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It helps explain how systems maintain balance and stability, as well as the principles governing motion and interactions.","shortDefinition":null,"relatedTerms":[{"term":"Kinetic Energy","definition":"The energy an object possesses due to its motion, which can be converted from potential energy when an object starts moving.","keyTermSlug":"kinetic-energy"},{"term":"Mechanical Energy","definition":"The sum of potential and kinetic energy in a system, representing the total energy available for doing work.","keyTermSlug":null},{"term":"Work","definition":"The process of energy transfer that occurs when a force is applied to an object causing it to move, often resulting in a change in potential or kinetic energy.","keyTermSlug":"work"}],"parents":[{"id":"CMbsO4YG9bKPo8yI","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8e7e7229d26a708e4ef6","slug":"kinetic-energy","subjectSlug":"fluid-mechanics","term":"Kinetic Energy","definition":"Kinetic energy is the energy that an object possesses due to its motion. It depends on both the mass of the object and the square of its velocity, expressed mathematically as $$KE = \\frac{1}{2}mv^2$$. This concept is fundamental in understanding how energy transforms and conserves in various physical systems, as well as its relationship to momentum and external forces acting on moving objects.","shortDefinition":null,"relatedTerms":[{"term":"Potential Energy","definition":"Potential energy is the stored energy of an object due to its position or state, which can be converted into kinetic energy when the object moves.","keyTermSlug":"potential-energy"},{"term":"Conservation of Energy","definition":"The principle stating that energy cannot be created or destroyed, only transformed from one form to another, ensuring that the total energy of an isolated system remains constant.","keyTermSlug":"conservation-of-energy"},{"term":"Momentum","definition":"Momentum is the product of an object's mass and velocity, representing the quantity of motion an object has, which is closely related to kinetic energy.","keyTermSlug":null}],"parents":[{"id":"CMbsO4YG9bKPo8yI","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ed63c0d0cde089bb864","slug":"lift-force","subjectSlug":"fluid-mechanics","term":"Lift Force","definition":"Lift force is the aerodynamic force that acts perpendicular to the relative motion of an object through a fluid, typically enabling an object to rise or stay aloft. This force plays a crucial role in various applications, such as the flight of aircraft and the functioning of certain sports equipment. Understanding lift involves principles of fluid dynamics, including pressure differences and flow behavior around objects.","shortDefinition":null,"relatedTerms":[{"term":"Bernoulli's Principle","definition":"A principle that states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy.","keyTermSlug":"bernoullis-principle"},{"term":"Angle of Attack","definition":"The angle between the chord line of an airfoil and the oncoming airflow, which significantly affects lift generation.","keyTermSlug":null},{"term":"Drag Force","definition":"The aerodynamic force that opposes an object's motion through a fluid, acting parallel to the flow direction.","keyTermSlug":null}],"parents":[{"id":"Sh2XJeSMnrGxNe8T","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ee127350945d8d25efc","slug":"pressure-gradient","subjectSlug":"fluid-mechanics","term":"Pressure Gradient","definition":"A pressure gradient is the rate at which pressure changes in a fluid per unit distance, typically described as a vector pointing from high pressure to low pressure. This concept is fundamental in understanding fluid flow, as it drives the movement of fluids and influences how they behave under different conditions. It is connected to various principles that describe how fluids interact with forces and energy changes in different systems.","shortDefinition":null,"relatedTerms":[{"term":"Hydrostatic Pressure","definition":"The pressure exerted by a fluid at rest due to the weight of the fluid above it, crucial for understanding pressure gradients in static fluids.","keyTermSlug":"hydrostatic-pressure"},{"term":"Bernoulli's Equation","definition":"A principle that relates the pressure, velocity, and elevation in a flowing fluid, showing how pressure gradients influence fluid motion.","keyTermSlug":"bernoullis-equation"},{"term":"Viscous Shear","definition":"The internal resistance of a fluid to flow, which can be affected by the pressure gradient and plays a role in fluid dynamics.","keyTermSlug":null}],"parents":[{"id":"URKkyq57ssrDAfhS","type":"content"},{"id":"6pmzcuZ26tMkl7Om","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ef57229d26a708e5215","slug":"flow-rate","subjectSlug":"fluid-mechanics","term":"flow rate","definition":"Flow rate is the volume of fluid that passes through a given surface per unit time, typically measured in cubic meters per second (m³/s) or liters per minute (L/min). Understanding flow rate is crucial as it connects various principles of fluid mechanics, influencing how fluids behave in different scenarios, such as movement through pipes or the operation of pumps.","shortDefinition":null,"relatedTerms":[{"term":"continuity equation","definition":"A principle that states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a pipe to