Water in a Branched Pipe — Nothing Piles Up at the Junction
A clear acrylic tank on a sliding carriage is kept at a fixed level by a tap and an overflow pipe. Water leaves it through a hose and a brass water meter, then reaches a clear acrylic junction block that splits it into two branches, A and B. Each branch has a brass ball valve and pours into its own 1 L measuring cylinder. Three sliders set the head of water h and the two valve openings. Press play for 30 s of flow and compare the meter's count with the water the two cylinders collect; drag the timeline to any moment. Tiny bubbles ride the water at its true speed in every pipe.
How to use this simulation
- Head of water h — 0.10 to 0.80 m, starting at 0.40 m: the height of the tank's water surface above the two spouts. Moving it raises or lowers the tank on its rail, and every flow is proportional to it.
- Valve A opening f_A — 0 to 100 %, starting fully open: the red lever turns from along the pipe (open) to across it (shut).
- Valve B opening f_B — 0 to 100 %, starting at 50 %.
- Play/pause, back to the start, a timeline you can drag to any moment, and ½×, ¼×, ⅛× slow motion.
- Drag anywhere on the scene to look around.
What to look for
- The meter's count always equals what cylinders A and B have collected together: 450 mL = 300 + 150 mL after 30 s at the start values.
- Shut valve B and every millilitre that passes the meter goes on to A: 10.0 mL/s in, 10.0 mL/s out.
- Shut both valves and the meter stops dead, however high the tank is raised: if nothing can leave the junction, nothing can enter it. All 50 mL/s from the tap goes down the overflow instead.
- Double the head to 0.80 m and every flow doubles; with both valves open the branches carry 20.0 + 20.0 = 40.0 mL/s and each cylinder reaches 600 mL in 30 s.
- The bubbles in the feed pipe move as fast as those in A and B together — 13.3 cm/s against 8.8 and 4.4 cm/s — because the three pipes have the same bore.
The physics behind it
The flow here is slow and smooth (laminar), so each branch carries a flow proportional to the push, just as Ohm's law makes a current proportional to the potential difference: Q = ρgh·f / R₀, where f is the valve's opening and R₀ = 3.92 × 10⁸ Pa·s/m³ lets a fully open branch pass 10.0 mL/s under a 0.40 m head. A half-shut valve doubles its branch's resistance and halves its flow. The junction cannot store water — the pipes are full and water does not compress — so whatever arrives each second must leave: Q_in = Q_A + Q_B. At the start values 10.0 + 5.0 = 15.0 mL/s, and after 30 s the meter has counted 450 mL while the cylinders hold 300 mL and 150 mL. Charge in a circuit behaves the same way: a node cannot store charge, so the total current in equals the total current out, ΣI_in = ΣI_out — Kirchhoff's first law, which is conservation of charge. The analogy holds for the junction rule; it does not make a circuit like a set of water pipes in every detail.