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Understanding molecular weight helps explain why different gases can travel at varying speeds through a medium.","shortDefinition":null,"relatedTerms":[{"term":"Gas Constant","definition":"A physical constant that relates the pressure, volume, and temperature of an ideal gas, used in equations of state.","keyTermSlug":null},{"term":"Density","definition":"The mass per unit volume of a substance, which directly affects how sound waves propagate through different media.","keyTermSlug":"density"},{"term":"Kinetic Molecular Theory","definition":"A theory that explains the behavior of gases in terms of particle motion, temperature, and intermolecular forces.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dd89af0a058d9c1d77d","slug":"speed-of-sound-in-air","subjectSlug":"fluid-mechanics","term":"speed of sound in air","definition":"The speed of sound in air is the distance traveled by a sound wave in a unit of time, typically measured in meters per second (m/s). This speed is influenced by factors such as temperature, humidity, and atmospheric pressure, and it serves as a critical parameter in fluid mechanics, particularly in the study of compressible flows and shock waves.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Compressibility","definition":"The property of a fluid that describes how its density changes when subjected to pressure changes, affecting sound propagation.","keyTermSlug":null},{"term":"Adiabatic Process","definition":"A thermodynamic process in which no heat is transferred to or from the system, influencing the speed of sound in gases.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8e0027350945d8d25907","slug":"mach-number","subjectSlug":"fluid-mechanics","term":"Mach Number","definition":"Mach number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium. This term is crucial in understanding fluid dynamics, particularly when analyzing compressible flows, shock waves, and various flow regimes that occur in different fluid mechanics applications.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which pressure waves travel through a medium, determined by the medium's properties such as temperature and density.","keyTermSlug":null},{"term":"Compressibility","definition":"A measure of how much a substance can be compressed, which significantly affects fluid behavior when speeds approach or exceed the speed of sound.","keyTermSlug":null},{"term":"Normal Shock Wave","definition":"A type of shock wave that occurs when a supersonic flow encounters a sudden change in conditions, causing an abrupt increase in pressure, temperature, and density.","keyTermSlug":null}],"parents":[{"id":"mehkXYISatbF3X93","type":"content"},{"id":"RdYf92hHe3xY3F9h","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"},{"id":"pWNUtHJ5jahiSXg9","type":"content"},{"id":"6RWaXIksUnLyaTRt","type":"content"}]},{"_id":"66ba8eb07229d26a708e50a4","slug":"incompressible-flow","subjectSlug":"fluid-mechanics","term":"Incompressible Flow","definition":"Incompressible flow refers to a fluid flow where the fluid density remains essentially constant throughout the motion. This concept is crucial in fluid mechanics as it simplifies many calculations, especially when analyzing the behavior of liquids, which typically exhibit little to no compressibility under standard conditions. Recognizing a flow as incompressible allows for the application of specific equations and principles, streamlining the analysis of fluid dynamics.","shortDefinition":null,"relatedTerms":[{"term":"Density","definition":"Density is the mass per unit volume of a substance, crucial in determining whether a fluid can be treated as incompressible.","keyTermSlug":"density"},{"term":"Viscosity","definition":"Viscosity is a measure of a fluid's resistance to deformation or flow, impacting how incompressible flow behaves in different scenarios.","keyTermSlug":"viscosity"},{"term":"Bernoulli's Equation","definition":"Bernoulli's Equation describes the relationship between pressure, velocity, and elevation in an incompressible flow, helping predict fluid behavior in various conditions.","keyTermSlug":"bernoullis-equation"}],"parents":[{"id":"JMcW8VYure8gcTC7","type":"content"},{"id":"GwTHtoBAqQy3qBXz","type":"content"},{"id":"oqiw1gU7t60M3AG5","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8eb29af0a058d9c1dd69","slug":"compressible-flow","subjectSlug":"fluid-mechanics","term":"compressible flow","definition":"Compressible flow refers to the behavior of fluids when their density changes significantly due to variations in pressure and temperature. This phenomenon typically occurs in high-speed flows, such as those encountered in aerodynamics and gas dynamics, where the effects of compressibility cannot be ignored. Understanding compressible flow is essential for analyzing the performance of aircraft, rockets, and other systems operating at high velocities.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity that represents the ratio of the speed of an object moving through a fluid to the speed of sound in that fluid.","keyTermSlug":"mach-number"},{"term":"Speed of Sound","definition":"The speed at which pressure waves propagate through a medium, which varies based on the medium's temperature and composition.","keyTermSlug":null},{"term":"Shock Wave","definition":"A sharp change in pressure, temperature, and density that occurs when an object travels through a medium at a speed greater than the speed of sound, creating a sudden disturbance in the flow field.","keyTermSlug":null}],"parents":[{"id":"JMcW8VYure8gcTC7","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee1e70dc17dfe1a863e","slug":"john-william-strutt-lord-rayleigh","subjectSlug":"fluid-mechanics","term":"John William Strutt (Lord Rayleigh)","definition":"John William Strutt, known as Lord Rayleigh, was a prominent British physicist and engineer who made significant contributions to the study of sound and acoustics, among other areas. His work in the late 19th century laid the foundation for understanding the speed of sound in various media and the concept of the Mach number, which describes the relationship between an object's speed and the speed of sound in the surrounding medium.