How can water go uphill, then down?
An empty tube over a rim does not carry water over the top by itself. Use the illustrated primer to remove air and connect the water column. A free outlet below the source surface can then keep water flowing.
Follow the gold marker. It climbs a short part of the route, but the end of the whole journey is lower. Energy released as water moves downhill drives the connected flow.
Raise the outlet too far, or let air into the top, and the flow cannot continue as before. A siphon needs a suitable height difference and a continuous water column.
Change one thing: does it still flow?
- Remove the air first. Compare the empty and primed tube. Which carries water over the rim?
- Raise the outlet slowly. Keep tube length fixed. What happens as the outlet approaches the source surface?
- Let air enter. The outlet is still lower, but air breaks the water column. Can siphoning continue?
Head, losses and the column’s limits
More: additional comparisons and controls
- Prime first. Start with an empty tube, inspect the air at the crest, then prime it and advance trial time.
- Raise the outlet. The short rigid tube rotates about its submerged inlet without changing length. As the outlet approaches the source surface, flow decreases. At or above that level, this free outlet cannot sustain forward discharge.
- Admit air at the crest. In the film, water retreats down both legs while the head difference remains. The manual vent button starts a fresh comparison in the drained equilibrium state.
- Use a taller crest. This prepares a different tube with longer upright legs. The tube is refilled, and the same total water inventory determines the new source level.
- Lower ambient pressure. The short tube keeps essentially the same flow. A tall tube can cross the vapor-pressure boundary. Warmer water also has a higher saturation vapor pressure.
Starting again with an empty tube also restores the default shaded cutaway. Changing an apparatus setting restarts trial time. Scrubbing time reconstructs the accumulated transfer from the beginning, independently of earlier interactions.
Which two heights define the head?
The outlet discharges into air above the receiving surface. The driving head is therefore source-surface elevation zₛ minus outlet elevation zₒ. It is not the difference between vessel bottoms or the length of the descending leg. A submerged outlet requires a downstream free-surface boundary condition instead. The model rejects that condition rather than applying the free-jet equation to it.
The US Bureau of Reclamation’s siphon measurement guidance distinguishes free and submerged exits and describes air locking at low discharge.
What produces the displayed numbers?
Neglecting source-surface velocity, the energy balance from the source surface to the free outlet is:
Authored parameters are bore D = 12 mm, Darcy friction factor f = 0.03, entrance loss coefficient 0.5 and total bend loss coefficient 0.4. The coefficients remain fixed to isolate changes in head; they are not recomputed from Reynolds number or fitted to a particular hose. Density is 998.2 kg/m³ and gravitational acceleration is 9.80665 m/s². Temperature changes vapor pressure only, not viscosity or density.
The upright short tube has a crest at 1.9 m, bend radius 0.8 m and inlet at 0.2 m above the source floor. Source cross-sectional area is 0.06 m²: width 1.25 m and depth 0.048 m. The receiver has area 0.12 m²: width 0.65 m and depth about 0.185 m, with its floor at −0.5 m. Drawing depth is compressed while in-plane connections and clearances are preserved. The receiver moves horizontally with the rotating outlet.
Local pressure uses that same speed, centerline and accumulated losses:
Entrance loss occurs at entry, wall loss accumulates with tube length, and bend loss is distributed along the semicircular arc. Pressure returns to ambient at the free outlet. The crest neighborhood has low pressure. The crest reading samples the geometrical highest point. Because losses continue to accumulate downstream, the actual pressure minimum usually lies a little beyond that point. The two readings are calculated separately. All pressures are absolute, not gauge pressure relative to the room.
See OpenStax on Bernoulli’s equation and energy conservation. These are one-dimensional, quasi-steady calculations rather than CFD.
Why is crest height limited?
In ordinary water containing gas, vapor formation, dissolved-gas release or air leakage can interrupt the column when absolute pressure becomes too low. The model stops its single-phase flow output when the minimum pressure anywhere along the tube reaches saturation vapor pressure. The separate crest reading still describes the highest point; the margin bar uses minimum pressure minus vapor pressure. Gold glyphs mark the calculated minimum-pressure location. They do not predict real bubble size, formation time or gas volume; liquid inventory remains accounted for.
The minimum is not chosen from a sparse set of samples. Pressure has a constant gradient along each straight leg, so their endpoints suffice. Within the circular bend, the solver also finds the stationary pressure point:
Comparing that point with both joins and both mouths gives the global minimum for the current rotation and flow. At zero flow, losses vanish and the minimum returns to the geometrical crest.
At 20 °C, water’s saturation vapor pressure is about 2.34 kPa. Ignoring speed and losses gives roughly 10.1 m of static water-column allowance at standard atmospheric pressure. Flow subtracts velocity head and upstream losses from that allowance. This is an ordinary-water engineering assumption, not an absolute theorem covering specially treated liquids under all conditions.
Vapor pressure uses the NIST Chemistry WebBook Antoine fit, restricted to its 273–303 K range. The NIST water-vapor-pressure table gives approximately 2338 Pa at 20 °C; the finite-range fit differs slightly.
What is reconstructed, and what is intentionally simplified?
The first six chapters track one batch of water. Chapter progress maps to eight authored 22-second physics windows; discharge uses a 0.1 s fixed step, and every seek reconstructs the same cached history. The last two chapters are independent prefilled comparisons, not one hose stretching between different lengths.
Priming and air-driven drainage use prescribed teaching progress rather than a startup, air-compression or two-phase solver. Water displaced from each leg is assigned to the appropriate reservoir. Water hammer and transient inertia are omitted. After the vapor boundary is crossed, the display reports the pressure demanded by the continuous-column assumption and stops its flow output. A negative computed margin is not a measurement of negative absolute pressure.