This calculator compares two user-entered efficiency percentages under explicitly different equal-input and equal-output scenarios. It does not model an internal-fired boiler or predict steam generation, fuel consumption or stack loss.
Internal Fired Cylindrical Tubular Boiler Interactive Calculator
Explore percentage-point gain, equal-input useful-output ratio, equal-output input reduction and loss-fraction reduction from two entered efficiencies.
Equation Used
- Both entered efficiencies are positive values on the same gross/net fuel basis and system boundary.
- Equal-input output comparison holds energy input fixed.
- Equal-output input-reduction comparison holds useful output fixed.
- Loss-fraction comparison treats all unconverted input as one aggregate remainder.
- No fuel composition/flow, combustion, excess air, flue-gas state, radiation, blowdown, steam pressure/temperature/quality/flow, feedwater, heat-transfer surface, fouling, draft, emissions, pressure vessel, controls or safety model.
The two efficiencies must use the same valid basis, boundary, fuel heat-value convention, load and measurement method. ‘More output’ assumes equal energy input; ‘input reduction’ assumes equal useful output. Neither scenario predicts a real boiler retrofit.
Two efficiency comparison scenarios
Efficiency is useful output divided by input. Holding input fixed makes useful output proportional to efficiency; holding useful output fixed makes required input inversely proportional to efficiency.
The visual is an abstract energy-share comparison, not a boiler section or heat-flow simulation.
Use as ratio arithmetic
The outputs compare two independently established efficiencies on the same basis. They cannot establish either efficiency, attribute losses or forecast savings from changing boiler passes.
Do not mix scenarios
At equal input, output2/output1=eta2/eta1. At equal useful output, input2/input1=eta1/eta2. These percentages differ because their denominators differ.
Loss-fraction reduction compares 1−eta values as one aggregate remainder and must not be labeled stack loss unless stack loss is the only loss, which is not established here.
Worked example
For entered efficiencies 55% and 72.5%, difference is 17.5 percentage points. Equal-input useful output rises 31.82%; equal-output input falls 24.14%; aggregate unconverted fraction falls from 45% to 27.5%, a 38.89% reduction.
Conditions for comparing efficiencies
Use efficiencies established with the same energy basis, system boundary and comparable operating conditions. Steam output also depends on its pressure, temperature and feedwater state. Individual boiler losses and retrofit savings require actual measurements or a suitable thermal model; these entered percentages do not supply them.
Questions
Does equal-input output change mean more steam?
Only if all other output conditions are identical; this calculator does not establish that.
Is aggregate loss reduction stack-loss reduction?
No. Individual loss mechanisms are not separated.
Can entered efficiencies predict retrofit savings?
No. They must first be measured or derived on a consistent basis for the actual system.
Percentage points and relative change
A change from 55% to 72.5% efficiency is 17.5 percentage points. Relative changes use a denominator, so the equal-input output increase and equal-output input reduction have different percentages. Keep the comparison conditions attached to each result.
References & Further Reading
- Wikipedia contributors. Fire-tube boiler. Wikipedia
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
