms of y level:
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[Unification](https://quartz-akz.pages.dev/Unification) - [Unified Modelling Language](https://quartz-akz.pages.dev/Unified-Modelling-Language) - [Uniformly Charged Sphere](https://quartz-akz.pages.dev/Uniformly-Charged-Sphere) - [Universal Quantifier](https://quartz-akz.pages.dev/Universal-Quantifier) - [Universe](https://quartz-akz.pages.dev/Universe) - [Unrecognisable Language](https://quartz-akz.pages.dev/Unrecognisable-Language) - [Validity](https://quartz-akz.pages.dev/Validity) - [Van de Graaff Generator](https://quartz-akz.pages.dev/Van-de-Graaff-Generator) - [Variable Assignment](https://quartz-akz.pages.dev/Variable-Assignment) - [VCE Algorithmics (HESS)](https://quartz-akz.pages.dev/VCE-Algorithmics-\(HESS\)) - [Vector Basics](https://quartz-akz.pages.dev/Vector-Basics) - [Vector Calculus](https://quartz-akz.pages.dev/Vector-Calculus) - [Vector Field](https://quartz-akz.pages.dev/Vector-Field) - [Vector Line](https://quartz-akz.pages.dev/Vector-Line) - [Vector Operator Identities](https://quartz-akz.pages.dev/Vector-Operator-Identities) - [Vector Potential](https://quartz-akz.pages.dev/Vector-Potential) - [Vector Space](https://quartz-akz.pages.dev/Vector-Space) - [Vector Space Axioms](https://quartz-akz.pages.dev/Vector-Space-Axioms) - [Vector Space Examples](https://quartz-akz.pages.dev/Vector-Space-Examples) - [Viscosity](https://quartz-akz.pages.dev/Viscosity) - [Visibility Modifier](https://quartz-akz.pages.dev/Visibility-Modifier) - [Warshall's Algorithm](https://quartz-akz.pages.dev/Warshall's-Algorithm) - [Wavelength](https://quartz-akz.pages.dev/Wavelength) - [Well-Formed Formula](https://quartz-akz.pages.dev/Well-Formed-Formula) - [Work](https://quartz-akz.pages.dev/Work) - [Work-Energy Theorem](https://quartz-akz.pages.dev/Work-Energy-Theorem) # Hydrostatic Pressure Nov 09, 2025, 3 min read - [phyc10002](https://quartz-akz.pages.dev/tags/study/unimelb/phyc10002) - [static](https://quartz-akz.pages.dev/tags/physics/motion/static) - [fluid](https://quartz-akz.pages.dev/tags/physics/fluid) - [tosee](https://quartz-akz.pages.dev/tags/tosee) - [todo](https://quartz-akz.pages.dev/tags/todo) When [Fluid](https://quartz-akz.pages.dev/fluid)s are defined to be ‘at rest’ (that is, all forces are balanced) they are called hydrostatic. In hydrostatic fluids, the pressure increases the ‘deeper’ we go. ### Definition [§](https://quartz-akz.pages.dev/Hydrostatic-Pressure#definition) ##### Formula - 1 [§](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---1) > Hydrostatic pressure > > ΔP\=−ρfluidgΔy\=ρfluidgd > > Py2\=Py1\+ρfluid⋅g(y2−y1) ##### Formula - 2 [§](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---2) > Hydrostatic Pressure of Water at a Depth > > Ph\=P0\+ρwatergh ##### Formula - 3 [§](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---3) > Hydrostatic Pressure of Air at an altitude > > Ph\=P0−ρairgh > > > Note > > > > - P = [Pressure](https://quartz-akz.pages.dev/Pressure) (in Pa) \* Ph = Pressure at depth/altitude h. This is also referred to as the absolute pressure \* P0 =[Atmospheric Pressure](https://quartz-akz.pages.dev/Pressure#atmospheric-pressure) ≈100 kPa - ρ = [Density (Physics)](https://quartz-akz.pages.dev/Density-\(Physics\)) (in kg/m3) - g = Acceleration due to gravity ≈9\.8 m/s2 - y = Height relative to sea level. (in m) - d = Depth (negative height relative to sea level) - Δy = y2−y1 = Change in y position. - h = Change in height from sea level (always positive!)