Tuesday Sept. 9, 2014

Brandi Carlile "Touching the Ground" (3:37), "It's Over" (3:58), "Looking Out" (3:28), Laura Marling "Blackberry Stone" (3:31)

A pretty good time-lapse video and approaching dust storm.  The video was shot last Saturday from the Sky Harbor Airport in Pheonix.  Here's a sketch of a thunderstorm showing both an updraft and a downdraft.


The cloud of dust is found at the leading edge of the cold air as it moves outward at the ground under the thunderstorm.  Winds behind the gust front can reach 100 MPH which is tornado strength.  The video is nice because you can see the thunderstorm in the distance that produced the dust storm (also commonly called a "haboob").  Often you will just see the dust and not the storm that caused it.

The dust storm was followed by record rainfall and severe flooding in Pheonix on Monday.  See the photo gallery embedded in this story from The Weather Channel.

Here is a pretty good set of photographs from yesterday's flooding in Tucson from the Arizona Daily Star.  Two people died when they were swept away by flood waters in Tucson.  You can find the rainfall totals on the Pima County Regional Flood Control District ALERT System.  You can also check Rainlog.org which has state wide coverage.

Today's class was all (perhaps too much so) about mass, weight, density, and especially pressure.  Weight is something you can feel so I passed an iron bar (it's sketched below) around class.  You were supposed to estimate it's weight.  The fact that it was 1" by 1" is significant.  More about the bar later in today's notes.




A couple of small plastic bottles were passed during class.  One contained some water the other an equal volume of mercury (here's the source of the nice photo of liquid mercury below at right).  I wanted you to appreciate how much heavier and denser mercury is than water. 




Thanks for being careful with the mercury.  A spill would have shut down the classroom and perhaps more of the building until the hazardous materials people could come in and clean it up.  It isn't so much the liquid mercury that is a hazard, but rather the mercury vapor.  Mercury vapor is used in fluorescent bulbs (including the new energy efficient CFL bulbs) which is why they need to be disposed of carefully.  That is something we'll mention again later in the class.

I am hoping that you will remember and understand the following statement
atmospheric pressure at any level in the atmosphere
depends on (is determined by)
the weight of the air overhead

We'll first review the concepts of mass, weight, and density.  I've inserted some numbers to help with the organization.

1. weight
A good place to start because we are most familiar with this term.  We can feel weight and we routinely measure weight.



A person's weight also depends on something else.




A person's weight depends on the person and also on the pull of gravity.

 


We measure weight all the time.  What units do we use?  Usually pounds, but sometimes ounces or maybe tons. 

Mass is a better way of expressing the amount of matter in an object.

2. mass





Grams (g) and kilograms (kg) are commonly used units of mass (1 kg is 1000 g). 

3.  gravitational acceleration



On the surface on the earth, weight is mass times a constant, g,  known as the gravitational acceleration.  We tend to use weight and mass interchangeably: one kilogram (units of mass) equals 2.2 pounds (units of weight) because we spend all our lives on earth where the value of the gravitational acceleration never changes.

On another planet the value of g would be different.  If you click here you'll find a little (actually a lot) more information about Newton's Law of Universal Gravitation.  You'll see how the value of g is determined and why it is called the gravitational acceleration.  These aren't details you need to worry about but I feel they should be available in case you're curious.
Here's a question to test your understanding.



The masses are all the same.  On the earth's surface the masses would all be multiplied by the same value of g.  The weights would all be equal.  If all 3 objects had a mass of 1 kg, they'd all have a weight of 2.2 pounds.

This next figure wasn't shown or discussed in class today.  Here's a situation where two objects with the same mass would have different weights


On the earth a brick has a mass of about 2.3 kg and weighs 5 pounds.  If you were to travel to the moon the mass of the brick wouldn't change (it's the same brick, the same amount of stuff).  Gravity on the moon is weaker (about 6 times weaker) than on the earth because the moon is smaller.  The brick would only weigh 0.8 pounds on the moon.  The brick would weigh almost 12 pounds on the surface on Jupiter where gravity is stronger than on the earth.


The three objects below were not passed around class (one of them is pretty heavy).  The three objects all had about the same volumes.  One is a piece of wood, another a brick, and the third something else. 




A student volunteer was able to determine relatively easily which was which by lifting each of the objects and judging its weight.




The brick in the back weighed about 5 pounds, the piece of wood about 1 pound.  The third object was made out of lead and weighed 15 pounds.

Here we had three objects of about the same size with different weights.  That means they each had different masses since weight depends on mass.  Thee different amounts of material, three different masses, were squeezed into roughly the same volume. 