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves propagate through a medium, determined by factors such as temperature, pressure, and density.","keyTermSlug":null},{"term":"Mach Number","definition":"A dimensionless quantity that represents the ratio of an object's speed to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Acoustics","definition":"The branch of physics that deals with the production, transmission, and effects of sound waves.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee8f9443f90e28d3206","slug":"bulk-modulus","subjectSlug":"fluid-mechanics","term":"Bulk Modulus","definition":"Bulk modulus is a measure of a material's resistance to uniform compression, defined as the ratio of volumetric stress to the change in volume strain. It reflects how much pressure is needed to compress a given volume of material and is crucial for understanding how sound propagates through different media and influences Mach number calculations.","shortDefinition":null,"relatedTerms":[{"term":"Sound Speed","definition":"The speed at which sound waves travel through a medium, influenced by the medium's density and bulk modulus.","keyTermSlug":null},{"term":"Density","definition":"The mass per unit volume of a substance, which, along with bulk modulus, affects the propagation of sound waves.","keyTermSlug":"density"},{"term":"Pressure Wave","definition":"A disturbance that travels through a medium, transmitting energy from one location to another, characterized by its speed, which depends on bulk modulus.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8eece70dc17dfe1a866f","slug":"humidity-effect","subjectSlug":"fluid-mechanics","term":"humidity effect","definition":"The humidity effect refers to the influence of moisture content in the air on the speed of sound and the Mach number. Increased humidity lowers the density of air, which leads to an increase in the speed of sound. This is significant because as humidity changes, it can affect various aerodynamic calculations and the performance of aircraft, particularly when flying at high speeds.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves travel through a medium, influenced by temperature, pressure, and humidity.","keyTermSlug":null},{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Density","definition":"The mass per unit volume of a substance, which plays a critical role in fluid mechanics and affects the behavior of sound waves in different environments.","keyTermSlug":"density"}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee83c0d0cde089bb8a6","slug":"isaac-newton","subjectSlug":"fluid-mechanics","term":"Isaac Newton","definition":"Isaac Newton was a groundbreaking physicist and mathematician whose work laid the foundation for classical mechanics, especially through his laws of motion and universal gravitation. His insights into the behavior of objects in motion significantly advanced the understanding of fluid dynamics, particularly regarding the behavior of fluids in motion and the forces acting on them.","shortDefinition":null,"relatedTerms":[{"term":"Laws of Motion","definition":"Three fundamental principles formulated by Newton that describe the relationship between a body and the forces acting upon it, laying the groundwork for classical mechanics.","keyTermSlug":null},{"term":"Universal Gravitation","definition":"Newton's law stating that every point mass attracts every other point mass in the universe, which explains gravitational forces that also influence fluid behavior under varying conditions.","keyTermSlug":null},{"term":"Calculus","definition":"A branch of mathematics developed by Newton (and Leibniz) that allows for the analysis of changes and motion, crucial for modeling fluid behavior.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]}]},"pageData":{"subject":{"id":"fluid-mechanics","name":"Fluid Mechanics","generationMetadata":{"group":"Group 5 – learning objectives v5.2","level":"college undergraduate","branch":"Engineering","duration":"one semester","subBranch":"Chemical Engineering","lengthVariant":"less text","model":"opus"}},"unit":{"id":"yzcdXi0ZXG5qbVCW","publicId":"yzcdXi0ZXG5qbVCW","name":"Unit 13 – Compressible Flow","order":13,"slug":"unit-13","description":"Unit 13 – Compressible Flow","h1":null,"active":true,"emoji":"📚","hasResources":true},"topic":{"id":"TjL4kadBx1kr8dt2","name":"13.1 Speed of Sound and Mach Number","fullNumber":"13.1"},"content":{"id":"FlUOqiZgGn5JByZy","topics":[{"id":"TjL4kadBx1kr8dt2","name":"13.1 Speed of Sound and Mach Number","fullNumber":"13.1"}],"title":"13.1 Speed of Sound and Mach Number","desc":null,"summary":null,"type":"STUDY_GUIDE","slug":"speed-sound-mach-number","date":null,"vimeoLiveLink":null,"url":null,"markdown":"Sound travels through fluids at different speeds, depending on the medium's properties. The speed of sound in air is about 343 m/s, while in water it's much faster at 1,480 m/s. Temperature, compressibility, and molecular weight all affect sound speed.\n\nMach number, the ratio of flow velocity to local sound speed, helps categorize flow regimes. It's crucial in aerodynamics, determining whether a flow is subsonic, transonic, supersonic, or hypersonic. This impacts vehicle design and performance in high-speed applications.\n\n## Speed of Sound and Mach Number\n\n### Speed of sound in fluids\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Speed at which small pressure disturbances travel through a fluid medium\n- For ideal gases, calculated using the equation: $c = \\sqrt{\\gamma R T}$\n - $\\gamma$: ratio of specific heats (heat capacity ratio) represents the fluid's compressibility (air at standard conditions: 1.4)\n - $R$: gas-specific constant depends on the gas composition (air: 287 J/kg·K)\n - $T$: absolute temperature of the gas affects molecular motion and energy (room temperature: 293 K)\n- Depends on fluid compressibility more compressible fluids have lower sound speeds (water: 1,480 m/s, air: 343 m/s)\n- Increases with temperature due to higher molecular motion and energy transfer (air at 20℃: 343 m/s, air at 100℃: 386 m/s)\n- Decreases with molecular weight heavier molecules have slower sound propagation (helium: 1,007 m/s, carbon dioxide: 259 m/s)\n\n### Calculation of Mach number\n- Dimensionless ratio of flow velocity to local speed of sound represents compressibility effects\n- Defined as: $M = \\frac{V}{c}$\n - $V$: flow velocity in the medium (aircraft speed, wind tunnel velocity)\n - $c$: local speed of sound depends on fluid properties and temperature\n- Calculation steps:\n 1. Determine flow velocity ($V$) from given information or flow equations (pitot tube measurement, numerical simulation)\n 