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

If you need to find an estimate for how much time it will take to fill your air tank, you’ve come to the right place.

Let’s say you have an air tank, or some other suitably rated pressure vessel, and you want to figure out how long it will take to bring the pressure up to a certain level using an air compressor of known capacity (CFM).

In this article, we’ll tell you how to calculate the air tank fill time using common sense, and not a lot of formulas.

3 Things You Need To Know To Get Started

  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 essentially 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

For example, a 30 CFM compressor will pull in about this much air in a minute:

dog-house-drawing

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

How To Calculate Time To Fill Questions

With this background information in mind, we can start to calculate time to fill questions using simple logic. In the following examples, we demonstrate the logic one of our air compressor engineers used to answer these questions, so you can replicate similar logic during your own calculations.

Example 1

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

Additional Background Information

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

Time To Fill Logic

  1. 1 ft³ = 1728/232 = 7.5 gallons.
  2. The tank is 100/7.5 = about 13 ft³.
  3. Therefore, there is 13 ft³ of atmospheric air in the tank to start with.
  4. There is 135/15 x 13 = 117 ft³ of atmospheric air packed into the tank when it is up to the target pressure of 120 PSIG (135 PSIA).
  5. The difference is 117-13 = 104 ft³.
  6. The 15 CFM compressor processes 15 ft³ of atmospheric air every minute:
    1. 1 minute produces 15 ft³.
    2. 2 minutes produces 30 ft³.
    3. 4 minutes produces 60 ft³.
    4. 7 minutes produces 105 ft³.
  7. Therefore, 104 ft³ / 15 ft³ per Min = 6.9 minutes.

It will take about 7 minutes.

Example 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?

Additional Background Information

  • Pipe ID is 6.07 inches
  • Area of a circle is about ¾ the area of the square that surrounds it
  • (6.07 x 6.07) x 0.75 = 27.6
  • The pipe has an area of approximately 28 inches

Time To fill Logic

  1. There are 144 SQ inches in one square foot (ft²).
    1. Area = 28/144 = 0.19 ft².
  2. The pipe volume is simply the circular area times length.
    1. Volume = 0.19 x 5280 ft (1 Mile) = 1000 ft³.
  3. There is 1000 ft³ of atmospheric air in the pipe to start with.
  4. There will be 45/15 x 1000 = 3000 ft³ of atmospheric air packed into the pipe when it is up to the target pressure of 30 PSIG.
  5. The difference is 3000 – 1000 = 2000 ft³.
  6. The 120 CFM compressor processes 120 ft³ of atmospheric air every minute:
    1. 1 minute produces 120 ft³.
    2. 8 minutes produces 960 ft³.
    3. 16 minutes produces 1920 ft³.
    4. 17 minutes produces 2040 ft³.

It will take about 17 minutes.

Example 3

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

Time To Fill Logic

  • As we saw in Example 1, there is about 7 ½ gallons in a cubic foot. Therefore, 35 gallons is roughly 5 ft³.
  • At 145 (160 PSIA) PSIG the tank will have 160/15 x 5 = 53 ft³ of atmospheric air in it
  • Likewise, at 110 PSIG the tank will have 125/15 x 5 = 42 ft³ of atmospheric air in it
  • The difference is 11 ft³
  • 30 CFM compressor processes 30 ft³ of atmospheric air every minute
    • In 10 seconds, it produces 5 ft³ (1/6 of 30)
    • In 20 seconds, it produces 10 ft³,

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.

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