another.","keyTermSlug":"continuity-equation"},{"term":"velocity","definition":"The speed of fluid particles in a given direction, which affects the flow rate depending on the cross-sectional area of the flow.","keyTermSlug":null},{"term":"Bernoulli's equation","definition":"An energy conservation principle for flowing fluids that relates pressure, velocity, and height, often used to analyze changes in flow rate.","keyTermSlug":null}],"parents":[{"id":"URKkyq57ssrDAfhS","type":"content"},{"id":"aNfcNZFcLvQk2W8h","type":"content"},{"id":"7Z7t2yk3SWe5yxrQ","type":"content"},{"id":"N50WJZ3HTkNAaVCa","type":"content"},{"id":"7DJ6iWpjz4wuhzVE","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"},{"id":"8GIKFgoWsNoSDxma","type":"content"}]},{"_id":"66ba8efa7229d26a708e523a","slug":"drag-force","subjectSlug":"fluid-mechanics","term":"drag force","definition":"Drag force is the resistance force experienced by an object moving through a fluid, which opposes the direction of the object's motion. This force depends on several factors, including the shape of the object, the properties of the fluid, and the velocity of the object. Understanding drag force is crucial for analyzing how objects interact with fluids, affecting their motion and stability.","shortDefinition":null,"relatedTerms":[{"term":"lift force","definition":"A force that acts perpendicular to the direction of motion of an object in a fluid, often generated by airfoil shapes or wings.","keyTermSlug":null},{"term":"viscosity","definition":"A measure of a fluid's resistance to deformation or flow, affecting how easily an object moves through it.","keyTermSlug":null},{"term":"Reynolds number","definition":"A dimensionless quantity that helps predict flow patterns in different fluid flow situations, indicating whether the flow is laminar or turbulent.","keyTermSlug":null}],"parents":[{"id":"aNfcNZFcLvQk2W8h","type":"content"},{"id":"Sh2XJeSMnrGxNe8T","type":"content"},{"id":"Z34xKshVcuApmcJU","type":"content"},{"id":"tVnFW942t5aok4BX","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":"A5oFyErV13iGyhop","publicId":"A5oFyErV13iGyhop","name":"Unit 12 – Open Channel Flow","order":12,"slug":"unit-12","description":"Unit 12 – Open Channel Flow","h1":null,"active":true,"emoji":"📚","hasResources":true},"topic":{"id":"zzm1m9IdP7JkPXsU","name":"12.2 Energy and Momentum Principles","fullNumber":"12.2"},"content":{"id":"tVnFW942t5aok4BX","topics":[{"id":"zzm1m9IdP7JkPXsU","name":"12.2 Energy and Momentum Principles","fullNumber":"12.2"}],"title":"12.2 Energy and Momentum Principles","desc":null,"summary":null,"type":"STUDY_GUIDE","slug":"energy-momentum-principles","date":null,"vimeoLiveLink":null,"url":null,"markdown":"Open channel flows are governed by energy and momentum principles. These concepts help engineers analyze and predict flow behavior in rivers, canals, and other open waterways. Understanding energy equations, critical depth, and specific energy is crucial for designing hydraulic structures and managing water resources effectively.\n\nMomentum principles play a vital role in analyzing hydraulic jumps, which occur when flow transitions from supercritical to subcritical. These principles help engineers design stilling basins and energy dissipators to control flow and prevent erosion downstream of hydraulic structures like dams.\n\n## Energy and Momentum Principles in Open Channel Flows\n\n### Energy equation in open channels\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Derived from Bernoulli equation accounts for elevation head ($z$), pressure head ($\\frac{p}{\\gamma}$), and velocity head ($\\frac{V^2}{2g}$)\n- Total energy at any cross-section is the sum of these three components\n- Energy equation between two cross-sections: $z_1 + \\frac{p_1}{\\gamma} + \\frac{V_1^2}{2g} + h_p = z_2 + \\frac{p_2}{\\gamma} + \\frac{V_2^2}{2g} + h_L$\n - $h_p$ represents energy added by a pump (if present)\n - $h_L$ represents energy lost due to friction and other factors\n- In open channels, pressure head equals depth of flow ($y$) due to hydrostatic pressure distribution\n- Simplified energy equation for open channels: $z_1 + y_1 + \\frac{V_1^2}{2g} = z_2 + y_2 + \\frac{V_2^2}{2g} + h_L$\n- Analyzes changes in flow depth, velocity, and energy between different cross-sections along the channel (culverts, weirs)\n\n### Critical depth concept and significance\n- Depth of flow at which specific energy is minimum for a given discharge\n- Represents condition where Froude number ($Fr$) equals 1\n - $Fr = \\frac{V}{\\sqrt{gy}}$, where $V$ is average velocity, $g$ is gravitational acceleration, and $y$ is flow depth\n - $Fr < 1$ indicates subcritical (tranquil) flow\n - $Fr > 1$ indicates supercritical (rapid) flow\n- At critical depth, flow is unstable and can transition between subcritical and supercritical states (hydraulic jump)\n- Critical depth equation: $y_c = \\sqrt[3]{\\frac{q^2}{g}}$, where $q$ is discharge per unit width ($\\frac{Q}{b}$), $Q$ is total discharge, and $b$ is channel width\n- Important in designing hydraulic structures (spillways, chutes) to ensure proper flow conditions\n\n### Specific energy and critical depth\n- Specific energy ($E$) is the sum of flow depth and velocity head at a given cross-section: $E = y + \\frac{V^2}{2g}$\n- For a given discharge and channel geometry, specific energy curve plots $y$ on x-axis and $E$ on y-axis\n- Critical depth corresponds to point on specific energy curve where slope is