[\#tosee](https://quartz-akz.pages.dev/tags/tosee)[\#todo](https://quartz-akz.pages.dev/tags/todo) is it? > Gauge pressure > > Pressure gauges (devices that measure pressure) don’t actually measure Ph, the absolute pressure. They measure the gauge pressure: ρfluid⋅gh ### Derivation [§](https://quartz-akz.pages.dev/Hydrostatic-Pressure#derivation) The formula for hydrostatic pressure is derived by using [Newton’s first law of motion](https://quartz-akz.pages.dev/Newton's-Laws-of-Motion#first-law-law-of-inertia) and [Pascal’s Law](https://quartz-akz.pages.dev/Pascal's-Law). Recall that for a body at rest, the sum of all forces must be zero: ∑ F \= 0 Let’s start by looking at an [incompressible fluid](https://quartz-akz.pages.dev/Fluid#compressibility) that starts from sea level, and extends downwards. We know that for the forces to balance out, the force from the water must balance that from the atmosphere. Furthermore, the atmospheric force is from the weight of all the air molecules: Fatmosphere\=matmos⋅g Then the force from the fluid comes from the molecules inside the fluid. Ffluid\=Fatmosphere ![700](https://quartz-akz.pages.dev/Hydrostatic-Pressure-.excalidraw) Again, we tend to talk about things in terms of pressure, so for the rectangular area that is contact with the air, the pressures are equal: ![](https://quartz-akz.pages.dev/Pressure#formula) Patmosphere\=AFatmos Py\=0\=AFfluid Patmosphere\=Pfluid at y\=0 Now, since we defined the fluid to be incompressible and it is confined, we can apply Pascal’s Law, which says the pressure is equal in a fluid without gravity. If we take a circular disc of area, C at height y\=−h inside the fluid, due to Pascal’s Law, it must have the same pressure, meaning for each side of the disc (top and bottom), the forces must be equal: [Hydrostatic Pressure \_1.excalidraw](https://quartz-akz.pages.dev/Hydrostatic-Pressure-_1.excalidraw) Makes sense so far? Now let’s introduce [Gravitational Forces](https://quartz-akz.pages.dev/Gravitational-Force) into the system. Pascal’s Law, unfortunately, doesn’t quite behave the same anymore. At y\=0, we have the top surface experiencing a force due to the weight of air: Pfluid\=Pair\=Py\=0 On the disk, C with area A we have cylindrical column of water above it, which adds extra force on top of the pressure force\! ∑FC\=Ffluid\+Fweight of column [Hydrostatic Pressure \_2.excalidraw](https://quartz-akz.pages.dev/Hydrostatic-Pressure-_2.excalidraw) In terms of pressure and density: Fweight of column\=mcolumng\=ρfluidVcolumn⋅g PC⋅A\=Pfluid⋅A\+ρVcolumn⋅g Since Vcolumn\=A⋅h, where h is the difference in y, we have: PC⋅A\=Pfluid⋅A\+ρAhg dividing by A: PC\=Pfluid\+ρhg Now express everything in terms of y level: P−h\=P0\+ρhg ### Table of Contents - [Definition](https://quartz-akz.pages.dev/Hydrostatic-Pressure#definition) - [Formula - 1](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---1) - [Formula - 2](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---2) - [Formula - 3](https://quartz-akz.pages.dev/Hydrostatic-Pressure#formula---3) - [Derivation](https://quartz-akz.pages.dev/Hydrostatic-Pressure#derivation) ### Related Concepts Press to search Search ### See Also: - [Archimedes' Principle](https://quartz-akz.pages.dev/Archimedes'-Principle) - [Physics 2 (Advanced)](https://quartz-akz.pages.dev/Physics-2-\(Advanced\)) Site made by [Sujay Lobo](https://github.com/slimeborger) Created using [Quartz v4.1.1](https://quartz.jzhao.xyz/) by [Jacky Zhao](https://github.com/jackyzha0) Favicon by [juicy\_fish](https://www.freepik.com/free-vector/set-network-lines-circles-flat_41681654.htm#query=network%20icon&position=5&from_view=search&track=ais&uuid=f427ea34-d92d-4b6e-838a-cc096cdee92c) on Freepik This work is licensed under [CC BY-SA 4.0](http://creativecommons.org/licenses/by-sa/4.0/?ref=chooser-v1) ![](https://mirrors.creativecommons.org/presskit/icons/cc.svg?ref=chooser-v1)![](https://mirrors.creativecommons.org/presskit/icons/by.svg?ref=chooser-v1)![](https://mirrors.creativecommons.org/presskit/icons/sa.svg?ref=chooser-v1)
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