2. Calculate local speed of sound ($c$) based on fluid properties and temperature (ideal gas equation, experimental data)\n 3. Divide flow velocity by local speed of sound to obtain Mach number (subsonic: < 0.8, supersonic: > 1.2)\n\n### Flow regimes vs Mach number\n- Subsonic flow: $M < 0.8$\n - Flow velocity below local sound speed minimal compressibility effects\n - Density variations small often treated as incompressible (low-speed wind tunnels, propeller aircraft)\n- Transonic flow: $0.8 \\leq M \\leq 1.2$\n - Flow velocity near sound speed significant compressibility effects\n - Shock waves may form leading to abrupt changes in flow properties (transonic aircraft, high-speed wind tunnels)\n- Supersonic flow: $1.2 < M < 5$\n - Flow velocity exceeds sound speed compressibility effects dominate\n - Shock waves present leading to discontinuities in flow properties (supersonic aircraft, rocket nozzles)\n- Hypersonic flow: $M \\geq 5$\n - Flow velocity greatly exceeds sound speed extreme compressibility and high-temperature effects\n - Strong shock waves and complex gas dynamics observed (hypersonic vehicles, reentry vehicles)\n\n### Significance of Mach number\n- Determines flow regime and applicable equations/assumptions (incompressible vs compressible flow)\n- Indicates importance of compressibility effects (negligible at low Mach, significant at high Mach)\n- Affects shock wave formation and behavior (location, strength, and impact on flow properties)\n- Influences design of vehicles and devices in compressible flow (aerodynamics, propulsion, high-speed vehicles)\n - Subsonic aircraft design focuses on lift generation and drag reduction (wing shape, streamlining)\n - Supersonic aircraft design considers shock wave management and heat transfer (swept wings, thermal protection)\n - Rocket nozzle design optimizes expansion and thrust generation based on Mach number (converging-diverging nozzle)","cheatsheet":null,"publishDate":null,"updatedAt":"2024-07-19T00:32:54.859Z","status":"PUBLISHED","images":[{"url":"https://storage.googleapis.com/static.prod.fiveable.me/search-images%2F%22Speed_of_sound_in_fluids_ideal_gases_compressibility_temperature_effects_molecular_weight_comparison%22-Figure_14_05_01.jpg","description":"Phase Changes – Fundamentals of Heat, Light & Sound","sourceUrl":"https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/222/2014/12/20104455/Figure_14_05_01.jpg","hostUrl":"https://pressbooks.nscc.ca/heatlightsound/chapter/13-5-phase-changes/","altText":null,"sectionTitle":"Speed of sound in 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The speed of sound in air is about 343 m/s, while in water it's much faster at 1,480 m/s. Temperature, compressibility, and molecular weight all affect sound speed.\n\nMach number, the ratio of flow velocity to local sound speed, helps categorize flow regimes. It's crucial in aerodynamics, determining whether a flow is subsonic, transonic, supersonic, or hypersonic. This impacts vehicle design and performance in high-speed applications.\n\n## Speed of Sound and Mach Number\n\n### Speed of sound in fluids\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Speed at which small pressure disturbances travel through a fluid medium\n- For ideal gases, calculated using the equation: $c = \\sqrt{\\gamma R T}$\n - $\\gamma$: ratio of specific heats (heat capacity ratio) represents the fluid's compressibility (air at standard conditions: 1.4)\n - $R$: gas-specific constant depends on the gas composition (air: 287 J/kg·K)\n - $T$: absolute temperature of the gas affects molecular motion and energy (room temperature: 293 K)\n- Depends on fluid compressibility more compressible fluids have lower sound speeds (water: 1,480 m/s, air: 343 m/s)\n- Increases with temperature due to higher molecular motion and energy transfer (air at 20℃: 343 m/s, air at 100℃: 386 m/s)\n- Decreases with molecular weight heavier molecules have slower sound propagation (helium: 1,007 m/s, carbon dioxide: 259 m/s)\n\n### Calculation of Mach number\n- Dimensionless ratio of flow velocity to local speed of sound represents compressibility effects\n- Defined as: $M = \\frac{V}{c}$\n - $V$: flow velocity in the medium (aircraft speed, wind tunnel velocity)\n - $c$: local speed of sound depends on fluid properties and temperature\n- Calculation steps:\n 1. Determine flow velocity ($V$) from given information or flow equations (pitot tube measurement, numerical simulation)\n 2. Calculate local speed of sound ($c$) based on fluid properties and temperature (ideal gas equation, experimental data)\n 3. Divide flow velocity by local speed of sound to obtain Mach number (subsonic: < 0.8, supersonic: > 1.2)\n\n### Flow regimes vs Mach number\n- Subsonic flow: $M < 0.8$\n - Flow velocity below local sound speed minimal compressibility effects\n - Density variations small often treated as incompressible (low-speed wind tunnels, propeller aircraft)\n- Transonic flow: $0.8 \\leq M \\leq 1.2$\n - Flow velocity near sound speed significant compressibility effects\n - Shock waves may form leading to abrupt changes in flow properties (transonic aircraft, high-speed wind tunnels)\n- Supersonic flow: $1.2 < M < 5$\n - Flow velocity exceeds sound speed compressibility effects dominate\n - Shock waves present leading to discontinuities in flow properties (supersonic aircraft, rocket nozzles)\n- Hypersonic flow: $M \\geq 5$\n - Flow velocity greatly exceeds sound speed extreme compressibility and high-temperature effects\n - Strong shock waves and complex gas dynamics observed (hypersonic vehicles, reentry vehicles)\n\n### Significance of Mach number\n- Determines flow regime and applicable equations/assumptions (incompressible vs compressible flow)\n- Indicates importance of compressibility effects (negligible at low Mach, significant at high Mach)\n- Affects shock wave formation and behavior (location, strength, and impact on flow properties)\n- Influences design of vehicles and devices in compressible flow (aerodynamics, propulsion, high-speed vehicles)\n - Subsonic aircraft design focuses on lift generation and drag reduction (wing shape, streamlining)\n - Supersonic aircraft design considers shock wave management and heat transfer (swept wings, thermal protection)\n - Rocket nozzle design optimizes expansion and thrust generation based on Mach number (converging-diverging nozzle)","cheatsheet":null,"publishDate":null,"updatedAt":"2024-07-19T00:32:54.859Z","status":"PUBLISHED","images":[{"url":"https://storage.googleapis.com/static.prod.fiveable.me/search-images%2F%22Speed_of_sound_in_fluids_ideal_gases_compressibility_temperature_effects_molecular_weight_comparison%22-Figure_14_05_01.jpg","description":"Phase Changes – Fundamentals of Heat, Light & Sound","sourceUrl":"https://s3-us-west-2.amazonaws.com/courses-images-archive-read-only/wp-content/uploads/sites/222/2014/12/20104455/Figure_14_05_01.jpg","hostUrl":"https://pressbooks.nscc.ca/heatlightsound/chapter/13-5-phase-changes/","altText":null,"sectionTitle":"Speed of sound in 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and in motion. You'll study fluid properties, hydrostatics, fluid dynamics, and flow analysis. The course dives into Bernoulli's equation, momentum conservation, and viscous flow. You'll also learn about dimensional analysis, boundary layers, and turbulence. It's all about understanding how fluids behave in various engineering scenarios.