zero (minimum specific energy)\n- To find critical depth, set derivative of specific energy equation to zero and solve for $y$: $\\frac{dE}{dy} = 1 - \\frac{V^2}{gy} \\frac{dV}{dy} = 0$\n- Problems involve:\n 1. Determining critical depth for given discharge and channel geometry\n 2. Finding discharge required to maintain specific flow depth\n 3. Analyzing change in specific energy and flow depth when channel slope or roughness changes (concrete vs. natural channels)\n\n### Momentum equation for hydraulic jumps\n- Based on conservation of momentum principle\n- Momentum equation between two cross-sections: $\\beta_1 \\rho Q V_1 + \\frac{\\gamma}{2} A_1 y_1 = \\beta_2 \\rho Q V_2 + \\frac{\\gamma}{2} A_2 y_2 + F_f$\n - $\\beta$ is momentum correction factor for non-uniform velocity distribution\n - $\\rho$ is fluid density\n - $A$ is cross-sectional area of flow\n - $F_f$ represents external forces (friction, pressure)\n- Hydraulic jump occurs when flow transitions from supercritical to subcritical, causing sudden increase in flow depth and decrease in velocity\n- Analyzes hydraulic jump characteristics, such as conjugate depths ($y_1$ and $y_2$) and energy dissipation\n- Froude number upstream of hydraulic jump ($Fr_1$) classifies jump type:\n 1. $1 < Fr_1 < 1.7$: Undular jump\n 2. $1.7 < Fr_1 < 2.5$: Weak jump\n 3. $2.5 < Fr_1 < 4.5$: Oscillating jump\n 4. $4.5 < Fr_1 < 9.0$: Steady jump\n 5. $Fr_1 > 9.0$: Strong jump\n- Applied to design stilling basins and energy dissipators downstream of hydraulic structures (dams) to control hydraulic jump and prevent erosion","cheatsheet":null,"publishDate":null,"updatedAt":"2024-07-19T00:32:54.072Z","status":"PUBLISHED","images":[{"url":"https://storage.googleapis.com/static.prod.fiveable.me/search-images%2F%22Energy_equation_open_channels_Bernoulli_elevation_pressure_velocity_head_flow_depth_velocity_changes%22-Bernoul.gif","description":"Bernoulli equation - WikiLectures","sourceUrl":"https://www.wikilectures.eu/images/7/77/Bernoul.gif","hostUrl":"https://www.wikilectures.eu/w/Bernoulli_equation","altText":null,"sectionTitle":"Energy equation in open 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Mechanics","emoji":"📚","keyTopics":{"1.0":{"items":[{"url":"/fluid-mechanics/unit-1/fundamentals-fluid-mechanics/study-guide/URKkyq57ssrDAfhS#undefined","title":"Introduction to Fluid Mechanics"},{"url":"/fluid-mechanics/unit-1/historical-development-applications/study-guide/4lc8OY6GhSVcDMhN#undefined","title":"Historical Development and Applications of Fluid Mechanics"},{"url":"/fluid-mechanics/unit-1/classification-fluid-flows/study-guide/JMcW8VYure8gcTC7#undefined","title":"Classification of Fluid Flows"}],"title":"Classification of Fluid Flows"}}},{"id":"dTOAEGzMU6IROPtR","title":"Unit 2 – Fluid Properties and Statics","emoji":"📚","keyTopics":{"2.0":{"items":[{"url":"/fluid-mechanics/unit-2/physical-properties-fluids/study-guide/sF7R1aO2woTr2RmO#undefined","title":"Fluid Properties"},{"url":"/fluid-mechanics/unit-2/thermodynamic-properties-fluids/study-guide/fGYt5H2smmGi7TmG#undefined","title":"Fluid Properties"},{"url":"/fluid-mechanics/unit-2/thermodynamic-properties-fluids/study-guide/fGYt5H2smmGi7TmG#undefined","title":"Ideal Gas Law and Fluid Statics"},{"url":"/fluid-mechanics/unit-2/surface-tension-capillarity/study-guide/b1suEf6smX7Ndlos#undefined","title":"Surface Tension and Capillarity"}],"title":"Surface Tension and Capillarity"}}},{"id":"MjobGsC1tm5hHa9a","title":"Unit 3 – Pressure and Fluid Forces","emoji":"📚","keyTopics":{"3.0":{"items":[{"url":"/fluid-mechanics/unit-3/pressure-measurement-distribution/study-guide/B4gAIYUuOhE7rsq9#undefined","title":"Pressure Fundamentals"},{"url":"/fluid-mechanics/unit-3/pressure-measurement-distribution/study-guide/B4gAIYUuOhE7rsq9#undefined","title":"Hydrostatic Pressure Applications"},{"url":"/fluid-mechanics/unit-3/manometry-pressure-instruments/study-guide/1Gh0Xv0LrXMggCXQ#undefined","title":"Manometry and Pressure Measurement"},{"url":"/fluid-mechanics/unit-3/manometry-pressure-instruments/study-guide/1Gh0Xv0LrXMggCXQ#undefined","title":"Pressure Measurement Devices"},{"url":"/fluid-mechanics/unit-3/hydrostatic-forces-submerged-surfaces/study-guide/QOpE33gnioi97NTf#undefined","title":"Hydrostatic Forces and Buoyancy"}],"title":"Hydrostatic Forces on Submerged Surfaces"}}},{"id":"xpjNjU8CX3m2WOZ6","title":"Unit 4 – Buoyancy and Stability","emoji":"📚","keyTopics":{"4.0":{"items":[{"url":"/fluid-mechanics/unit-4/archimedes-principle-buoyancy/study-guide/M8hsuyHJyDp30A8k#undefined","title":"Archimedes' Principle and Buoyancy"},{"url":"/fluid-mechanics/unit-4/stability-floating-bodies/study-guide/9qPmfMdOnVu9DQqO#undefined","title":"Stability and Equilibrium Concepts"},{"url":"/fluid-mechanics/unit-4/stability-floating-bodies/study-guide/9qPmfMdOnVu9DQqO#undefined","title":"Factors Affecting Stability and Stability Analysis"},{"url":"/fluid-mechanics/unit-4/metacenter-metacentric-height/study-guide/FY9RFUnByrIrtBZz#undefined","title":"Metacenter and Metacentric Height"}],"title":"Metacenter and Metacentric Height"}}},{"id":"l53fcVBovbK36PP9","title":"Unit 5 – Fluid Kinematics","emoji":"📚","keyTopics":{"5.0":{"items":[{"url":"/fluid-mechanics/unit-5/eulerian-lagrangian-descriptions/study-guide/aNfcNZFcLvQk2W8h#undefined","title":"Eulerian and Lagrangian Descriptions of Fluid Motion"},{"url":"/fluid-mechanics/unit-5/streamlines-pathlines-streaklines/study-guide/MjaiC5F5So6kWP1Z#undefined","title":"Fluid