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Dynamics chapter 1
Notes, Test, Homework
| Question | Answer |
|---|---|
| Order of Magnitude Reasoning | quick approx answer to a problem. |
| Scale analysis | how big are the terms in an equation? want to throw out the unimportant terms -estimating typical order of magnitude of terms in governing equations |
| Newtons 2nd Law | F=Ma can use because earth's atmosphere has mass |
| contiuum mechanics | object is a tiny infintesimal chunk of fluid(liquid or gas) or an elastic solid -dynamics os branch of this |
| What 2 forces act on blobs of air? | body forces and surface forces |
| body force | force on an object is proportinal to mass of object. Force due to action at a distance ex: gravity |
| surface force | forces on an object is porportional to surface area of object. force due to contact of object with surroundings. force exerted on surface of fluid element by outside fluid ex: pressure force, friction |
| Pressure Gradient Force | considering the net pressure forece acting on a blob of air force is proportional to gradient of p -acts in opposite direction of grad p |
| Gravitational Force | applies to 2 forces w mass M and m. |
| Viscous force | Friction force -force due to molecular friction |
| inertial reference frames | non accelerating frames -stationary or moves at constant velocity F=Ma is with real forces(only true for intertial reference frames) |
| non-inertial reference frame | speeds up or rotates -it accelerates -we use this one because fixed point on earth(earth rotates) |
| F=ma can be modified to use for non-inertial frame. Introduce what 2 apparent forces? | apparent force=due to acceleration of the reference frame -centrifugal and Coriolis force |
| geopotential? | work pum required to lift a mass from earth's surface to a height z |
| latitude | rotation east and west for spherical coords |
| meridian | rotation north and south for spherical coords |
| Exact way, almost exact way, quick-n-dirty way are used to find what? | distances due to coriolis force. hockey puck |
| if atmosphere is at rest then... | coriolis force=0 friction=0 acceleration=0 p isnt a function of x or y so have hydrostatic equation |
| density is bigger for ___ air | colder |
| relation between definite integral and average | average=have a dependent variable, independent variable and interval of independent variable. |
| independent variable | time or space |
| dependent variable | temp, pressure, u or v |
| hypsometric equation | transform hydrostatic equation to treat z as dependent variable and p as independent variable |
| thickness is proportional to ___ in a layer | temperature |
| when to use isobaric coords? | when hydrostatic approx is available -uses pressure as the vertical coord(not z) |
| lagrangian | describe how quantities change with time for an air parcel following the motion |
| dependent variables of lagrangian | x(t), y(t), z(t) |
| independent variables of lagrangian | t |
| Eularian | describe how quantities change with time at a fixed point in space(not following blob) |
| independent variables of eularian | x(t), y(t), z(t), t |
| degrees into radians | multiply degree by 2 pi/360 |
| typical radius for low pressure system | 1000 km |
| typical radius for a tornado | 100 m |
| typical horizontal length of tornado | 100m-1000m |
| typical horizontal length of cumulonimbus | 1 km-10 km |
| typical horizontal length of fronts (width) | 10 km-100 km |
| typical horizontal length of H or L pressure systems | 1000 km |
| starting point for dynamics is ___. translate this law into different equations to understand/predict air morion(weather) | newtons 2nd law |
| F=ma means | sum of forces acting on object=mass of object+acceleration of object |
| a=? | Dv/Dt v= velocity |
| V=? | Dr/Dt r=position vector |
| pgf equation? | F/m=-1/row(grad p) |
| magnitude of grad p is big when | there is close packing of isobars |
| newtons law of gravitation? | Fg=(-GMm/r^2)(r vector/r) Fg= gravitational force on m due to M |
| r vector | directed distance between 2 masses, points from big mass M to little mass m |
| rvector/r | r hat (is of unit length) |
| Fg is ___ proportional to the square of the distance between 2 masses | inversely |
| G | universal gravitational constant 6.67*10^/-11 Nm^2/Kg^2 |
| g* | Fg/m gravitational force per unit mass |
| a | 6370 km |
| in troposphere, z<__km so r=Z+_=_ | 15, a,z |
| mass of earth | M=4/3(pi)(a^3)(density of earth) |
| N | kg*m/s^2 |
| density of earth | 5520 kg/m^3 |
| no-slip condition | molecular friction causes fluid to stick to solid objects/boundaries |
| steady state condition | d( )/dt=0 stops changing in time |
| sheearing stress | proportional to vertical derivative of x-comp velocity |
| newtons 3rd law | fluid below box above it exerts equal and opposite force on bottom face |
| real forces | gravitational, pgf, viscous force |
| earth rotates with angular velocity __ | omega |
| if rotating, observers in that reference frame are ___ to be subject to a ___ force | perceived, centrifugal |
| gravity force pum | gravitational force pum + centrifugal force pum |
| centrifugal force= | m*omega^2*R(vector) |
| u absolute= | omega*R |
| magnitude of omega= | 7.27*10^-5 1/s |
| coriolis force= | m(-2omegaxu) |
| components of coriolis force | Fx=m(2omegavsin(latitude)-2omegawcos(latitude)) Fy=m(-2omegausin(latitude)) Fz=m(2omegaucos(latitude)) |
| if puck stays on flat ice | z(t)=constant so w(t)=0 |
| horizontal equations of motion(with w=0) | du/dt=2omegavsin(latitude) dv/dt=-2omegausin(latitude) |
| f | 2omegasin(latitude) |
| hydrostatic equation is an ___ equation for ___ atmosphere | exact, resting |
| hydrostatic is a good approx for real moving atmosphere except when | vertical accelerations are large (supercell, tornado) |
| integrating hydrostatic shows | at any point in the resting atmosphere, pressure=weight(per unit area) of all air above it |
| p(H) | (e^-1)Po |
| ___ on constant z-surface carry same info as height contours on ____ | isobars, isobaric surface |
| local derivative of T used for | eularian |
| geosynchronous orbit | hover over the same location on earth -angular velocity of object and eaerth are the same |
| absolute | as observed in an inertial reference frame |
Created by:
leebee05
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