\n\n## Is Fluid Mechanics hard?\n\nFluid Mechanics has a reputation for being tough, and honestly, it can be. The concepts can get pretty abstract, and there's a lot of math involved. But here's the thing - once you get the hang of it, it's not as bad as people make it out to be. The key is to stay on top of the material and practice solving problems regularly. It's challenging, but definitely manageable.\n\n## Tips for taking Fluid Mechanics in college\n\n1. Use [Fiveable Study Guides](https://fiveable.me/cram-mode) to help you cram 🌶️\n2. Master the basics of calculus and physics before diving in\n3. Draw diagrams for every problem - it helps visualize fluid flow\n4. Practice applying Bernoulli's equation to different scenarios\n5. Use dimensional analysis to check your work\n6. Watch YouTube videos on fluid dynamics experiments\n7. Join a study group to tackle complex problems together\n8. Review real-world applications, like how airplanes generate lift\n9. Don't fall behind - the concepts build on each other\n10. Check out \"An Introduction to Fluid Dynamics\" by G.K. Batchelor for deeper insights\n\n## Common pre-requisites for Fluid Mechanics\n\n1. Calculus III: This course covers multivariable calculus and vector analysis. You'll learn about partial derivatives, multiple integrals, and vector fields - all crucial for understanding fluid mechanics.\n\n2. Physics II: This class focuses on electricity, magnetism, and waves. It provides a solid foundation in physical principles that apply to fluid behavior.\n\n3. Differential Equations: Here, you'll learn to solve various types of differential equations. This skill is essential for analyzing fluid flow and solving complex fluid mechanics problems.\n\n## Classes similar to Fluid Mechanics\n\n1. Thermodynamics: This course deals with heat, energy, and their interactions. You'll study the laws of thermodynamics and their applications to engineering systems.\n\n2. Heat Transfer: This class focuses on the transfer of thermal energy between physical systems. You'll learn about conduction, convection, and radiation.\n\n3. Computational Fluid Dynamics (CFD): This course teaches you how to use computer simulations to analyze fluid flow. You'll learn about numerical methods and software tools for modeling fluid behavior.\n\n4. Transport Phenomena: This class combines fluid mechanics, heat transfer, and mass transfer. You'll study the transport of momentum, energy, and mass in various systems.\n\n## Majors related to Fluid Mechanics\n\n1. Chemical Engineering: Focuses on designing and optimizing chemical processes. Students learn to apply fluid mechanics principles to reactor design, separations, and process equipment.\n\n2. Mechanical Engineering: Deals with the design and manufacturing of mechanical systems. Fluid mechanics is crucial for understanding hydraulics, pneumatics, and aerodynamics in mechanical systems.\n\n3. Aerospace Engineering: Concentrates on aircraft and spacecraft design. Fluid mechanics is fundamental to understanding aerodynamics and propulsion systems.\n\n4. Civil Engineering: Involves the design and construction of infrastructure. Fluid mechanics is essential for hydraulics, water resources management, and environmental engineering aspects.\n\n## What can you do with a degree in Fluid Mechanics?\n\n1. Process Engineer: Designs and optimizes industrial processes in chemical plants. They use fluid mechanics principles to design piping systems, reactors, and separation equipment.\n\n2. Aerospace Engineer: Develops aircraft and spacecraft. They apply fluid mechanics to design aerodynamic structures and propulsion systems.\n\n3. HVAC Engineer: Designs heating, ventilation, and air conditioning systems. They use fluid mechanics to optimize air flow and thermal comfort in buildings.\n\n4. Environmental Engineer: Works on solutions for environmental issues. They apply fluid mechanics to water treatment processes, air pollution control, and waste management systems.\n\n## Fluid Mechanics FAQs\n\n1. How much programming is involved in Fluid Mechanics? While the core course doesn't usually involve much programming, you might use some computational tools for data analysis or simple simulations. More advanced courses like CFD will involve more programming.\n\n2. Are there any hands-on experiments in Fluid Mechanics? Many Fluid Mechanics courses include lab components where you'll conduct experiments. These might involve measuring flow rates, pressure drops, or visualizing flow patterns.\n\n3. How does Fluid Mechanics relate to other engineering disciplines? Fluid Mechanics principles are widely applicable in various engineering fields. You'll find its concepts used in designing everything from blood pumps in biomedical engineering to oil pipelines in petroleum engineering.","emoji":"💧","order":null,"numResources":null,"active":true,"slug":"fluid-mechanics","generationMetadata":{"group":"Group 5 – learning objectives v5.2","level":"college undergraduate","branch":"Engineering","duration":"one semester","subBranch":"Chemical Engineering","lengthVariant":"less text","model":"opus"}},"pageParams":{"communitySlug":"fluid-mechanics","unitSlug":"unit-13","contentSlug":"speed-sound-mach-number","docId":"FlUOqiZgGn5JByZy"},"children":["$","$L1c",null,{"content":{"id":"FlUOqiZgGn5JByZy","topics":[{"id":"TjL4kadBx1kr8dt2","name":"13.1 Speed of Sound and Mach Number","fullNumber":"13.1"}],"title":"13.1 Speed of Sound and Mach Number","desc":null,"summary":null,"type":"STUDY_GUIDE","slug":"speed-sound-mach-number","date":null,"vimeoLiveLink":null,"url":null,"markdown":"Sound travels through fluids at different speeds, depending on the medium's properties. The [speed of sound in air](https://www.fiveableKeyTerm:speed_of_sound_in_air) is about 343 m/s, while in water it's much faster at 1,480 m/s. Temperature, [compressibility](https://www.fiveableKeyTerm:compressibility), and [molecular weight](https://www.fiveableKeyTerm:molecular_weight) all affect sound speed.