# Lecture 9 Dynamics of vertical motion (convection)

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Lecture 9 Dynamics of vertical motion (convection)

Vertical Forces Fluid Parcel Up Gravity Vertical pressure-gradient force

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

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

Free Convection

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

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

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

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

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

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

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)

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

Convection Cell

Fair-Weather Cumulus Clouds form in updrafts

Forced Convection

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

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