Transcript Lecture 9
Lecture 9 Dynamics of vertical motion (convection) Vertical Forces Up Vertical pressure-gradient force Fluid Parcel Gravity Newton’s 2nd Law dw/dt upward force – downward force Upward force > downward force upward acceleration Downward force > upward force downward acceleration Convection Free Buoyancy-Induced (Archimedes’ Principle) Upward force is related to density variations Forced Non-Buoyancy-Induced Upward force due to dynamic pressure effects 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 Buoyancy = fl Vg Density = obj Density of fluid = fl Gravity = -mobjg = -objVg Resultantforce fl V g obj V g fl obj V g Resultant force is upward if obj < fl Resultant force is downward if obj > fl Balloons (Not Hot-Air) obj = density of gas inside balloon = gas (I’m ignoring mass of fabric.) fl = density of air = air (Same temperature and pressure) Balloon will rise only if gas < air More p p * M, RT R T where M molecular weight What gases have a molecular weight less than air? Hydrogen, helium Hot-Air Balloons Tin Tout Gas inside balloon is air, but Tin > Tout in < 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 These pressure gradients can lift objects that are denser than the fluid E.g., Airplanes Lifting Mechanisms in Atmosphere Orographic lifting Air forced up a mountain Weather systems Fronts Low-pressure areas