## HEAD OF COMPRESSION

For compressing a gas to higher pressures, certain amount of work has to be done on the gas. The work done on a gas may be expressed as foot pounds or kilogram meters.

When 1 lb of gas is lifted or moved to a distance of 1 ft, then the work done by the compressor is 1 ft·lb. Similarly, when 10 lb of gas is moved to a distance of 1 ft, then the work done by the compressor is 10 ft·lb. When 1 lb of gas is lifted/moved to a distance of 10 feet, then also the work done by the compressor is 10 ft·lb.

The head developed by a compressor is the distance or height to which a column of gas can be moved at the average density of gas. This is an important factor in calculating the head developed by a compressor. For each pound of gas the compressor raises the head, a corresponding amount of work in foot pounds has to be done on the gas. As shown above, if the head increases, the number of foot pounds of work to be done on the gas per pound also increases.

Pressure may also be converted to head, as shown in the example below.

Example:

1,000 cfm of air is compressed by a compressor to a pressure of 6 kg/cm2g

pressure. What is the work required to be done by the compressor on the

air and what is the head developed?

Air inlet pressure = atmospheric pressure = 14.7 psia

Air outlet pressure = 6 × 14.22 + 14.7 psia = 100 psia

Air density at atmospheric pressure = 28.84/359 lb/ft3 = .0803 lb/ft3

Weight flow rate of air = 1,000 × 0.0803 lb/min = 80.3

Air density at 100 psia = 28.84/50.19 = 0.5746 lb/ft3

Average density of air = (0.0803 + 0.5746)/2 = 0.3274 lb/ft3

Differential pressure developed by the compressor = 6 × 14.22 psi

= 85.32 psia

= 12,286.08 lb/ft2

Dividing the above value by the average air density, we get

= 12,286.08/0.3277 ft

= 37,491.8 ft

Work done on 1,000 cfm air = 80.3 × 37,491.8 ft·lb/min

This is the work to be done by the compressor on 1,000 cfm of air.