Calculate liquid-water specific enthalpy and enthalpy flow from temperature and absolute pressure, use a supplied specific enthalpy, or reverse-solve mass flow and liquid temperature with unit conversions.
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Feed Water Enthalpy Flow Rate Formula
The following formula is used to calculate the feed water enthalpy flow rate (energy rate) for a given mass flow rate and specific enthalpy.
Variables:
- Ḣ is the feed water enthalpy flow rate (kJ/s or kW)
- ṁ is the mass flow rate of feed water (kg/s)
- h is the specific enthalpy of feed water (kJ/kg)
To calculate enthalpy flow, multiply mass flow by specific enthalpy on a consistent reference basis. Liquid-property modes here use IAPWS-IF97 Region 1 over 0.01–350 °C, from saturation pressure to 100 MPa absolute. At saturation the selected phase is saturated liquid. Vapor and two-phase states are outside these modes; a supplied enthalpy is used directly without phase validation.
What is Feed Water Enthalpy?
Feed water specific enthalpy is a reference-dependent thermodynamic property of water entering a boiler, steam generator, or heat recovery system. In thermodynamic terms, specific enthalpy (h) combines the internal energy of the water with the pressure-volume work required to push the fluid into the system. Near ordinary ambient conditions, a constant heat-capacity estimate may be useful, but 4.18 kJ/(kg·K) is not a universal slope over the supported temperature and pressure range.
The enthalpy flow rate extends this concept to flowing systems. For an arithmetic example, 25 kg/s with a supplied specific enthalpy of 632.2 kJ/kg carries 15,805 kW of enthalpy flow on that reference basis. Boiler heat duty uses the difference between outlet and inlet enthalpies; the absolute reference-based flow alone is not recovered heat or fuel savings.
Feed Water Specific Enthalpy Reference Data
The specific enthalpy of liquid water varies with temperature and, to a lesser degree, with pressure. The table below provides saturated liquid enthalpy values at common feed water temperatures used in industrial and power generation applications. These rounded values describe saturated liquid, not compressed water at an unspecified pressure. Btu/lb uses the International Table convention. Use the entered pressure in the calculator for a specific liquid state.
| Temp (C) | Temp (F) | Sat. Pressure (bar) | h (kJ/kg) | h (BTU/lb) |
|---|---|---|---|---|
| 20 | 68 | 0.023 | 83.9 | 36.1 |
| 50 | 122 | 0.123 | 209.3 | 90.0 |
| 80 | 176 | 0.474 | 334.9 | 144.0 |
| 100 | 212 | 1.013 | 419.0 | 180.1 |
| 120 | 248 | 1.985 | 503.7 | 216.6 |
| 150 | 302 | 4.758 | 632.2 | 271.8 |
| 180 | 356 | 10.02 | 763.2 | 328.1 |
| 200 | 392 | 15.55 | 852.4 | 366.5 |
| 230 | 446 | 27.95 | 990.1 | 425.6 |
| 250 | 482 | 39.73 | 1085.4 | 466.6 |
Compressed-liquid enthalpy depends on both temperature and pressure. A saturated-liquid value is an approximation for a different state, with no general 0.5% error guarantee. The calculator evaluates the Region 1 equation at the entered absolute pressure instead of adding a constant-volume pressure correction.
Role of Feed Water Enthalpy in Boiler Efficiency
Boiler efficiency is fundamentally determined by the energy balance between the fuel input and the useful steam output. The core thermal output equation for any steam generator is: Boiler Output = mass flow of steam x (h_steam – h_feedwater). This means feed water enthalpy directly offsets the energy the boiler must supply from combustion. The higher the feed water enthalpy entering the boiler, the less fuel is required to reach the target steam conditions.
Fuel savings cannot be inferred from a universal feedwater-temperature increment. At unchanged steam production, outlet state and boiler efficiency, raising inlet enthalpy by Δh reduces ideal boiler heat duty by mass flow × Δh. Fuel-input change also depends on efficiency and the source of the feedwater heat. Evaluate these quantities on a consistent energy-balance basis; see the U.S. DOE economizer guidance.
Feed Water Heating Systems
Power plants and industrial boiler systems use several methods to raise feed water enthalpy before the water enters the boiler. Each method recovers heat that would otherwise be rejected from the cycle.
Feedwater Heaters (Closed Type) are shell-and-tube heat exchangers where extraction steam condenses on one side while feed water flows on the other. The streams do not mix. Staging, inlet and outlet states, and any efficiency benefit depend on the actual cycle; there is no universal fraction of plant efficiency attributable to these heaters.
Deaerators (Open Feedwater Heaters) heat water by direct steam contact and remove dissolved gases. Near-equilibrium outlet water approaches the saturation temperature at its absolute pressure. Actual temperature, pressure and venting requirements come from the equipment design and operating instructions.
Economizers recover heat from boiler exhaust to preheat feed water. Temperature rise and fuel savings depend on the measured heat balance. Minimum exhaust and surface temperatures depend on fuel composition, acid and water dew points, materials and whether the system is designed for condensation; 150 °C is not a universal safe threshold.
Enthalpy Change Across Boiler Zones
For a subcritical boiler, the heat added in each zone is the difference between its outlet and inlet specific enthalpies. Use property data for each actual pressure, temperature and phase rather than treating all feedwater as saturated liquid.
In the economizer and preheating zone, liquid water gains enthalpy until it reaches saturation at the local pressure. In the evaporator zone, the saturated liquid becomes vapor; the enthalpy change depends on pressure and phase quality. In the superheater zone, vapor gains further enthalpy above saturation. The total ideal heat duty is mass flow × (outlet enthalpy − inlet enthalpy). This calculator’s liquid-property modes do not predict vapor or two-phase enthalpy; use validated steam data for those zones.
Common Feed Water Conditions by Application
| Application | Typical FW Temp (C) | Typical Pressure (bar) | Approx. h (kJ/kg) |
|---|---|---|---|
| Small package boiler (no economizer) | 40 to 60 | 8 to 15 | 168 to 251 |
| Industrial fire-tube boiler with economizer | 80 to 105 | 10 to 25 | 335 to 441 |
| Combined cycle HRSG | 30 to 60 | 25 to 170 | 126 to 251 |
| Subcritical utility coal plant | 200 to 250 | 100 to 180 | 852 to 1085 |
| Supercritical utility plant | 250 to 290 | 250 to 310 | 1085 to 1290 |
| Nuclear PWR steam generator | 220 to 230 | 60 to 70 | 944 to 990 |
The table gives illustrative operating ranges, not equipment design limits or guaranteed property values. Its rounded enthalpy ranges do not include a pressure-specific calculation for every listed combination. For actual work, enter the measured liquid temperature and absolute pressure or obtain a validated property value for the actual phase. High pressure can permit liquid water above the normal atmospheric boiling temperature.
