Boyer’s historical water-tube boiler uses pipe coils to form furnace walls, with heated coils over the fire connected to circulating pipes and a steam drum. This simplified sectional illustration follows that coiled arrangement. The accompanying calculator explores an equivalent density-head comparison; it is not a dimensional reconstruction or a boiler-performance model.
Boyer's Water Tube Boiler Interactive Calculator
Explore density-driven pressure using an equivalent height H=L sin(theta). The right-hand triangle follows those two geometry inputs. The historical coil-wall illustration is separate: these controls do not imply that Boyer used straight inclined tubes.
Equation Used
- Equivalent rise H=L sin(theta); illustrative coil geometry is not dimensioned by L.
- Constant cool-leg and mean hot-leg densities over the equivalent height.
- Non-positive forward density difference is clamped to zero; reverse flow is not calculated.
- Pressure deduction is a user assumption, not a measured fouling or hydraulic-resistance model.
- No tube diameter, heating rate, steam quality, operating pressure or loop resistance solution; no steam-output or flow-rate rating.
The coil-wall illustration shows the historical arrangement. The separate triangle defines the elevation used in the density-head calculation. Energy-equivalent speed converts pressure into kinetic-energy units; it is not actual circulation velocity.
Coils form the furnace walls
Hiscox figure 191 shows Boyer’s boiler with a steam drum above a network of pipes. Coils form the furnace walls, and heated coils over the fire connect circulating pipes to the drum.
The section shows the drum, coiled walls, over-fire section, lower circulating pipe and an explanatory cooler return. The loops stay connected. Tube routing, coil count and the cutaway are schematic; this is not an exact fabrication drawing.
Historical mechanism and educational calculation
The illustration explains a historical water-tube arrangement. The calculator compares an idealized density-driving head; it does not determine boiler capacity, working pressure or steam production.
The calculator can help distinguish elevation, mean density difference and pressure. Actual boiler circulation requires substantially more information, including heat transfer, phase change and hydraulic losses.
Equivalent density-head comparison
Define an equivalent vertical rise H=L sin(theta). L is the length of the line in the small triangle, not the total length of a coiled pipe. With uniform mean densities, the hydrostatic driving-pressure difference is gH(rho_c−rho_h), using g=9.80665 m/s².
The forward-only calculator clamps a negative density difference to zero. It then multiplies the result by 1−f, where f is the chosen pressure-deduction fraction. This deduction is an assumption; no friction law is solved. Dividing pressure by rho_c g gives an equivalent cool-fluid head.
The square-root result sqrt(2 deltaP/rho_h) is an energy-equivalent speed. It is the speed whose kinetic-energy density equals the reported pressure. It must not be read as the actual speed in a boiling circulation loop.
Worked equivalent-head comparison
For L=4 m and theta=20 degrees, H=1.368 m. Using cool-leg density 960 kg/m³ and hot-leg mean density 650 kg/m³ gives gross forward driving pressure 4.159 kPa. With no percentage deduction, equivalent cool-fluid head is 0.442 m and energy-equivalent speed 3.58 m/s.
A 20% deduction reduces the pressure and equivalent head by 20%; the energy-equivalent speed is multiplied by sqrt(0.8). Neither result predicts steam production or actual circulation flow. If the density difference becomes zero or negative, the forward-only outputs become zero and the animation pauses its forward-flow markers.
Reading the model without over-interpreting it
The historical drawing establishes the coiled arrangement. The calculator’s triangle independently defines an equivalent elevation difference. Increasing L or its angle increases H within the slider range, but does not determine the length or bend losses of the historical coils.
A density difference can provide a driving head. Flow in a real system also depends on a connected circuit, a maintained thermal difference and the pressure losses along that circuit. The entered percentage deduction does not replace those calculations. The animation illustrates a direction, not measured fluid or steam speed.
Questions about Boyer’s boiler model
How are the heated tubes arranged?
Coils form the furnace walls, and coils above the fire connect the circulating pipes to the steam drum, as shown in Hiscox figure 191.
Do length and angle resize the boiler coils?
No. They define the equivalent height in the separate triangle. Exact Boyer tube dimensions and routing are not established by these inputs.
Is energy-equivalent speed the circulation velocity?
No. It is a pressure-to-kinetic-energy conversion. Real circulation requires the loop geometry, hydraulic losses and thermal/two-phase behavior.
Why are some pressure results zero?
The model calculates only positive forward density head. Equal or reversed density contrast produces zero, rather than a reverse-flow solution. Forward markers are paused in that condition.
References
- Hiscox, Mechanical Movements, figure 191 — coiled furnace walls, overhead tubes and steam drum.
- U.S. Department of Energy, Fluid Flow Fundamentals — natural circulation, thermal driving head and required conditions, module HT-03 pages 37–40.
Building or designing a mechanism like this?
Explore the precision-engineered motion control hardware used by mechanical engineers, makers, and product designers.
