The Eberman injector uses a steam jet to draw in water and form a condensed delivery stream. Hiscox’s historical cross-section shows a sliding combining tube and a gravity check that closes the overflow after delivery is established. The animation distinguishes those moving parts from the steam and water paths. The calculator compares ideal steady heat-and-mass balances.
Eberman Injector · Condensation Balance Calculator
Compare an ideal fully condensed steam-and-water mixture. Enter the inlet steam enthalpy from steam tables. Results are a heat-and-mass balance, not an injector pressure or capacity rating.
Equation Used
- All inlet steam condenses in the steady calculation.
- No external heat loss or overflow loss in the balance.
- Liquid enthalpy is approximated by 4.18T kJ/kg.
- Kinetic and potential energy differences between external balance boundaries are neglected.
- Animation timing and nozzle proportions are illustrative.
The overflow-check inset unfolds one passage to make the seat visible. It shows the same check D as the main cutaway.
Steam nozzle, combining tube and overflow check
Steam enters the upper connection and flows through the nozzle. Water enters below and surrounds the steam jet at the mouth of the combining tube. The jet entrains water, and condensation forms a denser liquid stream. The delivery diffuser converts part of that stream’s kinetic energy into pressure.
In Hiscox 377, the combining tube slides to regulate lift and overflow. A separate gravity check D closes the overflow when delivery is established. The animation shows the same horizontal arrangement, followed by an enlarged, unfolded view of the overflow check. The inset is the same valve, not an additional check.
The illustrative sequence starts with overflow open, moves the combining tube, seats the check, and then shows established delivery. It returns to its starting state for replay. These phases explain the parts; they do not simulate startup dynamics or calculate valve forces.
Use the calculator to compare feedwater heating
Enter steam mass flow and its specific enthalpy, incoming water temperature, and the desired condensed-mixture temperature. The calculator finds the water flow that satisfies an ideal energy balance if all the steam condenses and there is no overflow loss.
Use a steam-table enthalpy for the inlet state. Pressure alone is insufficient if the steam quality or superheat is unknown. NIST’s IAPWS-based tables give liquid and vapor enthalpies; the default 2750 kJ/kg is an illustrative input, not a steam-pressure conversion.
Changing the flow scales both water and total mixture flow. Changing either temperature or steam enthalpy changes the required water-to-steam ratio. The balance relates steam enthalpy and both water temperatures to the required mass flows.
Mass and energy balance
For steam flow ms, water flow mw and condensed-mixture flow mf, conservation of mass gives mf=ms+mw. Neglecting heat loss and inlet/outlet kinetic and potential energy differences, ms hs+mw hw=mf hf.
Therefore mw/ms=(hs−hf)/(hf−hw). The liquid enthalpy approximation is h≈cpT with cp=4.18 kJ/(kg·K), using the conventional near 0°C liquid reference. This constant-cp approximation is for liquid temperatures in the selected 5–95°C range.
With flows in kg/h, heat transferred to the incoming water is Q=mw cp(Tf−Tw)/3600 kW. The same result follows from Q=ms(hs−cpTf)/3600.
This is a thermal balance only. Nozzle area, steam expansion, mixing momentum, diffuser loss, suction head and boiler pressure are not solved. A thermally balanced combination is not proof that an injector will start or deliver against a given boiler pressure.
Example: 20 kg/h of steam
At hs=2750 kJ/kg, incoming water at 20°C and a condensed mixture at 80°C, the approximate water enthalpies are 83.6 and 334.4 kJ/kg. The resulting water-to-steam ratio is 9.6316 kg/kg.
Water flow is 192.63 kg/h, total mixture flow is 212.63 kg/h, and the incoming water receives 13.42 kW. Doubling steam flow doubles both mass flows and heating power while leaving the mass ratio unchanged.
Raising the inlet-water temperature reduces the enthalpy rise available per kilogram of water. More water is then needed per kilogram of steam to maintain the same selected outlet temperature. This does not imply that an actual injector can entrain that amount.
What the illustration and numbers represent
The cross-section follows the source’s arrangement. Nozzle proportions, tube adjustment travel and demonstration timing are selected for readability; they are not manufacturing dimensions. Moving dots indicate flow direction and are not individual molecules or calibrated mass parcels.
The calculation assumes steady, fully condensed liquid output, no overflow discharge, no external heat loss and constant liquid specific heat. It does not estimate injector capacity, lifting height, efficiency, operating-pressure range or reliable startup. Those require a fuller model and device data.
Eberman injector questions
Does this injector have moving parts?
Yes. The source explicitly identifies a sliding combining tube and a gravity-operated overflow check.
Why does overflow appear during startup?
The illustration distinguishes startup discharge from established delivery. Once delivery is established, check D closes the overflow.
Does the calculator tell me what boiler pressure it can overcome?
No. It solves mass and thermal energy balances. Pressure delivery depends on the nozzle, entrainment, condensation, diffuser and operating conditions.
Does all the outlet water come from the water inlet?
No. Condensed steam adds its mass to the incoming water, so total mixture flow is the sum of both inlet mass flows.
References
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 104, figure 377: Eberman injector arrangement, sliding combining tube and gravity check D.
N. Hawkins, Maxims and Instructions for the Boiler Room, injector discussion: steam condensation, combining-tube adjustment and operating conditions.
NIST, NISTIR 5078, Thermodynamic Properties of Water: steam-table enthalpies calculated from the IAPWS formulation. The calculator uses an entered steam enthalpy and a stated constant-cp approximation for liquid water.
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