4. density


The three objects have very different densities.

The bottle of mercury passed around class weighed more than the bottle of water even though the volumes were equal.  The mercury had more mass and a higher density than the water.  Densities of some common materials are shown below.
 
material
 density g/cc
air
 0.001
redwood
 0.45
water
 1.0
iron
 7.9
lead
 11.3
mercury
 13.6
gold
 19.3
platinum
 21.4
iridium
 22.4
osmium
 22.6

g/cc = grams per cubic centimeter


Note also that lead is denser than iron, mercury is denser than lead.  I wish I could bring in brick size pieces of gold, platinum, iridium, or osmium to pass around class.  They're even denser and would be even heavier than the lead and mercury. 

We'll be more concerned about air in this class than wood, brick, or lead.

In the first example below we have two equal volumes of air but the amount in each is different (the dots represent air molecules). 



The amounts of air (the masses) in the second example are the same but the volumes are different.  The left example with air squeezed into a smaller volume has the higher density. 

Here's a more subtle concept.  What if we were in outer space with the three wrapped blocks of lead, wood, and brick.  They'd be weightless.
Could we tell them apart then?  They would still have very different densities and masses but we wouldn't be able to feel how heavy they were.

5. inertia



This definition comes from Newton's 2nd law of motion
F = m a
F is force, m is mass, and a is acceleration.  We can rewrite the equation
a = F/m
This shows cause and effect more clearly.  If you exert a force (cause) on an object it will accelerate (effect).  Acceleration can be a change in speed or a change in direction (or both).  The acceleration will be less when mass (inertia) is large.

I think the following illustration will help to understand inertia.





Two stopped cars.  They are the same size except one is made of wood and the other of lead.  Which would be hardest to get moving (a stopped car resists being put into motion).  It would take considerable force to get the lead car going.  Once the cars are moving they resist a change in that motion.  The lead car would be much harder to slow down and stop.
This is the way you could try to distinguish between blocks of lead, wood, and brick in outer space.  Give them each a push.  The wood would begin moving more rapidly than the block of lead even if  both are given the same strength push.

Here's everything so far.




The weight of the iron bar is still unknown.





A very tall 1 inch x 1 inch column of air has been added to the picture.  Other than being a gas and being invisible it's really no different from the other objects.

Now we're ready to define (and hopefully understand) pressure.  It's a pretty important concept.  A lot of what happens in the atmosphere is caused by pressure differences.  Pressure differences cause wind.  Large pressure difference (such as you might find in a tornado or a hurricane) create powerful and destructive storms. 

The air that surrounds the earth has mass.  Gravity pulls downward on the atmosphere giving it weight.  Galileo conducted (in the 1600s) a simple experiment to prove that air has weight.  The experiment wasn't mentioned in class.

Atmospheric pressure at any level in the atmosphere depends on (is determined by) the weight of the air overhead  This is one way, a sort of large, atmosphere size scale way, of understanding air pressure.

6. pressure

and here we'll apply the definition to a column of air stretching from sea level to the top of the atmosphere
Pressure is defined as force divided by area.  Atmospheric pressure is the weight of the air column divided by the area at the bottom of the column (as illustrated above). 

Under normal conditions a 1 inch by 1 inch column of air stretching from sea level to the top of the atmosphere will weigh 14.7 pounds.  Normal atmospheric pressure at sea level is 14.7 pounds per square inch (psi, the units you use when you fill up your car or bike tires with air).

Now back to the iron bar.  A lot of people felt it weighed more than 20 pounds.  The bar actually weighs 14.7 pounds.  When you stand the bar on end, the pressure at the bottom would be 14.7 psi.



the weight of the 1" x 1" steel bar 52 inches long is the same as a 1" x 1" column of air that extends from sea level to the top of the atmosphere 100 or 200 miles (or more) high.  The pressure at the bottom of both would be 14.7 psi.

7. pressure units
Pounds per square inch, psi, are perfectly good pressure units, but they aren't the ones that most meteorologists use.


Typical sea level pressure is 14.7 psi or about 1000 millibars (the units used by meteorologists and the units that we will use in this class most of the time) or about 30 inches of mercury.    Milli means 1/1000 th.  So 1000 millibars is the same as 1 bar.  You sometimes see typical sea level pressure written as 1 atmosphere.

Inches of mercury refers to the reading on a mercury barometer.  This seems like unusual units for pressure.  But if you remember the chart earlier, Mercury (13.6 grams/cm3)  is denser than steel ( about 7.9 grams/cm3 ).  If we could some how construct a 1" x 1" bar of mercury it would need to be 30 inches long to equal the weight or the iron bar or the weight of a tall column of air.