\n\n[Mach number](https://www.fiveableKeyTerm:Mach_Number), the ratio of flow velocity to local sound speed, helps categorize flow regimes. It's crucial in aerodynamics, determining whether a flow is [subsonic](https://www.fiveableKeyTerm:subsonic), [transonic](https://www.fiveableKeyTerm:transonic), [supersonic](https://www.fiveableKeyTerm:supersonic), or [hypersonic](https://www.fiveableKeyTerm:hypersonic). This impacts vehicle design and performance in high-speed applications.\n\n## Speed of Sound and Mach Number\n\n### Speed of sound in fluids\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Speed at which small pressure disturbances travel through a fluid medium\n- For ideal gases, calculated using the equation: $c = \\sqrt{\\gamma R T}$\n - $\\gamma$: ratio of specific heats (heat capacity ratio) represents the fluid's compressibility (air at standard conditions: 1.4)\n - $R$: gas-specific constant depends on the gas composition (air: 287 J/kg·K)\n - $T$: absolute temperature of the gas affects molecular motion and energy (room temperature: 293 K)\n- Depends on fluid compressibility more compressible fluids have lower sound speeds (water: 1,480 m/s, air: 343 m/s)\n- Increases with temperature due to higher molecular motion and energy transfer (air at 20℃: 343 m/s, air at 100℃: 386 m/s)\n- Decreases with molecular weight heavier molecules have slower sound propagation (helium: 1,007 m/s, carbon dioxide: 259 m/s)\n### Calculation of Mach number\n- Dimensionless ratio of flow velocity to local speed of sound represents compressibility effects\n- Defined as: $M = \\frac{V}{c}$\n - $V$: flow velocity in the medium (aircraft speed, wind tunnel velocity)\n - $c$: local speed of sound depends on fluid properties and temperature\n- Calculation steps:\n 1. Determine flow velocity ($V$) from given information or flow equations (pitot tube measurement, numerical simulation)\n 2. Calculate local speed of sound ($c$) based on fluid properties and temperature ([ideal gas equation](https://www.fiveableKeyTerm:Ideal_Gas_Equation), experimental data)\n 3. Divide flow velocity by local speed of sound to obtain Mach number (subsonic: < 0.8, supersonic: > 1.2)\n\n### Flow regimes vs Mach number\n- Subsonic flow: $M < 0.8$\n - Flow velocity below local sound speed minimal compressibility effects\n - [Density variations](https://www.fiveableKeyTerm:density_variations) small often treated as incompressible (low-speed wind tunnels, propeller aircraft)\n- Transonic flow: $0.8 \\leq M \\leq 1.2$\n - Flow velocity near sound speed significant compressibility effects\n - [Shock waves](https://www.fiveableKeyTerm:Shock_Waves) may form leading to abrupt changes in flow properties (transonic aircraft, high-speed wind tunnels)\n- Supersonic flow: $1.2 < M < 5$\n - Flow velocity exceeds sound speed compressibility effects dominate\n - Shock waves present leading to discontinuities in flow properties (supersonic aircraft, rocket nozzles)\n- Hypersonic flow: $M \\geq 5$\n - Flow velocity greatly exceeds sound speed extreme compressibility and high-temperature effects\n - Strong shock waves and complex gas dynamics observed (hypersonic vehicles, reentry vehicles)\n### Significance of Mach number\n- Determines flow regime and applicable equations/assumptions (incompressible vs [compressible flow](https://www.fiveableKeyTerm:compressible_flow))\n- Indicates importance of compressibility effects (negligible at low Mach, significant at high Mach)\n- Affects shock wave formation and behavior (location, strength, and impact on flow properties)\n- Influences design of vehicles and devices in compressible flow (aerodynamics, propulsion, high-speed vehicles)\n - Subsonic aircraft design focuses on lift generation and drag reduction (wing shape, streamlining)\n - Supersonic aircraft design considers shock wave management and heat transfer (swept wings, thermal protection)\n - Rocket nozzle design optimizes expansion and thrust generation based on Mach number (converging-diverging 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This term is important for understanding various applications in aerodynamics, such as the design of aircraft and missiles that can travel faster than sound.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Subsonic","definition":"Refers to speeds that are below the speed of sound; typically associated with conventional aircraft.","keyTermSlug":null},{"term":"Transonic","definition":"Describes speeds that are close to the speed of sound, usually between Mach 0.8 and Mach 1.2, where both subsonic and supersonic flow can exist.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dbd749917179a870c2c","slug":"mach-number-formula","subjectSlug":"fluid-mechanics","term":"Mach Number Formula","definition":"The Mach number formula is a dimensionless quantity that represents the ratio of the speed of an object moving through a fluid to the speed of sound in that same fluid. It is a crucial concept in fluid mechanics and aerodynamics, helping to categorize the flow regime of an object as subsonic, transonic, supersonic, or hypersonic based on its velocity relative to the local speed of sound.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves propagate through a medium, dependent on factors like temperature and pressure.","keyTermSlug":null},{"term":"Subsonic Flow","definition":"Flow conditions where the velocity of the fluid is less than the speed of sound, typically characterized by a Mach number less than 1.","keyTermSlug":null},{"term":"Supersonic Flow","definition":"Flow conditions where the velocity of the fluid exceeds the speed of sound, typically characterized by a Mach number greater than 1.","keyTermSlug":"supersonic-flow"}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dbfe70dc17dfe1a7d79","slug":"hypersonic","subjectSlug":"fluid-mechanics","term":"hypersonic","definition":"Hypersonic refers to speeds that exceed Mach 5, which is five times the speed of sound in air at sea level. At these speeds, the dynamics of fluid flow change dramatically, leading to significant aerodynamic heating and pressure effects that influence vehicle design and stability. Understanding hypersonic flight is essential for advancements in aerospace engineering and defense applications.