How many cubic feet are in a 1000 gallon tank

The water meters in Athens and many other places measure your water usage in Cubic Feet.   Most of us have very little intuition about how much water is in a cubic foot. In recent years the new water statements and rates in Athens are in terms of gallons (x 1000). The meter readings are still in cubic feet. 

The point of this problem is to develop intuitive estimates of the number of gallons of water in a cubic foot, using items that might be familiar to us.

Modern Plastic One Gallon Milk Jug.

The bulk of the milk is in a more or less cubical region in the bottom of the jug.   In making an estimate we can concentrate on where the bulk of the milk is rather than the diminishing spaces at the top.    The base is a little over 5 inches square so it is not unreasonable to ESTIMATE the volume of the milk jug (in cubic inches) to be in a 6 x 6 x 6 cube.   So how many such cubes would fit in a  12 x 12 x 12 space  (a cubic foot)?   We can argue with some degree of confidence for an estimate of between 7 and 8 gallons in a cubic foot.

Compare a known gallon.

Compare a gallon container, such as a paint can, and a box or stick structure 12 inches on a side. Visually estimate or guess how many gallon in a cubic foot. Have students estimate from the visual comparison.

The can pictured at the right is a one gallon container, roughly 4 inches by 6 inches on the bottom and slightly over 9 inches tall.   Six of these would sit compactly in the bottom 9 inches of a 12 x 12 x 12 box.   So these 6 gallons are about 9/12, or 3/4, of a cubic foot.    The other 1/4  would be a bit less than 2 gallons so once again we have a cubic foot is between 7 and 8 gallons.

How many gallons in a cubic foot?

How many cubic inches in a gallon?

How many cubic feet of gasoline in a Studebaker gasoline tank with a capacity of 17 gallons?        What's a Studebaker?    (Don't laugh.   I owned one of these.   Gasoline was under 20 cents per gallon.)

Primary storage volume requirements

Traditionally, air receivers were sized for reciprocating air compressors. The general guideline was that every cfm of air produced required one gallon of storage. Today, with lubricant-injected rotary screw compressors using load/unload controls, the suggested minimum size is between three and five gallons of storage per cfm produced. Air receiver size requirements can also vary by the type of compressor and the type of compressor capacity control.  When determining the volume of system storage required for multiple compressor systems, only the capacity of the trim compressor needs to be considered for reducing part-load energy requirements.

A larger air receiver will also provide other benefits such as stabilizing pressure or to prevent another compressor from coming online to meet large intermittent air demand requirements.  To satisfy high volume intermittent demands air receiver sizing must address the total cubic feet of air required for the duration of transient demand events and the interval between them.  Further consideration must be given to having ample storage to cover the time required to bring an additional compressor on line, should the size and duration of a demand event require it.  

Pressure differential and the effects on storage

For storage to work there must be a pressure differential and an allowable pressure band. The usable pressure differential and the air receiver size determine the available storage.  A receiver has a given volume, normally measured in gallons. Larger sizes are generally expressed, or measured, in cubic feet.

There are 7.48 gallons in a cubic foot. The amount of free air in the receiver depends on the size and on the pressure.  At sea level, the atmospheric pressure is 14.7 psia (0 psig).  If compressed air in the receiver is at 100 psig, the absolute pressure is 114.7 psia (100 psig + 14.7).

A 1,000 gallon receiver at 100 psig will hold the equivalent of: (1,000 *114.7)/(7.48 * 14.7) = 1,043 cubic feet  of free air.  The amount of usable compressed air would depend on the pressure differential.  For example: with the 1000 gallon air receiver and an allowable pressure differential of 10 psi (100 to 90 psig) the available compressed air in storage would be:

 1000  gal. x (100 - 90)/(7.48 * 14.7) = 91 cu. ft.

Be careful not to raise compressor operating pressure to increase storage. For positive displacement compressors at a nominal 100 psig, a 2 psi increase in operating pressure increases input power one percent.  For example, the increase in energy cost for raising a 100-hp air compressor’s operating pressure 10 psi is five percent, which may also overload the motor.  For a 24/7 operation having a $0.10 per kWh energy rate, this is $3,800 per year in additional energy costs.

Purchasing additional storage is a one-time cost and can often provide a rapid payback compared to raising compressor operating pressure.

How many feet is a 1000 gallon tank?

How many cubic feet does 1 gallon of water take up?

How many cubic feet is 100 gallons of liquid?

What is the cubic feet of 1 gallon?