Particle Trajectories"},{"url":"/fluid-mechanics/unit-5/velocity-acceleration-fields/study-guide/mgYDgolTFghWJyGo#undefined","title":"Velocity and Acceleration Fields"},{"url":"/fluid-mechanics/unit-5/vorticity-rotation/study-guide/cuBuKWcK9tOUtCvW#undefined","title":"Vorticity and Rotation in Fluid Mechanics"}],"title":"Vorticity and Rotation"}}},{"id":"R55fxzbxgpeE8gE5","title":"Unit 6 – Control Volume Analysis","emoji":"📚","keyTopics":{"6.0":{"items":[{"url":"/fluid-mechanics/unit-6/conservation-momentum/study-guide/GwTHtoBAqQy3qBXz#undefined","title":"Conservation of Momentum in Fluid Mechanics"},{"url":"/fluid-mechanics/unit-6/conservation-energy/study-guide/CMbsO4YG9bKPo8yI#undefined","title":"Conservation of Energy in Fluid Mechanics"},{"url":"/fluid-mechanics/unit-6/reynolds-transport-theorem/study-guide/6pmzcuZ26tMkl7Om#undefined","title":"Control Volumes and the Reynolds Transport Theorem"},{"url":"/fluid-mechanics/unit-6/conservation-mass-continuity-equation/study-guide/oqiw1gU7t60M3AG5#undefined","title":"Conservation of Mass (Continuity Equation)"}],"title":"Conservation of Mass (Continuity Equation)"}}},{"id":"fZKaMQYu0Vh4pVSS","title":"Unit 7 – Differential Analysis of Fluid Flow","emoji":"📚","keyTopics":{"7.0":{"items":[{"url":"/fluid-mechanics/unit-7/navier-stokes-equations/study-guide/FZktBZRLOgVZ05cD#undefined","title":"Derivation and Components of the Navier-Stokes Equations"},{"url":"/fluid-mechanics/unit-7/navier-stokes-equations/study-guide/FZktBZRLOgVZ05cD#undefined","title":"Application and Limitations of the Navier-Stokes Equations"},{"url":"/fluid-mechanics/unit-7/eulers-equation-bernoullis-equation/study-guide/RCX6T6RJDMwby0tv#undefined","title":"Euler's Equation"},{"url":"/fluid-mechanics/unit-7/eulers-equation-bernoullis-equation/study-guide/RCX6T6RJDMwby0tv#undefined","title":"Bernoulli's Equation"},{"url":"/fluid-mechanics/unit-7/potential-flow-theory/study-guide/xwM5xs2O9CaL0LYE#undefined","title":"Potential Flow Fundamentals"}],"title":"Potential Flow Theory"}}},{"id":"8ANXM342AivGPOT4","title":"Unit 8 – Dimensional Analysis and Similitude","emoji":"📚","keyTopics":{"8.0":{"items":[{"url":"/fluid-mechanics/unit-8/buckingham-pi-theorem/study-guide/mehkXYISatbF3X93#undefined","title":"Buckingham Pi Theorem"},{"url":"/fluid-mechanics/unit-8/dimensionless-parameters-fluid-mechanics/study-guide/RdYf92hHe3xY3F9h#undefined","title":"Dimensionless Parameters in Fluid Mechanics"},{"url":"/fluid-mechanics/unit-8/modeling-scaling-laws/study-guide/uFzsymd6Cn62g4gu#undefined","title":"Modeling and Scaling Principles"},{"url":"/fluid-mechanics/unit-8/modeling-scaling-laws/study-guide/uFzsymd6Cn62g4gu#undefined","title":"Scaling Laws Application and Limitations"}],"title":"Modeling and Scaling Laws"}}},{"id":"H8KL1YOssD4Pv5M4","title":"Unit 9 – Viscous Flow in Pipes","emoji":"📚","keyTopics":{"9.0":{"items":[{"url":"/fluid-mechanics/unit-9/pipe-network-analysis/study-guide/7Z7t2yk3SWe5yxrQ#undefined","title":"Pipe Network Analysis"},{"url":"/fluid-mechanics/unit-9/major-minor-losses-pipe-systems/study-guide/1Z0UFXCWVr7rwocM#undefined","title":"Major Losses in Pipe Systems"},{"url":"/fluid-mechanics/unit-9/major-minor-losses-pipe-systems/study-guide/1Z0UFXCWVr7rwocM#undefined","title":"Total Losses and Equivalent Length"},{"url":"/fluid-mechanics/unit-9/laminar-turbulent-flow/study-guide/N50WJZ3HTkNAaVCa#undefined","title":"Laminar and Turbulent Flow in Pipes"},{"url":"/fluid-mechanics/unit-9/laminar-turbulent-flow/study-guide/N50WJZ3HTkNAaVCa#undefined","title":"Turbulent Flow and Pipe Flow Analysis"}],"title":"Laminar and Turbulent Flow"}}},{"id":"M7edOoA1iqAgsx3D","title":"Unit 10 – Flow over Immersed Bodies","emoji":"📚","keyTopics":{"10.0":{"items":[{"url":"/fluid-mechanics/unit-10/boundary-layer-theory/study-guide/6q6UKQKdvISj1wbX#undefined","title":"Boundary Layer Fundamentals"},{"url":"/fluid-mechanics/unit-10/boundary-layer-theory/study-guide/6q6UKQKdvISj1wbX#undefined","title":"Boundary Layer Characteristics"},{"url":"/fluid-mechanics/unit-10/drag-lift-forces/study-guide/Sh2XJeSMnrGxNe8T#undefined","title":"Drag and Lift Forces"},{"url":"/fluid-mechanics/unit-10/flow-separation-wakes/study-guide/Z34xKshVcuApmcJU#undefined","title":"Flow 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These concepts help engineers analyze and predict flow behavior in rivers, canals, and other open waterways. Understanding energy equations, critical depth, and specific energy is crucial for designing hydraulic structures and managing water resources effectively.\n\nMomentum principles play a vital role in analyzing hydraulic jumps, which occur when flow transitions from supercritical to subcritical. These principles help engineers design stilling basins and energy dissipators to control flow and prevent erosion downstream of hydraulic structures like dams.