Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

[Phys-l] the physics of muggy weather ... and the evil of axes



Hi Folks --

True story: Once upon a time, we were living in Tucson, in a house with
a swamp cooler (aka evaporative cooler). The principle of such a device
is that hot dry outside air is taken in. Water is added. The air is
cooled by the latent heat of evaporation, and of course becomes much more
humid. The cool air is then distributed inside the house. This technique
is usable throughout the desert Southwest, and Tucson is just about the
best place for it ... except for a few days per year when the humidity
starts to creep up and the swamp coolers don't work quite so well.

The question arises, how well /should/ a swamp cooler work? The summer
when I was 11 going on 12, my father came home with a psychrometric
chart.
http://en.wikipedia.org/wiki/Psychrometrics
http://upload.wikimedia.org/wikipedia/en/0/05/PsychrometricChart-SeaLevel-SI.jpg

He was able to conclude that our cooler was performing as well as the
chart permitted, so there was no point in wishing for better. If the
cooler had underperformed the chart, he would have been motivated to
debug the cooler.

I learned one thing from this: The idea of _wet bulb temperature_. I
already knew about temperature and humidity, and I more-or-less understood
humidity in terms of dew point. You can get temperature, humidity, and
dew point information from lots of official and unofficial sources (radio,
TV, newspaper, et cetera) ... but hardly anybody gives out wet-bulb temperature
information in a forum where ordinary families can get it ... not even in
Tucson in the summer, where oodles of people would be interested in it.

Wet-bulb temperature is basically what you get if you have a thermometer
that is soaking wet and you blow on it. You can easily demonstrate that
the wet-bulb temperature is always higher than the dew point and lower
than the plain old temperature (which in this context can be called the
dry-bulb temperature).

Similarly, wet-bulb temperature determines how cool you can be if you
are sweating and standing under a fan. Dew point is a wild underestimate;
you cannot cool yourself off to the dew point just with water and a fan.
At the other extreme, plain old temperature (dry-bulb temperature) is a
wild overestimate; you can live comfortably and even exercise in hot
and dry conditions, so long as you drink enough.

If you are not set up to measure the wet-bulb temperature, or if for any
reason you want to predict the wet-bulb temperature under this-or-that
conditions, you can predict it using the psychrometric chart. The contours
of constant temperature are vertical lines. Find the one that corresponds
to the temperature of interest. Meanwhile, the contours of constant relative
humidity sweep from west-southwest to northeast on the chart; find the
contour that corresponds to the humidity of interest. Find the intersection
of these two contours. That point represents the conditions of interest.
Let's suppose this point represents the ambient atmosphere, at the input to
the swamp cooler. The contours of constant wet-bulb temperature run from
southeast to northwest in the figure. Find the contour that crosses the
point of interest, interpolating if necessary. Evaporative cooling involves
moving along a contour of constant wet-bulb temperature. So if you follow
this contour up to the northwest until you reach the edge of the diagram,
i.e. the 100% relative humidity contour, you have found the (ideal) condition
for the output of the swamp cooler.

Numerical example:
Outside temperature: 40 C
Dew point: -4 C --> 6% relative humidity
Wet-bulb temperature: 17 C

============================================

My not-so-fond memory of this is that when I was 11, I could not figure out
how to use the psychrometric chart for myself. My father understood it, but
I did not.

With the benefit of a few decades of hindsight, I can identify a big part
of the problem: Axes.

I had been taught to understand charts in terms of the X-axis and the Y-axis.
That's a problem, because the psychrometric chart doesn't have a relative
humidity axis or a wet-bulb temperature axis. (It does have a dry-bulb
temperature axis and an absolute humidity axis, but that doesn't solve the
problem. There are four or five sets of contours, and only two axes.)

Axes are bogus. You don't ever need an X-axis. In contrast, you always
need the contours of constant X. These are hinted at by the tick marks on
the X axis ... but the axis itself is red herring, i.e. an unhelpful distraction.
The idea that there is an "X direction" is sometimes true, but sometimes
not true, and never necessary.

This is a never-ending source of confusion. In common parlance we speak
of the X axis and the X direction all the time ... even though that is not
the smart way to think about things.

The psychrometric chart has contours of constant relative humidity, but it
does not have (and cannot have) an axis representing "the" direction of
increasing relative humidity.

For more on this, see the first part of
http://www.av8n.com/physics/spacetime-momentum.htm

And if you go farther in this direction, you come to
http://www.av8n.com/physics/thermo-forms.htm

When you teach kids how to plot stuff on a chart, emphasize the
_contours of constant X_ and the _contours of constant Y_. Use graph paper.
Do not abstract away the grid too soon. This approach is simultaneously
simpler and more sophisticated. It is simultaneously easier, more powerful,
and more /physical/ than fussing with axes.

It may help to introduce rhombic graph paper sooner rather than later, to
emphasize that what matters are the _contours of constant X_ and such
contours need not be perpendicular to the "X axis" if any.
http://www.av8n.com/physics/spacetime005blue-only.pdf
http://www.av8n.com/physics/spacetime005red-only.pdf

Teaching kids how to read the contours on a topo map never hurts, either ...
although you need to choose the map carefully, since the contours on some
maps are not very clearly drawn.


===========================================================================

Take-home messages:
1) Wet-bulb temperature is a nifty concept
1a) It correlates with how comfortable you will be running around outside.
1b) It correlates with how comfortable you will be in a house with a
swamp cooler.

2) You can figure out a lot of good stuff using a psychrometric chart.

3) Axes are evil. Emphasize the _contours of constant X_ and the
_contours of constant Y_.