Steam Loss Through a Failed Steam Trap: How to Calculate It

Steam loss through a trap stuck in the open position is estimated with Napier's formula: W (kg/h) = 0.24725 × P × D², where P is the absolute steam pressure in bar and D is the seat diameter in millimetres. At 10 bar g and a 3 mm seat this gives about 24.5 kg/h, or roughly 215 t of steam a year in continuous operation. The money figure is the tonnes multiplied by the cost of steam.

Napier's formula

Every steam trap has an internal orifice (seat) that limits losses if the trap fails open. That is why losses are estimated with the formula for steam flow through a sharp-edged orifice developed by Napier. The Sustainable Energy Authority of Ireland (SEAI) recommends it as the method for calculating savings from trap replacement: it needs only two parameters that are known for every trap.

Units	Formula	Symbols
SI	W = 0.24725 × P × D²	W: loss, kg/h; P: absolute pressure upstream of the orifice, bar (gauge + atmospheric); D: orifice diameter, mm
Imperial	W = 24.24 × P × D²	W: lb/h; P: psia; D: inches

Important: use absolute pressure. Add atmospheric pressure, about 1.013 bar, to the gauge reading.

Loss table by Napier's formula

Calculated for a fully open trap discharging steam with no back pressure, kg/h:

Pressure, bar g	2 mm seat	3 mm	5 mm	8 mm
3	4.0	8.9	24.8	63.5
6	6.9	15.6	43.3	111.0
10	10.9	24.5	68.1	174.3
16	16.8	37.9	105.2	269.2

Losses grow with the square of the diameter: a seat twice as large loses four times as much steam.

Cross-check with the DOE table

The US Department of Energy (DOE) Steam Tip Sheet #1 gives its own table based on Boiler Efficiency Institute data: steam discharges to atmosphere through an orifice with a discharge coefficient of 0.72.

Orifice diameter, inches	15 psig	100 psig	150 psig	300 psig
1/32	0.85	3.3	4.8	-
1/16	3.4	13.2	18.9	36.2
1/8	13.7	52.8	75.8	145
3/16	30.7	119	170	326
1/4	54.7	211	303	579
3/8	123	475	682	1,303

Values are in pounds of steam per hour. For comparison: 150 psig is about 10.3 bar g and 1/8 inch is 3.175 mm. The DOE table gives 75.8 lb/h (about 34 kg/h), while Napier's formula gives about 62 lb/h (about 28 kg/h). The methods produce different numbers, so any calculation is an estimate, not a measurement. What matters is to choose one method and apply it consistently to all traps.

Worked example

Inputs:

• steam pressure 10 bar g, i.e. P = 10 + 1.013 = 11.013 bar abs;
• trap seat 3 mm;
• the system runs around the clock, 8,760 h a year (as in the DOE example);
• steam cost: an assumed 10,000 KZT per tonne. This is not a tariff or a market price, only a number to demonstrate the calculation. Replace it with your boiler house's steam cost or the price of purchased steam.

Calculation:

1. Hourly loss: W = 0.24725 × 11.013 × 3² = 24.5 kg/h.
2. Annual loss: 24.5 kg/h × 8,760 h = 214.7 t of steam.
3. Money, upper estimate: 214.7 t × 10,000 KZT/t ≈ 2.15 million KZT a year.
4. With a partial-flow correction: SEAI uses 50% of the calculated value to allow for a trap that may not be fully open. That gives 107.4 t of steam and about 1.07 million KZT a year for one trap.

The same trap with a 6 mm seat at 10 bar loses four times as much: about 98 kg/h, or 859 t of steam a year before correction.

For comparison, in the DOE example a trap on a 150 psig line with a 1/8 inch orifice loses 75.8 lb/h, and at a steam cost of $10.00 per 1,000 lb the repair saves $6,640 a year.

