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Boiler horsepower to a season of gas

Steam plant · boiler horsepower, steam rate and fuel cost

In the boiler room of a commercial laundry, a 150 boiler-horsepower firetube feeds the washers and presses with steam, and the office upstairs wants next season's fuel budget on one page. The nameplate riveted to the shell speaks a dialect of its own — boiler horsepower — which has to be translated before any modern number exists. The operating record supplies the run profile: the boiler runs the equivalent of 2,000 hours a season at nameplate, the on-off cycling already folded into that one figure. Combustion trims put the seasonal efficiency at 80% — a number that lives or dies with stack temperature and burner tune — and the gas contract prices delivery at $1.20 per therm. Nameplate to invoice is a chain of translations: horsepower to heat, heat to steam, output to input, and input-times-hours to the therms the utility will bill.

150 BHPsteam 5,175 lb/hgas $1.20/thermη 80% · 2,000 h

Every number in this problem is editable — change any value below and the whole chain recalculates.

Given
  • BHP = 150 hp (boiler) — Nameplate boiler horsepower
  • η = 80 % — Seasonal efficiency
  • t = 2,000 h — Equivalent full-load hours
  • p_e = 1.2 $/therm — Contract gas price
Determine
  1. (a)the heat the boiler delivers at nameplate
  2. (b)the steam it produces
  3. (c)the fuel input rate the burner must fire
  4. (d)the fuel energy a season consumes
  5. (e)what the season's gas costs
Step 1 of 5(a) · solve for Heat output

Boiler horsepower is an 1889 ASME unit, not a motor rating: one BHP is 33,475 BTU/h delivered to the water, so 150 BHP is 5.02 million BTU/h — 1.47 MW. Confuse it with the 746 W mechanical horsepower and every number downstream is thirteen times too small.

Rearranged for Q
Q=33,475  BHPQ = 33{,}475 \; \text{BHP}
Your values, in your units
Q=33,475×(150 bhp)Q = 33{,}475 \times \left( 150\ \text{bhp} \right)
Answer
Q=1.4716 MWQ = 1.4716\ \text{MW}

Carried onward at full precision, not this rounded figure.

Open the Boiler Horsepower to Heat Output solver →

Step 2 of 5(b) · solve for Steam production rate

The same definition fixes the steam side: 34.5 lb/h per BHP 'from and at 212 °F', so 150 BHP makes 5,175 lb/h. Real feedwater is colder than 212 °F, so actual steam runs a few percent under this — the 'from and at' figure is the honest comparison basis, not a delivery promise.

Rearranged for S
S=34.5  BHPS = 34.5 \; \text{BHP}
Your values, in your units
S=34.5×(150 bhp)S = 34.5 \times \left( 150\ \text{bhp} \right)
Answer
S=2.3473 t/hS = 2.3473\ \text{t/h}

Carried onward at full precision, not this rounded figure.

Open the Boiler Horsepower to Steam Rate solver →

Step 3 of 5(c) · solve for Fuel input rate

The meter reads input, not output, so divide by efficiency: 5.02 MBTU/h ÷ 0.80 = 6.28 MBTU/h of gas fired. Dividing — not multiplying — is the step people flip; multiplied, the budget comes in 36% light and the shortfall surfaces in January.

ηQinQout
Rearranged for Qin
Q˙in=Q˙outη\dot{Q}_{in} = \tfrac{\dot{Q}_{out}}{\eta}
1.4716 MWcarried from step 1
Your values, in your units
Q˙in=(1,471,580 W)(80 %)\dot{Q}_{in} = \tfrac{\left( 1{,}471{,}580\ \text{W} \right)}{\left( 80\ \text{\%} \right)}
Answer
Q˙in=1.8395 MW\dot{Q}_{in} = 1.8395\ \text{MW}

Carried onward at full precision, not this rounded figure.