Each of these columns would weigh 14.7 pounds.  The pressure at the base of each would be the same. 

A mercury barometer is, we'll find, just a balance.  You balance the weight of a very tall column of air with the weight of a much shorter column of mercury.

You never know where something you learn in ATMO 170A1 will turn up.  A long time ago, I lived and worked for a short time in France (I had a really great time and go back occasionally now to try to ride my bike up some of the famous Tour de France mountain stages).  Here's a picture of a car I owned when I was there (this one is in mint condition, mine was in far worse shape)


It's a Peugeot 404.  After buying it I took it to the service station to fill it with gas and to check the air pressure in the tires.  I was a little confused by the air compressor though, the scale only ran from 0 to 3 or 4.  I'm used to putting about 30 psi or so in my car tires (about 90 psi in my bike tires).  After staring at the scale for a while I finally realized the numbers were pressures in "bars" not "psi".  Since 14.7 psi is equivalent to 1 bar, 30 psi would be about 2 bars.  So I filled up all the tires and carefully drove off (one thing I quickly learned was you have to watch out for in France is the "Priority to the right" rule). 

You can learn a lot from bricks. 

For example the photo below (taken in my messy office) shows two of the bricks from class.  One is sitting flat, the other is sitting on its end.  Each brick weighs about 5 pounds.  Would the pressure at the base of each brick be the same or different in this kind of situation? 






Pressure is determined by (depends on) weight so you might think the pressures would be equal.  But pressure is weight divided by area.  In this case the weights are the same but the areas are different.  In the situation at left the 5 pounds must be divided by an area of about 4 inches by 8 inches = 32 inches.  That works out to be about 0.15 psi.  In the other case the 5 pounds should be divided by a smaller area, 4 inches by 2 inches = 8 inches.  That's a pressure of 0.6 psi, 4 times higher.  

Here's a picture of 5 bricks stacked on top of each other.



Would the pressure under this 5 brick tall pile be GREATER  or  LOWER  than normal atmospheric pressure at sea level?  (each brick weighs about 5 lbs and has dimensions 2" x 4" x 8").

There's a total of 25 pounds of weight.  Divide that by the 32 square inch area at the bottom of the pile and yet get less than 1 psi.  That's a lot LOWER than atmospheric pressure.  You'd need a 94 brick tall pile of bricks (470 pounds of bricks) to equal atmospheric pressure.

The main reason I brought the bricks was so that you could understand what happens to pressure with increasing altitude. 

At the bottom of the pile you would measure a weight of 25 pounds.  If you moved up a brick you would measure a weight of 20 pounds, the weight of the four bricks that are still above.  The pressure would be less.  Weight and pressure will decrease as you move up the pile.

8. pressure changes with altitude

The atmosphere is not too much different from a pile of bricks.  Pressure at any level is determined by the weight of the air still overhead.  Pressure decreases with increasing altitude because there is less and less air remaining overhead. 



At sea level altitude, at Point 1, the pressure is normally about 1000 mb.  That is determined by the weight of all (100%) of the air in the atmosphere.

Some parts of Tucson, at Point 2, are 3000 feet above sea level (most of central Tucson is a little lower than that around 2500 feet).  At 3000 ft. about 10% of the air is below, 90% is still overhead.  It is the weight of the 90% that is still above that determines the atmospheric pressure in Tucson.  If 100% of the atmosphere produces a pressure of 1000 mb, then 90% will produce a pressure of 900 mb. 

Pressure is typically about 700 mb at the summit of Mt. Lemmon (9000 ft. altitude at Point 3) because 70% of the atmosphere is overhead..

Pressure decreases rapidly with increasing altitude.  We will find that pressure changes more slowly if you move horizontally.  Pressure changes about 1 mb for every 10 meters of elevation change.  Pressure changes much more slowly normally if you move horizontally: about 1 mb in 100 km.  Still the small horizontal changes are what cause the wind to blow and what cause storms to form.

Point 4 shows a submarine at a depth of about 30 ft. or so.  The pressure there is determined by the weight of the air and the weight of the water overhead.  Water is much denser and much heavier than air.  At 30 ft., the pressure is already twice what it would be at the surface of the ocean (2000 mb instead of 1000 mb).

Here are a couple of links that I forgot to include in the notes for class.  The first is about the relatively new sport of free diving.  The 2nd is a link to an article about a diver that made it to a depth of 236 feet but died upon reaching the surface.  The divers hold their breath and must descend and return to the surface on just a single lungful of air.   Death was caused by the high pressure deep under water forcing fluid from the blood into the diver's lungs.