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Supersonic","definition":"Refers to speeds between Mach 1 and Mach 5, where an object travels faster than sound but slower than hypersonic speeds.","keyTermSlug":null},{"term":"Aerodynamic Heating","definition":"The increase in temperature of an object due to friction with the air as it moves at high speeds, particularly significant in hypersonic flight.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc09af0a058d9c1d6e7","slug":"sonic-boom","subjectSlug":"fluid-mechanics","term":"sonic boom","definition":"A sonic boom is a loud explosive sound caused by the shock waves created when an object travels through the air at a speed greater than the speed of sound. This phenomenon occurs when an object, such as an aircraft, breaks the sound barrier, producing pressure waves that coalesce and create a powerful noise that can be heard on the ground.","shortDefinition":null,"relatedTerms":[{"term":"Mach number","definition":"A dimensionless unit used to represent the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":null},{"term":"Shock wave","definition":"A type of propagating disturbance that moves faster than the speed of sound, creating a sudden change in pressure, temperature, and density.","keyTermSlug":null},{"term":"Supersonic","definition":"Referring to speeds that exceed the speed of sound, typically defined as speeds greater than Mach 1.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc0e70dc17dfe1a7d84","slug":"temperature-dependence","subjectSlug":"fluid-mechanics","term":"temperature dependence","definition":"Temperature dependence refers to how certain properties or behaviors of materials change with variations in temperature. In the context of fluid dynamics, particularly concerning the speed of sound and Mach number, this term highlights how the speed of sound in a fluid is influenced by temperature changes, affecting various applications like aerodynamics and thermodynamics.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves travel through a medium, which is affected by the medium's properties such as temperature and density.","keyTermSlug":null},{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium, often used to characterize high-speed flows.","keyTermSlug":"mach-number"},{"term":"Thermal Expansion","definition":"The increase in volume of a substance as its temperature rises, impacting the density and behavior of fluids.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc1f9443f90e28d29c7","slug":"ideal-gas-equation","subjectSlug":"fluid-mechanics","term":"Ideal Gas Equation","definition":"The ideal gas equation is a fundamental relation in thermodynamics that describes the behavior of an ideal gas. It combines several gas laws into one equation: PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the ideal gas constant, and T is the absolute temperature. Understanding this equation is crucial for analyzing the speed of sound in gases and determining the Mach number, as both concepts rely on the behavior of gas under varying conditions.","shortDefinition":null,"relatedTerms":[{"term":"Pressure","definition":"The force exerted by the gas per unit area on the walls of its container, which influences the gas's behavior in various processes.","keyTermSlug":"pressure"},{"term":"Density","definition":"The mass of gas per unit volume, which plays a significant role in determining both the speed of sound and the propagation of sound waves in a medium.","keyTermSlug":"density"},{"term":"Temperature","definition":"A measure of the average kinetic energy of the molecules in a gas, affecting both its pressure and volume in accordance with the ideal gas law.","keyTermSlug":"temperature"}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc0e70dc17dfe1a7d99","slug":"transonic","subjectSlug":"fluid-mechanics","term":"transonic","definition":"Transonic refers to the range of speeds that are around the speed of sound, typically defined as speeds between Mach 0.8 and Mach 1.2. In this regime, the flow characteristics change significantly due to the presence of both subsonic and supersonic flow patterns. This unique condition can lead to phenomena such as shock waves and changes in lift and drag on objects moving through the fluid.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Shock Wave","definition":"A discontinuity in pressure, temperature, and density that occurs when an object moves through a medium at a speed faster than sound.","keyTermSlug":null},{"term":"Supersonic","definition":"Refers to speeds that exceed the speed of sound (Mach 1), resulting in different aerodynamic characteristics compared to subsonic flow.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc1f9443f90e28d29ce","slug":"shock-waves","subjectSlug":"fluid-mechanics","term":"Shock Waves","definition":"Shock waves are abrupt changes in pressure, temperature, and density that occur when an object moves through a medium at a speed greater than the speed of sound in that medium. This phenomenon creates a wavefront that travels outward from the source, characterized by a steep gradient and leading to significant changes in local properties. Understanding shock waves is essential in fields like aerodynamics, where they play a crucial role in high-speed flows and interactions with surrounding media.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Supersonic Flow","definition":"Flow conditions in which the fluid velocity exceeds the speed of sound, resulting in the formation of shock waves.","keyTermSlug":"supersonic-flow"},{"term":"Pressure Wave","definition":"A wave created by the disturbance of pressure in a medium, which can occur at speeds less than or equal to the speed of sound.