Receiver Capacity N/A

[Terry]

Hi All:

I use the following formula supplied by the EPA to figure the receiver capacity of a refrigeration system.

It is basically a long cylinder that holds refrigerant. It is:

Circumference X Circumference X Length divided by 21721.

Let's say a 13" diameter tank. 3.14 X 13 = 40.82 circumference
71" long

40.82 X 40.82 X 71" = 118305.34 / 21721 = 5.45 Receiver volume

Then 5.45 X 1.5 X 76.77 (Refrigerant density of R22, from chart) = 627.6 Refrigerant capacity in pounds.

1. What is the number 21721 for?

2. When I multiply 5.45 X 1.5, what is the 1.5?


No one seems to know. Not even the EPA.

Hope some of you engineers will know.

Thanks;

Terry

 

[Let'sgoflying!]

why is the standard method of calculating the vol of a cylinder inappropriate?

 

[gismo]

Circumference X Circumference X Length divided by 21721.


40.82 X 40.82 X 71" = 118305.34 / 21721 = 5.45 Receiver volume

Then 5.45 X 1.5 X 76.77 (Refrigerant density of R22, from chart) = 627.6 Refrigerant capacity in pounds.

1. What is the number 21721 for?

2. When I multiply 5.45 X 1.5, what is the 1.5?

The formula for the volume of a cylinder is Pi*radius^2 * length. The circumference is equal to: 2*Pi*radius.

Circumference^2 = 2^2 * Pi^2 * radius^2
or 4*Pi * Pi * radius^2

So your formula: Circumference^2 * length / 21721
is really 4Pi/21721 * cylinder_volume(in inches).

4 * Pi/21721 is approximately equal to 1/1728

1728 is the number of cubic inches in a cubic foot.

Therefore your result is the volume of the cylinder in cubic feet.

I think the 1.5 is either a safety fudge factor (seems inverted for that) or something related to your density chart.

 

[Steve]

my HVAC engineering handbook is under 20 years of book storage dust...if i can dredge it up i'll try to find what that constant is derived from

 

[gismo]

my HVAC engineering handbook is under 20 years of book storage dust...if i can dredge it up i'll try to find what that constant is derived from

Steve, I think I explained what 21721 was about: 4* Pi * 12^3. And FWIW, the constant is a little off, to the nearest integer it should be 21715. I assume the error is due to someone using less precision for Pi than I did or they made a slight computational error.

What I don't really understand is the reason for the 1.5 multiplier. The formula given computes the volume of the cylinder in cubic feet. The refrigerant "density" value was given without units so it's hard to see if a conversion factor is needed. If the "density" was in pounds/cuft no conversion should be needed. I would also think that some room for expansion would be required, but that would mean a scale factor of less than 1 rather than something like 1.5, but if the density value was in some other units a factor of 1.5 might include both a unit conversion and an expansion factor. One other issue is that to get an accurate volume measurement, the circumference and length measurements would have to be of the interior although as long as the wall thickness was a tiny fraction of the measurement, it wouldn't affect the result by much.

 

[Terry]

Thanks Lance!

I am impressed.

Terry

p.s.> I think the 1.5 factor takes in account ambient temperatures. Also, I have a different density factor for every refrigerant.

Thanks again.