This educational calculator compares two selected average fluid densities and reports the signed hydrostatic head difference per metre. A positive result means the denser downcomer column has a hydrostatic tendency to drive upward flow in the lower-density riser.
Natural-Circulation Density-Head Reference
Compare two selected average densities and visualize the sign of the resulting hydrostatic tendency in a connected loop.
Equation Used
- The two selected values represent average densities over equal vertical heights.
- Gravity is 9.80665 m/s².
- Only static hydrostatic head is compared.
- Flow losses, two-phase distribution, heat transfer, controls and safe operation are excluded.
Negative outputs indicate a reversed selected density ordering, not a validated operating condition.
Density difference in a connected loop
Natural circulation can arise when a cooler, denser downcomer and a heated, lower-density riser are connected between common headers. The unequal column weights create a hydrostatic pressure difference.
The diagram is a schematic closed loop. Its particles indicate only the sign of the selected density difference, not an actual flow velocity.
What the calculator determines
Select average downcomer density ρd and average riser-mixture density ρr. The calculator reports Δρ, signed static head gradient gΔρ, relative density difference and density ratio.
Babcock & Wilcox describes natural circulation as using the density difference between the downcomers and the steam/water mixture in furnace tubes. The U.S. NRC likewise defines natural circulation as circulation caused by density differences rather than pumps.
Static hydrostatic reference
Δρ = ρd − ρr. The corresponding pressure difference per unit vertical height is Δp/H = gΔρ, reported here in kPa/m using g = 9.80665 m/s². Relative density difference is 100Δρ/ρd.
Selected-input arithmetic
For ρd = 920 kg/m³ and ρr = 600 kg/m³, Δρ = 320 kg/m³ and the ideal static head difference is about 3.138 kPa per metre of common vertical height. This does not determine a circulation rate.
Model boundary
This is a two-density hydrostatic comparison, not a boiler sizing, steam-output, safety or operating calculator. It does not model loop height, operating pressure, heat input, phase distribution, flow area, friction, local losses, void fraction, critical heat flux, water chemistry, materials, controls or code compliance.
Babcock & Wilcox notes that actual circulation also depends on boiler height, operating pressure, heat input and free-flow areas. Those inputs are absent, so no flow, capacity or safe operating conclusion is made.
Questions
Does a larger density gap mean a known flow rate?
No. It increases the ideal static driving-head gradient, but actual flow requires a complete pressure-loss and two-phase system model.
What does a negative value mean?
The selected density ordering reverses the hydrostatic tendency; it is not a normal-operation diagnosis.
Can this set boiler pressure or firing rate?
No.
Electrical checks for actuator-powered systems
In actuator systems, see water tube boiler should be checked against real current draw and duty cycle. A power supply that works on the bench may still dip under startup or stall current in the installed machine.
When comparing a cylinder to an electric actuator, convert the discussion into stroke, force, speed, duty cycle, and installed length. Matching one specification is not enough.
The electrical margin should be based on worst-case motion, not a free-running bench test. Higher load increases current and heat, and long cable runs can reduce voltage at the actuator just when the motor needs it most.
- Size the supply for startup and stall current, not just running current.
- Check wire length, voltage drop, fuse rating, and controller output limits.
- Verify duty cycle so motor heat does not become the real failure mode.
For FIRGELLI actuator systems, start with the linear actuator power-supply sizing guide, then use the actuator duty-cycle calculator when the actuator cycles repeatedly. After the electrical limits are known, compare mechanical options in the FIRGELLI linear actuator range.
References & Further Reading
- Wikipedia contributors. Water-tube boiler. Wikipedia
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