A crude but effective approach to estimate steam leak (in lb/hr) from an orifice is to use the following expression:

Estimate the hourly, monthly, and annual costs of steam leaks from a 300-psig pipe. The steam is generated from a gas boiler with an efficiency of 80 percent. The cost of natural gas is $0.90/therm (1 therm is equivalent to 100,000 Btu/hr). The heating season spans seven months per year. Provide the costs for the following orifice diameters: 1/16; 1/8; 1/4; 3/8; 1/2; and 1 in.

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lb/hr= C k At-A-P0.97 where Ca the coefficient of discharge (for a perfectly round orifice, C = 1. In most cases, C = 0.7). k = a constant (k = 0.0165). At = the number of seconds in 1 hour (At = 3,600). A = the area of the orifice (in in.). P = the pressure inside the steam pipe (in psia).