\n\n## Energy and Momentum Principles in Open Channel Flows\n\n### Energy equation in open channels\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Derived from Bernoulli equation accounts for elevation head ($z$), pressure head ($\\frac{p}{\\gamma}$), and velocity head ($\\frac{V^2}{2g}$)\n- Total energy at any cross-section is the sum of these three components\n- Energy equation between two cross-sections: $z_1 + \\frac{p_1}{\\gamma} + \\frac{V_1^2}{2g} + h_p = z_2 + \\frac{p_2}{\\gamma} + \\frac{V_2^2}{2g} + h_L$\n - $h_p$ represents energy added by a pump (if present)\n - $h_L$ represents energy lost due to friction and other factors\n- In open channels, pressure head equals depth of flow ($y$) due to hydrostatic pressure distribution\n- Simplified energy equation for open channels: $z_1 + y_1 + \\frac{V_1^2}{2g} = z_2 + y_2 + \\frac{V_2^2}{2g} + h_L$\n- Analyzes changes in flow depth, velocity, and energy between different cross-sections along the channel (culverts, weirs)\n\n### Critical depth concept and significance\n- Depth of flow at which specific energy is minimum for a given discharge\n- Represents condition where Froude number ($Fr$) equals 1\n - $Fr = \\frac{V}{\\sqrt{gy}}$, where $V$ is average velocity, $g$ is gravitational acceleration, and $y$ is flow depth\n - $Fr < 1$ indicates subcritical (tranquil) flow\n - $Fr > 1$ indicates supercritical (rapid) flow\n- At critical depth, flow is unstable and can transition between subcritical and supercritical states (hydraulic jump)\n- Critical depth equation: $y_c = \\sqrt[3]{\\frac{q^2}{g}}$, where $q$ is discharge per unit width ($\\frac{Q}{b}$), $Q$ is total discharge, and $b$ is channel width\n- Important in designing hydraulic structures (spillways, chutes) to ensure proper flow conditions\n\n### Specific energy and critical depth\n- Specific energy ($E$) is the sum of flow depth and velocity head at a given cross-section: $E = y + \\frac{V^2}{2g}$\n- For a given discharge and channel geometry, specific energy curve plots $y$ on x-axis and $E$ on y-axis\n- Critical depth corresponds to point on specific energy curve where slope is zero (minimum specific energy)\n- To find critical depth, set derivative of specific energy equation to zero and solve for $y$: $\\frac{dE}{dy} = 1 - \\frac{V^2}{gy} \\frac{dV}{dy} = 0$\n- Problems involve:\n 1. Determining critical depth for given discharge and channel geometry\n 2. Finding discharge required to maintain specific flow depth\n 3. Analyzing change in specific energy and flow depth when channel slope or roughness changes (concrete vs. natural channels)\n\n### Momentum equation for hydraulic jumps\n- Based on conservation of momentum principle\n- Momentum equation between two cross-sections: $\\beta_1 \\rho Q V_1 + \\frac{\\gamma}{2} A_1 y_1 = \\beta_2 \\rho Q V_2 + \\frac{\\gamma}{2} A_2 y_2 + F_f$\n - $\\beta$ is momentum correction factor for non-uniform velocity distribution\n - $\\rho$ is fluid density\n - $A$ is cross-sectional area of flow\n - $F_f$ represents external forces (friction, pressure)\n- Hydraulic jump occurs when flow transitions from supercritical to subcritical, causing sudden increase in flow depth and decrease in velocity\n- Analyzes hydraulic jump characteristics, such as conjugate depths ($y_1$ and $y_2$) and energy dissipation\n- Froude number upstream of hydraulic jump ($Fr_1$) classifies jump type:\n 1. $1 < Fr_1 < 1.7$: Undular jump\n 2. $1.7 < Fr_1 < 2.5$: Weak jump\n 3. $2.5 < Fr_1 < 4.5$: Oscillating jump\n 4. $4.5 < Fr_1 < 9.0$: Steady jump\n 5. $Fr_1 > 9.0$: Strong jump\n- Applied to design stilling basins and energy dissipators downstream of hydraulic structures (dams) to control hydraulic jump and prevent erosion","cheatsheet":null,"publishDate":null,"updatedAt":"2024-07-19T00:32:54.072Z","status":"PUBLISHED","images":[{"url":"https://storage.googleapis.com/static.prod.fiveable.me/search-images%2F%22Energy_equation_open_channels_Bernoulli_elevation_pressure_velocity_head_flow_depth_velocity_changes%22-Bernoul.gif","description":"Bernoulli equation - WikiLectures","sourceUrl":"https://www.wikilectures.eu/images/7/77/Bernoul.gif","hostUrl":"https://www.wikilectures.eu/w/Bernoulli_equation","altText":null,"sectionTitle":"Energy equation in open 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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-12","contentSlug":"energy-momentum-principles","docId":"tVnFW942t5aok4BX"},"children":["$","$L1c",null,{"content":{"id":"tVnFW942t5aok4BX","topics":[{"id":"zzm1m9IdP7JkPXsU","name":"12.2 Energy and Momentum Principles","fullNumber":"12.2"}],"title":"12.2 Energy and Momentum Principles","desc":null,"summary":null,"type":"STUDY_GUIDE","slug":"energy-momentum-principles","date":null,"vimeoLiveLink":null,"url":null,"markdown":"Open channel flows are governed by energy and momentum principles. These concepts help engineers analyze and predict flow behavior in rivers, canals, and other open waterways. Understanding energy equations, [critical depth](https://www.fiveableKeyTerm:Critical_Depth), and [specific energy](https://www.fiveableKeyTerm:specific_energy) is crucial for designing hydraulic structures and managing water resources effectively.\n\nMomentum principles play a vital role in analyzing [hydraulic jumps](https://www.fiveableKeyTerm:hydraulic_jumps), which occur when flow transitions from supercritical to subcritical. These principles help engineers design [stilling basins](https://www.fiveableKeyTerm:Stilling_Basins) and [energy dissipators](https://www.fiveableKeyTerm:energy_dissipators) to control flow and prevent erosion downstream of hydraulic structures like dams.