Why the calculation is an upper bound

The formula describes steam flowing through a fully open sharp-edged orifice. In practice:

• The trap is partly open. According to SEAI, a trap stuck open does not necessarily leak 100% of the calculated flow, because the seat design limits the leakage. SEAI applies a 50% correction for savings claims and mentions a manufacturer that uses 33% in its steam trap audit reports.
• Direct measurement is usually not possible. SEAI notes that measuring steam losses through traps is not feasible on most sites, so they are estimated by engineering calculation, and any calculation remains an estimate.

That is why a loss report should give a range: the calculated value and the corrected value.

How many traps are typically failed

According to DOE (Steam Tip Sheet #1):

• in systems not maintained for 3 to 5 years, 15% to 30% of installed traps may have failed, letting live steam escape into the condensate return system;
• with a regularly scheduled maintenance program, leaking traps should be less than 5% of the trap population;
• if a system has more than 500 traps, a survey will probably reveal significant steam losses.

SEAI adds that failure rates as high as 20% have been reported from audits, and even more reliable traps have shown failure rates of 12.5%.

How often to test

Steam pressure	DOE testing interval
High, 150 psig (about 10.3 bar g) and above	weekly to monthly
Medium, 30-150 psig (about 2-10 bar g)	monthly to quarterly
Low, below 30 psig (about 2 bar g)	annually

DOE also suggests considering online monitoring for the most important traps and keeping records of faults found, to document savings in money terms.

How to find a failed trap with ultrasound

DOE lists four ways of testing traps: temperature, sound, visual and electronic. Ultrasonic testing as recommended by SDT works like this:

1. Listen to a healthy cycle. Before making a diagnosis, touch the installation with the contact sensor and learn how the trap sounds in normal operation.
2. Place the contact sensor on the trap body. A healthy trap is heard cycling open and closed.
3. Assess the signal:

What you hear	Trap condition
Silence alternating with discharge	Working, cycling
Constant turbulent noise	Stuck open, passing steam
Silence	Stuck closed
Mechanical clattering	Valve fluttering, opening and closing rapidly

4. Measure temperature upstream and downstream of the trap. This is the second indicator: according to SDT, a complete inspection combines ultrasound and temperature.
5. Record the result for every trap: location, type, pressure, seat diameter and diagnosis. These data are then used to calculate losses with the formula above.

A detailed method by trap type is in Checking Steam Traps with Ultrasound and Steam Trap Diagnostics: Types and Failures. How to link a survey to an energy calculation is covered in SDT270 and TRAPChecker: Steam Trap Energy Audit.

Loss calculator

Losses for a whole trap population can be calculated in the steam trap loss calculator. It uses the same Napier formula and converts to money through the heat tariff in tenge per Gcal and the boiler house efficiency.

Which instrument to choose

• Surveying a trap population: TRAPChecker: according to SDT, a simple ultrasound instrument for assessing steam traps and valves; it detects the internal turbulence of a defective trap or a passing valve.
• Survey programme with routes and history: SDT270.
• Traps plus other tasks (bearings, lubrication, electrical): SDT340, SDT's versatile ultrasound instrument.

KEG TRK supplies these instruments in Kazakhstan and helps select them for the task. Price on request.

Sources

• U.S. Department of Energy, Advanced Manufacturing Office. Inspect and Repair Steam Traps, Steam Tip Sheet #1 (DOE/GO-102012-3401, January 2012): https://www.energy.gov/sites/prod/files/2014/05/f16/steam1_traps.pdf
• Sustainable Energy Authority of Ireland (SEAI). Guidelines for claiming energy savings from steam trap replacement (2023): https://www.seai.ie/publications/SEAI-Guidelines-for-claiming-energy-savings-from-steam-trap-replacement.pdf
• SDT Ultrasound Solutions. Steam Trap Testing and Maintenance: https://sdtultrasound.com/applications/steam-trap-testing/
• SDT Ultrasound Solutions. TRAPChecker: https://sdtultrasound.com/products/checker-range/trapchecker/