The Schaeffer and Budenberg exhaust injector uses a hinged section of its combining tube to help establish the feedwater current. Steam enters above and draws water in from the side; the hinged section then closes for feeding. Explore the illustrated starting sequence alongside a fixed-density nozzle calculation and a separately selected pressure margin.
Exhaust Injector: Fixed-Density Comparison
Explore the hinged-tube starting sequence and compare fixed-density nozzle arithmetic with a selected pressure margin.
Equation Used
- Density is fixed at 1 kg/m³.
- The throat is circular and the velocity expression is ideal.
- Delivery pressure recovery is selected, not predicted.
- Thermodynamics, entrainment, condensation, losses, valve dynamics and ratings are excluded.
Do not use this calculator to size, select or operate boiler equipment.
Hinged combining tube
Hiscox figure 373 shows a vertical exhaust injector. Steam enters at the top, water enters at the upper left, overflow leaves at the lower left and the boiler connection is at the lower right. The hinged section of the combining tube opens to let steam flow freely while drawing in water, then closes as the feed current becomes established.
The cutaway uses illustrative proportions and repeats starting followed by feeding. It does not predict the timing of the transition or animate the overflow and boiler-check internals. The flow markers show direction, not steam expansion, condensation or actual speed.
What the calculator determines
Select pressure drop, circular throat diameter, boiler pressure and an assumed recovery percentage. The calculator returns fixed-density ideal velocity and mass-flow arithmetic, selected delivery pressure and its arithmetic surplus.
It does not calculate injector capacity, starting range, suction lift, water temperature limit, steam consumption or suitability for a boiler.
Fixed-density and selected-pressure equations
With fixed ρ = 1 kg/m³, v = √(2ΔP/ρ), A = πd²/4 and ṁ = ρAv. Selected delivery pressure is Pd = Pb(1+M/100), so selected surplus is PbM/100.
Using incompressible Bernoulli arithmetic with fixed density does not represent real expanding steam.
Selected-input arithmetic
At ΔP = 10 bar and d = 8 mm with fixed ρ = 1 kg/m³, the idealized speed is about 1,414 m/s and the arithmetic mass flow is about 0.071 kg/s. At 10 bar boiler pressure and selected recovery 12.5%, delivery pressure is simply set to 11.25 bar.
Using the comparison
The fixed-density result lets you compare the equations as pressure drop and throat diameter change. Real steam expands and condenses while mixing with water, so this result is not an injector capacity or steam-consumption estimate.
Boiler pressure and the chosen percentage set the displayed delivery pressure by arithmetic alone. A positive surplus does not establish that an injector can feed a boiler; that requires the steam and water states, actual passage geometry, losses and valve behavior.
Questions
Is ρ = 1 kg/m³ a steam-property calculation?
No. It is a fixed assumption.
Is delivery pressure predicted?
No. It is boiler pressure multiplied by the selected recovery percentage.
Does positive surplus prove the check opens?
No. Losses and valve dynamics are absent.
Can this size a boiler injector?
No.
Technical references
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, figure 373: Shaeffer and Budenberg exhaust injector, hinged combining tube and flow connections.
- NIST Special Publication 811 — SI units.
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