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A gas flowing through an orifice is throttled (causing turbulence and heating), and expanded (causing cooling). Therefore, it is subject to energy conversions that reduce the amount of energy available to do work. The rate at which available energy is lost can be termed the pneumatic power — a function of the pressures, the Lohm rate of the orifice, and the flow. The graph below shows the relationship for nitrogen.
The power consumption can be determined from the graph when the flow rate and the pressure ratio are known. If the flow rate is not known, it can be calculated from the Lohm rate using the gas Lohm Law. Plot a point on the graph at the appropriate pressure ratio (X-axis), and follow the vertical line to the point of intersection corresponding to the applicable flow rate. The resulting power may be read via the horizontal line intersecting the Y-axis. Note that the pressure ratio is the ratio of the absolute pressures.
The following formula may be used for nitrogen or air for more precise calculations or to extend the range of the pneumatic power graph.
Where:
HP = Pneumatic power (Horsepower)
P1 = Absolute pressure upstream of orifice (psia)
P2 = Absolute pressure downstream of orifice (psia)
L = Lohm rate of orifice (Lohms)
Due to compressor inefficiencies, more power will be needed to compress the gas than will be expended when it flows through an orifice.
EXAMPLE:
For a 500 Lohm restrictor flowing nitrogen at 750 psia exhausting to 75 psia, the flow can be easily calculated from the gas Lohm Law.
Next, determine the pressure ratio, P1/P2, which in this example is 750/75 = 10. Then, from the graph:
Always verify flow calculations by experiment.
*There are many parameters to consider when determining V-Factor. Click here for more information.
