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How to work out “Time to Fill” type questions using simple logic

Say you have an air tank or some other suitably pressure rated vessel and you want to figure out how long it will take to bring the pressure up to a certain level using a compressor of known capacity (CFM) and you want to do it using common sense, not a lot of formulas.

First, three key things to be aware of:

  1. Atmospheric air at sea level has an Absolute Pressure of 14.7 PSIA : “Absolute”
    • Call it 15 PSI for the purpose of rough estimates
    • It is important to use PSIA when any pressure ratios are being considered
    • PSIA is PSIG : Gauge + 15 psi
      • Examples: If a pressure gauge is reading “0” the absolute pressure is about 15 PSIA
      • If a pressure gauge is reading “100” the absolute pressure is about 115 PSIA
  2. Air is pretty much a perfect spring:
    Finding absolute pressure

  3. The capacity of a compressor refers to the volume of atmosphere air that it is able to pull in and ‘”process” (ie squeeze down, or compress) in a given amount of time

So a 30 CFM compressor will pull in this much air in a minute…

dog-house-drawing

… and squeeze it down and discharge it along a pipe or hose at some high pressure.

Now let’s do some examples:

1. How long will it take a 15 CFM compressor to take a 100 gallon tank from 0 PSIG to 120 PSIG?

  • 1 Gallon is about 232 cubic inches
  • 1 cubic foot is exactly 12 x 12 x 12 = 1728 cubic inches

So 1 CU FT = 1728/232 = 7 ½ gallons and that tank is 100/7.5 = about 13 CU FT.

There is 13 CU FT of atmospheric air in the tank to start with.

There is 135/15 x 13 = 117 CU FT of atmospheric air packed into the tank when it is up to the target pressure of 120 PSIG (135 PSIA)

The difference is 117-13 = 104 CU FT.

The compressor processes 15 CU FT of atmospheric air every minute.

                1 minute gives 15 CU FT.

                2 minutes gives 30 CU FT.

                4 minutes gives 60 CU FT.

7 minutes gives 105 CU FT.

… quicker 104 CU FT/ 15 CU FT per Min = 6.9 minutes

It will take about 7 minutes.

2. How long will it take a 120 CFM compressor to take a 1 mile length of 6” schedule 40 pipe (deadheaded for testing) up to 30 PSIG from zero?

  • Pipe ID is 6.07 inches
  • Area of a circle is about ¾ the area of the square that surrounds it:
  • There are 144 SQ inches in a SQ Foot
    1. (12 x 12) → Area = 28/144 + .19 SQ Ft.
  • Pipe volume is simply the circular area times length
    1. Volume = .19 x 5280 FT (1 Mile) = 1000 CU Ft.
  • There is 1000 CU FT of atmospheric air in the pipe to start with
  • There is 45/15 x 1000 = 3000 CU FT of atmospheric air packed into the pipe when it is up to the target pressure of 30 PSIG
  • The difference is 3000 – 1000 = 2000 CU FT
  • The compressor processes 120 CU FT of atmospheric air every minute

1 minute gives 120 CU FT

8 minutes gives 960 CU FT

16 minutes gives 1920 CU FT

17 minutes gives 2040 CU FT

It will take about 17 minutes.

3. How long will it take a 30 CFM compressor to take a 35 Gallon tank from 110 PSIG to 145 PSIG?

  • As we saw in example 1, there is about 7 ½ gallons in a cubic foot
  • So 35 gallons is roughly 5 cubic feet
  • At 145 (160 PSIA) PSIG the tank will have 160/15 x 5 = 53 Cubic Ft. of atmospheric air in it
  • Likewise at 110 PSIG the tank will have 125/15 x 5 = 42 Cubic Ft. of atmospheric air in it
  • The difference is 11 Cubic Ft.
  • 30 CFM compressor processes 30 CU Ft of atmospheric air every minute
    • In 10 seconds it gives 5 Cu Ft (1/6 of 30)
    • In 20 seconds it gives 10 Cu Ft

It will take about 20 seconds to recover the tank to 145 PSIG

With some basic knowledge of your compressor, air pressure and the amount of air you need, figuring out the time to fill can be relatively easy without the use of complex formulas.

If you have any questions about this article or anything mobile compressor related, please contact us.