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc1749917179a870c7e","slug":"density-variations","subjectSlug":"fluid-mechanics","term":"density variations","definition":"Density variations refer to changes in the mass per unit volume of a substance, which can significantly affect the behavior of fluids under different conditions. In fluid mechanics, these variations play a crucial role in understanding phenomena like buoyancy, stability, and the propagation of sound waves. Changes in density can be influenced by temperature, pressure, and phase changes, which are essential factors when analyzing fluid flow and related concepts such as the speed of sound and Mach number.","shortDefinition":null,"relatedTerms":[{"term":"Buoyancy","definition":"The upward force exerted by a fluid on an object submerged in it, which is influenced by the density difference between the object and the fluid.","keyTermSlug":"buoyancy"},{"term":"Compressibility","definition":"The measure of how much a substance's volume decreases under pressure, which directly relates to density changes in gases.","keyTermSlug":null},{"term":"Speed of Sound","definition":"The speed at which sound waves travel through a medium, which is affected by the medium's density and temperature.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc3e981e15c73979a94","slug":"speed-of-sound-in-water","subjectSlug":"fluid-mechanics","term":"speed of sound in water","definition":"The speed of sound in water refers to the rate at which sound waves travel through water, which is influenced by various factors including temperature, salinity, and pressure. Sound travels faster in water than in air due to the higher density and incompressibility of water, allowing sound waves to transmit energy more efficiently. This concept is crucial for understanding underwater acoustics and has implications in fields such as marine biology, sonar technology, and fluid dynamics.","shortDefinition":null,"relatedTerms":[{"term":"Acoustic Impedance","definition":"A measure of how much resistance an acoustic wave encounters as it travels through a medium, defined as the product of the medium's density and the speed of sound within it.","keyTermSlug":null},{"term":"Sonar","definition":"A technique that uses sound propagation to navigate, communicate, or detect objects underwater, commonly employed in submarines and marine research.","keyTermSlug":null},{"term":"Hydrostatic Pressure","definition":"The pressure exerted by a fluid at equilibrium due to the force of gravity, which influences the speed of sound in water as depth increases.","keyTermSlug":"hydrostatic-pressure"}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dc7e981e15c73979ac0","slug":"molecular-weight","subjectSlug":"fluid-mechanics","term":"molecular weight","definition":"Molecular weight is the mass of a single molecule of a substance, typically measured in atomic mass units (amu) or grams per mole (g/mol). It plays a crucial role in determining the behavior of gases, including their speed of sound and the Mach number, as these properties are influenced by how heavy or light the molecules are. Understanding molecular weight helps explain why different gases can travel at varying speeds through a medium.","shortDefinition":null,"relatedTerms":[{"term":"Gas Constant","definition":"A physical constant that relates the pressure, volume, and temperature of an ideal gas, used in equations of state.","keyTermSlug":null},{"term":"Density","definition":"The mass per unit volume of a substance, which directly affects how sound waves propagate through different media.","keyTermSlug":"density"},{"term":"Kinetic Molecular Theory","definition":"A theory that explains the behavior of gases in terms of particle motion, temperature, and intermolecular forces.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8dd89af0a058d9c1d77d","slug":"speed-of-sound-in-air","subjectSlug":"fluid-mechanics","term":"speed of sound in air","definition":"The speed of sound in air is the distance traveled by a sound wave in a unit of time, typically measured in meters per second (m/s). This speed is influenced by factors such as temperature, humidity, and atmospheric pressure, and it serves as a critical parameter in fluid mechanics, particularly in the study of compressible flows and shock waves.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Compressibility","definition":"The property of a fluid that describes how its density changes when subjected to pressure changes, affecting sound propagation.","keyTermSlug":null},{"term":"Adiabatic Process","definition":"A thermodynamic process in which no heat is transferred to or from the system, influencing the speed of sound in gases.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8e0027350945d8d25907","slug":"mach-number","subjectSlug":"fluid-mechanics","term":"Mach Number","definition":"Mach number is a dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium. This term is crucial in understanding fluid dynamics, particularly when analyzing compressible flows, shock waves, and various flow regimes that occur in different fluid mechanics applications.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which pressure waves travel through a medium, determined by the medium's properties such as temperature and density.","keyTermSlug":null},{"term":"Compressibility","definition":"A measure of how much a substance can be compressed, which significantly affects fluid behavior when speeds approach or exceed the speed of sound.","keyTermSlug":null},{"term":"Normal Shock Wave","definition":"A type of shock wave that occurs when a supersonic flow encounters a sudden change in conditions, causing an abrupt increase in pressure, temperature, and density.","keyTermSlug":null}],"parents":[{"id":"mehkXYISatbF3X93","type":"content"},{"id":"RdYf92hHe3xY3F9h","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"},{"id":"pWNUtHJ5jahiSXg9","type":"content"},{"id":"6RWaXIksUnLyaTRt","type":"content"}]},{"_id":"66ba8eb07229d26a708e50a4","slug":"incompressible-flow","subjectSlug":"fluid-mechanics","term":"Incompressible Flow","definition":"Incompressible flow refers to a fluid flow where the fluid density remains essentially constant throughout the motion. This concept is crucial in fluid mechanics as it simplifies many calculations, especially when analyzing the behavior of liquids, which typically exhibit little to no compressibility under standard conditions. Recognizing a flow as incompressible allows for the application of specific equations and principles, streamlining the analysis of fluid dynamics.","shortDefinition":null,"relatedTerms":[{"term":"Density","definition":"Density is the mass per unit volume of a substance, crucial in determining whether a fluid can be treated as incompressible.","keyTermSlug":"density"},{"term":"Viscosity","definition":"Viscosity is a measure of a fluid's resistance to deformation or flow, impacting how incompressible flow behaves