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# Reference Areas, Volumes, Flows, ...

These are just the calculations for
the dimensions, areas, volumes, velocities, densities, ... that are used for
these tests of air collector performance.

Back to the Solar
Air Heating Collector test program home..

### Collector Dimensions::

Gross Area (less wheels and
handle)

48.5 * 96 = 4656 in^2 or 32.3
ft^2

Aperture Area

47 * 93 = 4371 in^2 or 30.35 ft^2

### Volume of Big Yellow Bag:

Diameter = 39.4 inches

Length = 11.5 left dome + 61 inch
cylinder + 11.5 inch right dome = 84 inches

The end domes are calculated as
half ellipsoids (
http://en.wikipedia.org/wiki/Ellipsoid )

End domes 0.5 ( 4/3 * Pi *
a*b*c) = 0.5*4/3*Pi*19.7*19.7*11.5) = 9345 in^3 or 5.41 ft^3 per dome

Main Cylinder = 39.4^2 * 0.785 *
61 = 74335 in^3 or 43.0 ft^3

Volume = 5.41 + 4.0 + 5.41 = 53.8 cubic ft

### Flow Rate From Big Yellow Bag Fill
Time:

Flow rate in cfm = 53.8
ft^3 / (fill time in minutes)

Fill times for various flow
rates:

Flow Rate |
Fill Time |

50 cfm |
64.6 sec |

60 |
53.8 |

70 |
46.1 |

80 |
40.4 |

### Flow Rate from Velocity at Exit
Duct:

Exit duct is 5 inches in diameter

Exit area = 4.75^2 * 0.785 =
17.71 in^2 or 0.122 ft^2

Flow rate with a 0.9 correction
for velocity profile

Flow = A*V = 0.136 ft^2 * 0.9 *
(Velocity in fpm)

eg at 680 fpm exit velocity, flow
is (0.122 ft^2) * 0.9 * (680 ft/min) = 74.7 cfm

### Air Density:

Air density varies with both
temperature and altitude (atmospheric pressure).

This handy calculator gives air
density as a function of altitude and air temperature.

http://www.denysschen.com/catalogue/density.asp

The temperature I use is the
average of the inlet and out temps, and our altitude is 5000 ft above seal
level.

So, for Tin = 55F and Tout = 120
F (average 87.5F), and 5000 ft elevation, the calculator gives 0.06 lbs/ft^3