\n\n## Energy and Momentum Principles in Open Channel Flows\n\n### Energy equation in open channels\n\n ###### ![fiveable_image_carousel](https://fiveable.me)\n\n- Derived from [Bernoulli equation](https://www.fiveableKeyTerm:Bernoulli_Equation) accounts for elevation head ($z$), pressure head ($\\frac{p}{\\gamma}$), and velocity head ($\\frac{V^2}{2g}$)\n- Total energy at any cross-section is the sum of these three components\n- [Energy equation](https://www.fiveableKeyTerm:energy_equation) between two cross-sections: $z_1 + \\frac{p_1}{\\gamma} + \\frac{V_1^2}{2g} + h_p = z_2 + \\frac{p_2}{\\gamma} + \\frac{V_2^2}{2g} + h_L$\n - $h_p$ represents energy added by a pump (if present)\n - $h_L$ represents energy lost due to friction and other factors\n- In open channels, pressure head equals depth of flow ($y$) due to hydrostatic pressure distribution\n- Simplified energy equation for open channels: $z_1 + y_1 + \\frac{V_1^2}{2g} = z_2 + y_2 + \\frac{V_2^2}{2g} + h_L$\n- Analyzes changes in flow depth, velocity, and energy between different cross-sections along the channel (culverts, weirs)\n### Critical depth concept and significance\n- Depth of flow at which specific energy is minimum for a given discharge\n- Represents condition where [Froude number](https://www.fiveableKeyTerm:Froude_Number) ($Fr$) equals 1\n - $Fr = \\frac{V}{\\sqrt{gy}}$, where $V$ is average velocity, $g$ is gravitational acceleration, and $y$ is flow depth\n - $Fr < 1$ indicates subcritical (tranquil) flow\n - $Fr > 1$ indicates supercritical (rapid) flow\n- At critical depth, flow is unstable and can transition between subcritical and supercritical states (hydraulic jump)\n- Critical depth equation: $y_c = \\sqrt[3]{\\frac{q^2}{g}}$, where $q$ is discharge per unit width ($\\frac{Q}{b}$), $Q$ is total discharge, and $b$ is channel width\n- Important in designing hydraulic structures (spillways, chutes) to ensure proper flow conditions\n### Specific energy and critical depth\n- Specific energy ($E$) is the sum of flow depth and velocity head at a given cross-section: $E = y + \\frac{V^2}{2g}$\n- For a given discharge and channel geometry, specific energy curve plots $y$ on x-axis and $E$ on y-axis\n- Critical depth corresponds to point on specific energy curve where slope is zero (minimum specific energy)\n- To find critical depth, set derivative of specific energy equation to zero and solve for $y$: $\\frac{dE}{dy} = 1 - \\frac{V^2}{gy} \\frac{dV}{dy} = 0$\n- Problems involve:\n 1. Determining critical depth for given discharge and channel geometry\n 2. Finding discharge required to maintain specific flow depth\n 3. Analyzing change in specific energy and flow depth when channel slope or roughness changes (concrete vs. natural channels)\n\n### Momentum equation for hydraulic jumps\n- Based on conservation of momentum principle\n- Momentum equation between two cross-sections: $\\beta_1 \\rho Q V_1 + \\frac{\\gamma}{2} A_1 y_1 = \\beta_2 \\rho Q V_2 + \\frac{\\gamma}{2} A_2 y_2 + F_f$\n - $\\beta$ is momentum correction factor for non-uniform velocity distribution\n - $\\rho$ is fluid density\n - $A$ is cross-sectional area of flow\n - $F_f$ represents external forces (friction, pressure)\n- Hydraulic jump occurs when flow transitions from supercritical to subcritical, causing sudden increase in flow depth and decrease in velocity\n- Analyzes hydraulic jump characteristics, such as conjugate depths ($y_1$ and $y_2$) and energy dissipation\n- Froude number upstream of hydraulic jump ($Fr_1$) classifies jump type:\n 1. $1 < Fr_1 < 1.7$: Undular jump\n 2. $1.7 < Fr_1 < 2.5$: Weak jump\n 3. $2.5 < Fr_1 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Their primary purpose is to protect downstream environments from the erosive forces of high-energy water flows by converting kinetic energy into other forms, such as thermal energy or sound energy, thus mitigating the impact on surrounding areas.","shortDefinition":null,"relatedTerms":[{"term":"hydraulic jump","definition":"A sudden change in flow regime that occurs when high-velocity flow transitions to lower velocity flow, often associated with energy dissipation.","keyTermSlug":null},{"term":"weir","definition":"A barrier across a river or stream that alters its flow characteristics, often used to create a controlled drop in water level, which can aid in energy dissipation.","keyTermSlug":null},{"term":"scour","definition":"The removal of sediment from around bridge piers or abutments due to flowing water, which can be mitigated through the use of energy dissipators.","keyTermSlug":null}],"parents":[{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8e4b9af0a058d9c1dac4","slug":"bernoulli-equation","subjectSlug":"fluid-mechanics","term":"Bernoulli Equation","definition":"The Bernoulli Equation is a fundamental principle in fluid mechanics that describes the conservation of energy in a flowing fluid. It relates the pressure, velocity, and elevation of a fluid along a streamline, showing how these factors interact under the influence of gravity and friction. This equation is crucial for understanding energy transformations in fluid flow, making it applicable in various scenarios including flow measurement techniques and energy analysis in fluids.","shortDefinition":null,"relatedTerms":[{"term":"Kinetic Energy","definition":"The energy possessed by an object due to its motion, which in the context of fluid mechanics relates to the velocity of the fluid.","keyTermSlug":"kinetic-energy"},{"term":"Pressure Energy","definition":"The potential energy stored in a fluid due to its pressure, which plays a key role in determining the flow characteristics.","keyTermSlug":null},{"term":"Streamline","definition":"An imaginary line that represents the flow of