I'm trying to calculate the steam loss (lb/hr) through a failed steam trap.  This is for a low pressure steam system operating at 8.5 psig, and the orifice diameter of the steam trap is 5/16".  I've come across various examples of calculating the steam loss, with the most common being:

Steam Loss (lb/hr) = 24.24 * Orifice Diameter^2 * PSIA

This is supposedly a variant of the Napier formula.  It has been awhile since thermo and fluids class, and I can't recall enough to determine how this formula was derived. 

You could calculate the flow of any fluid through an orifice with the orifice size and differential pressure.  However, you have to discount the flow due to the condensate present in the line, this will flash through the orifice and choke the flow.
The industry has used a figure of about 10% of the rated condensate flow as an estimate of steam loss through a failed open steam trap(Balance Valves).

The issue here isn't merely condensate discharging through the orifice.  Steam traps don't fail as an open orifice, they also have valve heads and disks that can get in the way periodically.  The formula you show is the generally accepted one when the trap is discharging to atmosphere.  The losses are typically reduced by an additional 50% when discharging into a closed return.  This is a conservative figure used to estimate steam losses in order to evaluate the financial loss and to calculate ROI for projects involving steam trap and steam system repair.

Depending upon how accurate you care to be, you could always put the outlet in a known weight of cooling water, run it for a few minutes with the outlet submerged and weigh the results and temperature rise.  Several manufactures have installed ISO test rigs to get even more accurate results, but based upon the accuracy of the measuring instrumentation, you still won't get that last btu.

What I'm saying, run with what you have and it will be fine for 99% of your needs.

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