in different scenarios.","keyTermSlug":"viscosity"},{"term":"Bernoulli's Equation","definition":"Bernoulli's Equation describes the relationship between pressure, velocity, and elevation in an incompressible flow, helping predict fluid behavior in various conditions.","keyTermSlug":"bernoullis-equation"}],"parents":[{"id":"JMcW8VYure8gcTC7","type":"content"},{"id":"GwTHtoBAqQy3qBXz","type":"content"},{"id":"oqiw1gU7t60M3AG5","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8eb29af0a058d9c1dd69","slug":"compressible-flow","subjectSlug":"fluid-mechanics","term":"compressible flow","definition":"Compressible flow refers to the behavior of fluids when their density changes significantly due to variations in pressure and temperature. This phenomenon typically occurs in high-speed flows, such as those encountered in aerodynamics and gas dynamics, where the effects of compressibility cannot be ignored. Understanding compressible flow is essential for analyzing the performance of aircraft, rockets, and other systems operating at high velocities.","shortDefinition":null,"relatedTerms":[{"term":"Mach Number","definition":"A dimensionless quantity that represents the ratio of the speed of an object moving through a fluid to the speed of sound in that fluid.","keyTermSlug":"mach-number"},{"term":"Speed of Sound","definition":"The speed at which pressure waves propagate through a medium, which varies based on the medium's temperature and composition.","keyTermSlug":null},{"term":"Shock Wave","definition":"A sharp change in pressure, temperature, and density that occurs when an object travels through a medium at a speed greater than the speed of sound, creating a sudden disturbance in the flow field.","keyTermSlug":null}],"parents":[{"id":"JMcW8VYure8gcTC7","type":"content"},{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee1e70dc17dfe1a863e","slug":"john-william-strutt-lord-rayleigh","subjectSlug":"fluid-mechanics","term":"John William Strutt (Lord Rayleigh)","definition":"John William Strutt, known as Lord Rayleigh, was a prominent British physicist and engineer who made significant contributions to the study of sound and acoustics, among other areas. His work in the late 19th century laid the foundation for understanding the speed of sound in various media and the concept of the Mach number, which describes the relationship between an object's speed and the speed of sound in the surrounding medium.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves propagate through a medium, determined by factors such as temperature, pressure, and density.","keyTermSlug":null},{"term":"Mach Number","definition":"A dimensionless quantity that represents the ratio of an object's speed to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Acoustics","definition":"The branch of physics that deals with the production, transmission, and effects of sound waves.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee8f9443f90e28d3206","slug":"bulk-modulus","subjectSlug":"fluid-mechanics","term":"Bulk Modulus","definition":"Bulk modulus is a measure of a material's resistance to uniform compression, defined as the ratio of volumetric stress to the change in volume strain. It reflects how much pressure is needed to compress a given volume of material and is crucial for understanding how sound propagates through different media and influences Mach number calculations.","shortDefinition":null,"relatedTerms":[{"term":"Sound Speed","definition":"The speed at which sound waves travel through a medium, influenced by the medium's density and bulk modulus.","keyTermSlug":null},{"term":"Density","definition":"The mass per unit volume of a substance, which, along with bulk modulus, affects the propagation of sound waves.","keyTermSlug":"density"},{"term":"Pressure Wave","definition":"A disturbance that travels through a medium, transmitting energy from one location to another, characterized by its speed, which depends on bulk modulus.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8eece70dc17dfe1a866f","slug":"humidity-effect","subjectSlug":"fluid-mechanics","term":"humidity effect","definition":"The humidity effect refers to the influence of moisture content in the air on the speed of sound and the Mach number. Increased humidity lowers the density of air, which leads to an increase in the speed of sound. This is significant because as humidity changes, it can affect various aerodynamic calculations and the performance of aircraft, particularly when flying at high speeds.","shortDefinition":null,"relatedTerms":[{"term":"Speed of Sound","definition":"The speed at which sound waves travel through a medium, influenced by temperature, pressure, and humidity.","keyTermSlug":null},{"term":"Mach Number","definition":"A dimensionless quantity representing the ratio of the speed of an object to the speed of sound in the surrounding medium.","keyTermSlug":"mach-number"},{"term":"Density","definition":"The mass per unit volume of a substance, which plays a critical role in fluid mechanics and affects the behavior of sound waves in different environments.","keyTermSlug":"density"}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]},{"_id":"66ba8ee83c0d0cde089bb8a6","slug":"isaac-newton","subjectSlug":"fluid-mechanics","term":"Isaac Newton","definition":"Isaac Newton was a groundbreaking physicist and mathematician whose work laid the foundation for classical mechanics, especially through his laws of motion and universal gravitation. His insights into the behavior of objects in motion significantly advanced the understanding of fluid dynamics, particularly regarding the behavior of fluids in motion and the forces acting on them.","shortDefinition":null,"relatedTerms":[{"term":"Laws of Motion","definition":"Three fundamental principles formulated by Newton that describe the relationship between a body and the forces acting upon it, laying the groundwork for classical mechanics.","keyTermSlug":null},{"term":"Universal Gravitation","definition":"Newton's law stating that every point mass attracts every other point mass in the universe, which explains gravitational forces that also influence fluid behavior under varying conditions.","keyTermSlug":null},{"term":"Calculus","definition":"A branch of mathematics developed by Newton (and Leibniz) that allows for the analysis of changes and motion, crucial for modeling fluid behavior.","keyTermSlug":null}],"parents":[{"id":"FlUOqiZgGn5JByZy","type":"content"}]}]}]}]]