# 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.

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### 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.

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