fluid, indicating the direction of the flow at any given point.","keyTermSlug":null}],"parents":[{"id":"tVnFW942t5aok4BX","type":"content"},{"id":"8GIKFgoWsNoSDxma","type":"content"}]},{"_id":"66ba8e4c27350945d8d25b69","slug":"specific-energy","subjectSlug":"fluid-mechanics","term":"specific energy","definition":"Specific energy is the total energy per unit weight of fluid in an open channel flow system, which consists of gravitational potential energy and kinetic energy. It is crucial for understanding how energy is distributed in the flow and plays a significant role in analyzing flow behavior, transitions, and classifications. Specific energy allows for the prediction of flow conditions and can help in determining critical depths and velocities.","shortDefinition":null,"relatedTerms":[{"term":"Hydraulic Grade Line","definition":"A graphical representation of the total hydraulic energy available to the flow at any point, calculated as the sum of the pressure head and elevation head.","keyTermSlug":"hydraulic-grade-line"},{"term":"Specific Force","definition":"The force exerted by a fluid per unit weight, important in analyzing forces acting on flow profiles.","keyTermSlug":null},{"term":"Critical Flow","definition":"A state of flow where specific energy is minimized for a given discharge, characterized by a critical depth that represents the transition between subcritical and supercritical flow regimes.","keyTermSlug":null}],"parents":[{"id":"tVnFW942t5aok4BX","type":"content"},{"id":"V8xDnBKH58lUQOfR","type":"content"}]},{"_id":"66ba8e75e70dc17dfe1a82db","slug":"energy-equation","subjectSlug":"fluid-mechanics","term":"energy equation","definition":"The energy equation is a fundamental principle in fluid mechanics that relates the energy changes within a fluid system to the work done on or by that system and the energy transferred as heat. This equation highlights the conservation of energy in fluid flow, illustrating how potential energy, kinetic energy, and internal energy are interrelated, ultimately describing the behavior of fluids in motion and under various forces.","shortDefinition":null,"relatedTerms":[{"term":"Bernoulli's Equation","definition":"A specific form of the energy equation that relates the pressure, velocity, and elevation of a fluid in steady, incompressible flow.","keyTermSlug":"bernoullis-equation"},{"term":"Conservation of Energy","definition":"A principle stating that the total energy in an isolated system remains constant over time, meaning energy cannot be created or destroyed, only transformed.","keyTermSlug":"conservation-of-energy"},{"term":"Mechanical Energy","definition":"The sum of potential energy and kinetic energy in a fluid system, which is crucial in analyzing the movement and behavior of fluids.","keyTermSlug":null}],"parents":[{"id":"CMbsO4YG9bKPo8yI","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8e7ce70dc17dfe1a8351","slug":"potential-energy","subjectSlug":"fluid-mechanics","term":"Potential Energy","definition":"Potential energy is the stored energy in an object due to its position or state, often related to the gravitational field or other forces acting upon it. This form of energy is critical in understanding how energy can be converted and conserved within a system, as it can be transformed into kinetic energy or other forms of energy when the conditions change. It helps explain how systems maintain balance and stability, as well as the principles governing motion and interactions.","shortDefinition":null,"relatedTerms":[{"term":"Kinetic Energy","definition":"The energy an object possesses due to its motion, which can be converted from potential energy when an object starts moving.","keyTermSlug":"kinetic-energy"},{"term":"Mechanical Energy","definition":"The sum of potential and kinetic energy in a system, representing the total energy available for doing work.","keyTermSlug":null},{"term":"Work","definition":"The process of energy transfer that occurs when a force is applied to an object causing it to move, often resulting in a change in potential or kinetic energy.","keyTermSlug":"work"}],"parents":[{"id":"CMbsO4YG9bKPo8yI","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8e7e7229d26a708e4ef6","slug":"kinetic-energy","subjectSlug":"fluid-mechanics","term":"Kinetic Energy","definition":"Kinetic energy is the energy that an object possesses due to its motion. It depends on both the mass of the object and the square of its velocity, expressed mathematically as $$KE = \\frac{1}{2}mv^2$$. This concept is fundamental in understanding how energy transforms and conserves in various physical systems, as well as its relationship to momentum and external forces acting on moving objects.","shortDefinition":null,"relatedTerms":[{"term":"Potential Energy","definition":"Potential energy is the stored energy of an object due to its position or state, which can be converted into kinetic energy when the object moves.","keyTermSlug":"potential-energy"},{"term":"Conservation of Energy","definition":"The principle stating that energy cannot be created or destroyed, only transformed from one form to another, ensuring that the total energy of an isolated system remains constant.","keyTermSlug":"conservation-of-energy"},{"term":"Momentum","definition":"Momentum is the product of an object's mass and velocity, representing the quantity of motion an object has, which is closely related to kinetic