Open the Boiler or Furnace Output from Input solver →

Step 4 of 5(d) · solve for Work or energy

Fire that input for the 2,000 equivalent full-load hours: 6.28 MBTU/h × 2,000 h = 12.55 billion BTU, which the gas bill will call 125,531 therms. Equivalent full-load hours already fold the on-off cycling into one honest number — do not also derate for cycling, that is counting it twice.

Rearranged for W
W=PtW = P t
1.8395 MWcarried from step 3
Your values, in your units
W=(1,839,480 W) (2,000 h)W = \left( 1{,}839{,}480\ \text{W} \right) \, \left( 2{,}000\ \text{h} \right)
Converted to base units
W=(1,839,480 W) (7,200,000 s)W = \left( 1{,}839{,}480\ \text{W} \right) \, \left( 7{,}200{,}000\ \text{s} \right)
Answer
W=13.244 TJW = 13.244\ \text{TJ}

Carried onward at full precision, not this rounded figure.

Open the Power (P = W/t) solver →

Step 5 of 5(e) · solve for Energy cost

125,531 therms at $1.20 is a $150,638 season. Set it beside the boiler-room payroll and every other line in the budget: the burner tune that bought the 80% — up from a neglected 76% — is worth about $7,500 a season on this one machine.

Rearranged for C_e
Ce=E peC_e = E \, p_e
13.244 TJcarried from step 4
Your values, in your units
Ce=(13,244,200,000,000 J) (1.2 $/therm)C_e = \left( 13{,}244{,}200{,}000{,}000\ \text{J} \right) \, \left( 1.2\ \text{\$/therm} \right)
Converted to base units
Ce=(3,678,960 kWh) (0.0409457 $/kWh)C_e = \left( 3{,}678{,}960\ \text{kWh} \right) \, \left( 0.0409457\ \text{\$/kWh} \right)
Answer
Ce=150,640 $C_e = 150{,}640\ \text{\$}

Carried onward at full precision, not this rounded figure.

Open the Energy Cost from a Utility Rate solver →

Answer

The 150 BHP boiler delivers 5.02 MBTU/h and about 5,175 lb/h of steam, fires 6.28 MBTU/h of gas at 80% efficiency, and a 2,000-hour season consumes 125,531 therms — roughly $150,638 at $1.20 per therm.

Why this order

This chain is a translation exercise, which is exactly what a steam budget is: the nameplate speaks in boiler horsepower, the operator in pounds of steam, the burner in BTU per hour of input, and the utility in therms and dollars — one machine, four dialects. The pivot is the ASME definition: one boiler horsepower evaporates 34.5 lb/h of water 'from and at 212 °F', and 34.5 lb/h times the 970.3 BTU/lb latent heat at atmospheric pressure is where 33,475 BTU/h comes from — the two nameplate numbers are one fact, which is the cross-check between parts (a) and (b). Output converts to input only through efficiency, and input times hours is the therm count the bill will show. The dollar arithmetic checks exactly in trade units: 33,475 × 150 / 0.8 = 6,276,562.5 BTU/h, × 2,000 h = 12.553 GBTU = 125,531.25 therms, × $1.20 = $150,637.50 — to the cent, because a therm is defined as 100,000 BTU.

The budget-killing mistakes are all one-liners. Treating boiler horsepower as motor horsepower (off by 13.4×). Multiplying by efficiency instead of dividing — a $54,000 error on this plant. Reading '34.5 lb/h per BHP' as a delivery promise when feedwater at 180 °F and steam at 100 psig yield 3–8% less than the 'from and at' basis. And double-derating: equivalent full-load hours already contain the cycling, the night setback and the shoulder seasons, so applying a load factor on top counts the same slack twice and produces a budget nobody can reconcile in March. The one number worth managing rather than calculating is the 80%: it is bought and maintained — combustion trim, stack temperature, blowdown heat recovery — and each point of it is worth about $1,880 a season here.

Carried values move at full precision, not the rounded figure shown — chaining rounded numbers compounds error.