There are two methods. One by good thumb rule of taking receiver tank volume as equal to 20% of compressor (add all, if more than one is installed) free air displacement. For example, if free air delivery is 100 CUBIC FEET PER MINUTE, the receiver volume will be 20% of 100 which is 20 cubic feet. Using this volume, you can design a tank in any shape, but usually follows circular profile. So, if the receiver tank should have a height of 5 feet, assuming some space restriction, the area will come down to (20/5 = 4 square feet) and hence diameter can be decided accordingly.
Two by scientific method of calculating the equipment's demand. The quantity of air consumed by all equipments put together is "demand" and what compressor outputs is called "supply." The (demand/supply) ratio should always be less than 1 to avoid compressor overloading.
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