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Lecture 9 Dynamics of vertical motion (convection)

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Vertical Forces Fluid Parcel Up Gravity Vertical pressure-gradient force

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Newton’s 2 nd Law dw/dt upward force – downward force Upward force > downward force upward acceleration Downward force > upward force downward acceleration

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Convection Free Free Buoyancy-Induced (Archimedes’ Principle) Buoyancy-Induced (Archimedes’ Principle) Upward force is related to density variations Upward force is related to density variations Forced Forced Non-Buoyancy-Induced Non-Buoyancy-Induced Upward force due to dynamic pressure effects Upward force due to dynamic pressure effects Parcel is said to be lifted Parcel is said to be lifted

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Free Convection

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Buoyancy Archimedes’ Principle: Object immersed in a fluid experiences an upward force equal to weight of displaced fluid Upward force called buoyancy Upward force called buoyancy

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Density = obj Density of fluid = fl Gravity = -m obj g = - obj V g Buoyancy = fl V g

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Resultant force is upward if obj < fl Resultant force is downward if obj > fl

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Balloons (Not Hot-Air) Balloons (Not Hot-Air) obj = density of gas inside balloon = gas (I’m ignoring mass of fabric.) (I’m ignoring mass of fabric.) fl = density of air = air (Same temperature and pressure) (Same temperature and pressure) Balloon will rise only if gas < air

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More What gases have a molecular weight less than air? Hydrogen, helium

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Hot-Air Balloons T in Gas inside balloon is air, but T in > T out in < out T out

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Air Parcel Treat air parcel as a balloon parcel temp > environment temp parcel accelerates upward (parcel is said to be buoyant) Parcel temp < environment temp parcel accelerates downward (parcel is negatively buoyant)

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Low-Level Free Convection During day, sun heats ground Ground warms air near surface Warm air parcels become buoyant and rise Cooler air aloft sinks to replace rising air

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Convection Cell

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Fair-Weather Cumulus Clouds form in updrafts

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Forced Convection

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Dynamic Pressure Motion of a fluid can cause pressure gradients E.g., Bernoulli’s principle E.g., Bernoulli’s principle These pressure gradients can lift objects that are denser than the fluid E.g., Airplanes E.g., Airplanes

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Lifting Mechanisms in Atmosphere Orographic lifting Air forced up a mountain Air forced up a mountain Weather systems Fronts Fronts Low-pressure areas Low-pressure areas

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