Steam Loss Through a Trap or Orifice (Napier)
Computes the saturated steam flow escaping through a trap stuck open or a leak hole, using the Napier formula for critical flow: ṁ = C_d · 0.5244 · A · P_abs, with the orifice area in mm² and the absolute line pressure in bar, giving kg/h. Above roughly 1.9 bar absolute the flow is choked, and from there on the rate depends only on the UPSTREAM pressure, not on downstream back pressure — which is why the loss grows linearly with line pressure and with the square of the hole diameter, and why a high-pressure line loses disproportionately more through the same defect. The constant 0.5244 kg/(h·mm²·bar) is the exact conversion of the published imperial form, ṁ[lb/h] = 51.43 · A[in²] · P[psia], and with C_d = 1 it reproduces the isentropic choked flow to within 1 %. A hole of just 3 mm at 8 bar, with a discharge coefficient of 0.7, lets 20.8 kg/h escape — over 180 tonnes of steam per year of continuous operation, the central economic argument of any steam trap maintenance programme. Enter the discharge coefficient, the orifice diameter and the absolute line pressure.
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Steam Loss Through a Trap Stuck Open (Napier Formula)
Every steam plant leaks through traps that failed open, and the leak is silent: the trap keeps discharging, the process never complains, and only the fuel bill moves. Once an ultrasonic or thermographic survey flags a trap as blowing through, someone has to turn it is passing steam into kilograms per hour to rank the repair queue — a 3 mm seat on an 8 bar header does not carry the urgency of a 1.5 mm hole on a 2 bar line. This page runs that conversion with the Napier critical-flow expression: enter the discharge coefficient, the orifice diameter and the absolute line pressure, and it returns the lost flow in kg/h.
Choked flow reads ṁ = C_d · 0.2472 · A · P_abs, with the hole area A = π·d²/4 in mm², absolute pressure in bar and the answer in kg/h. Area enters linearly, so the loss scales with the square of the diameter; upstream pressure enters linearly too, so doubling the header pressure doubles the loss. With the page defaults — C_d = 0.8, a 3 mm hole and 8 bar absolute — the area is 7.07 mm² and the output reads 11.18 kg/h; over 8,760 h of continuous service that adds up to 98 tonnes of steam a year. Shrink the hole to 1.5 mm and it falls to 2.80 kg/h; raise the header to 16 bar and it climbs to 22.37 kg/h.
The constant is empirical and holds for saturated steam: it reproduces the leak tables published by trap makers — with C_d = 0.8 and a 1/4 in (6.35 mm) orifice at 100 psig (7.9 bar absolute) the page returns 49.45 kg/h, or 109 lb/h, inside the tabulated band — rather than the isentropic flow of an ideal nozzle. Treat C_d as a hole-shape factor, 0.8 to 0.9 in field practice. Under 1.9 bar absolute the flow stops being choked and the page refuses the calculation, since back pressure would start to matter. A failed trap rarely blows dry steam either: while it still drains condensate, the real loss sits below this figure, which is a ceiling.
Frequently asked questions
Is the pressure absolute or gauge?
Which discharge coefficient should I use?
Does the tool work out the annual cost of the leak?
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.