energy.","keyTermSlug":null}],"parents":[{"id":"CMbsO4YG9bKPo8yI","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ed63c0d0cde089bb864","slug":"lift-force","subjectSlug":"fluid-mechanics","term":"Lift Force","definition":"Lift force is the aerodynamic force that acts perpendicular to the relative motion of an object through a fluid, typically enabling an object to rise or stay aloft. This force plays a crucial role in various applications, such as the flight of aircraft and the functioning of certain sports equipment. Understanding lift involves principles of fluid dynamics, including pressure differences and flow behavior around objects.","shortDefinition":null,"relatedTerms":[{"term":"Bernoulli's Principle","definition":"A principle that states that an increase in the speed of a fluid occurs simultaneously with a decrease in pressure or potential energy.","keyTermSlug":"bernoullis-principle"},{"term":"Angle of Attack","definition":"The angle between the chord line of an airfoil and the oncoming airflow, which significantly affects lift generation.","keyTermSlug":null},{"term":"Drag Force","definition":"The aerodynamic force that opposes an object's motion through a fluid, acting parallel to the flow direction.","keyTermSlug":null}],"parents":[{"id":"Sh2XJeSMnrGxNe8T","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ee127350945d8d25efc","slug":"pressure-gradient","subjectSlug":"fluid-mechanics","term":"Pressure Gradient","definition":"A pressure gradient is the rate at which pressure changes in a fluid per unit distance, typically described as a vector pointing from high pressure to low pressure. This concept is fundamental in understanding fluid flow, as it drives the movement of fluids and influences how they behave under different conditions. It is connected to various principles that describe how fluids interact with forces and energy changes in different systems.","shortDefinition":null,"relatedTerms":[{"term":"Hydrostatic Pressure","definition":"The pressure exerted by a fluid at rest due to the weight of the fluid above it, crucial for understanding pressure gradients in static fluids.","keyTermSlug":"hydrostatic-pressure"},{"term":"Bernoulli's Equation","definition":"A principle that relates the pressure, velocity, and elevation in a flowing fluid, showing how pressure gradients influence fluid motion.","keyTermSlug":"bernoullis-equation"},{"term":"Viscous Shear","definition":"The internal resistance of a fluid to flow, which can be affected by the pressure gradient and plays a role in fluid dynamics.","keyTermSlug":null}],"parents":[{"id":"URKkyq57ssrDAfhS","type":"content"},{"id":"6pmzcuZ26tMkl7Om","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]},{"_id":"66ba8ef57229d26a708e5215","slug":"flow-rate","subjectSlug":"fluid-mechanics","term":"flow rate","definition":"Flow rate is the volume of fluid that passes through a given surface per unit time, typically measured in cubic meters per second (m³/s) or liters per minute (L/min). Understanding flow rate is crucial as it connects various principles of fluid mechanics, influencing how fluids behave in different scenarios, such as movement through pipes or the operation of pumps.","shortDefinition":null,"relatedTerms":[{"term":"continuity equation","definition":"A principle that states that for an incompressible fluid, the mass flow rate must remain constant from one cross-section of a pipe to another.","keyTermSlug":"continuity-equation"},{"term":"velocity","definition":"The speed of fluid particles in a given direction, which affects the flow rate depending on the cross-sectional area of the flow.","keyTermSlug":null},{"term":"Bernoulli's equation","definition":"An energy conservation principle for flowing fluids that relates pressure, velocity, and height, often used to analyze changes in flow rate.","keyTermSlug":null}],"parents":[{"id":"URKkyq57ssrDAfhS","type":"content"},{"id":"aNfcNZFcLvQk2W8h","type":"content"},{"id":"7Z7t2yk3SWe5yxrQ","type":"content"},{"id":"N50WJZ3HTkNAaVCa","type":"content"},{"id":"7DJ6iWpjz4wuhzVE","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"},{"id":"8GIKFgoWsNoSDxma","type":"content"}]},{"_id":"66ba8efa7229d26a708e523a","slug":"drag-force","subjectSlug":"fluid-mechanics","term":"drag force","definition":"Drag force is the resistance force experienced by an object moving through a fluid, which opposes the direction of the object's motion. This force depends on several factors, including the shape of the object, the properties of the fluid, and the velocity of the object. Understanding drag force is crucial for analyzing how objects interact with fluids, affecting their motion and stability.","shortDefinition":null,"relatedTerms":[{"term":"lift force","definition":"A force that acts perpendicular to the direction of motion of an object in a fluid, often generated by airfoil shapes or wings.","keyTermSlug":null},{"term":"viscosity","definition":"A measure of a fluid's resistance to deformation or flow, affecting how easily an object moves through it.","keyTermSlug":null},{"term":"Reynolds number","definition":"A dimensionless quantity that helps predict flow patterns in different fluid flow situations, indicating whether the flow is laminar or turbulent.","keyTermSlug":null}],"parents":[{"id":"aNfcNZFcLvQk2W8h","type":"content"},{"id":"Sh2XJeSMnrGxNe8T","type":"content"},{"id":"Z34xKshVcuApmcJU","type":"content"},{"id":"tVnFW942t5aok4BX","type":"content"}]}]}]}]]