Worked example: a tank filled by a pump on level control

Most pipe-network questions are steady-state, but a tank filling and draining is not: the level rises and falls over time, and a pump switches on and off to keep it between two thresholds. This worked example is a time simulation (an extended-period run) of exactly that, and it is where you watch a network behave over a timeline rather than at a single instant.

The setup

A pump draws from a source at zero head and lifts water into an open tank, with a head-flow curve from 20 m at shut-off to 15 m at 50 L/s and zero at 100 L/s. The tank has a plan area of 3 square metres, an initial level of 2 m and a working range of 0 to 10 m. A leak line, 200 m of DN150 pipe, drains the tank continuously to a sink at zero head.

The control is a level trigger with a deadband: the pump starts when the tank level falls below 2 m and stops when it rises above 5 m. The run uses a time step of 20 seconds over a total of 2000 seconds, long enough to see several on-off cycles.

The physics and the method

This is a quasi-steady (extended-period) simulation. At each time step the solver treats the tank level as a fixed head and solves the steady hydraulics of the pump and the leak line, then integrates the tank level forward over the step from the net inflow, the pump delivery minus the leak. The level trigger switches the pump with hysteresis, so once it starts it runs until the level clears 5 m, and once it stops it stays off until the level drops back below 2 m. The result is a saw-tooth: the level climbs while the pump runs and falls while it rests.

This is a slow, level-driven transient, not water hammer or surge. Fluid Network Studio models the change in tank storage over time, not the pressure waves that travel when a valve slams. Those fast, inertial transients stay with the specialist surge packages.

What you learn

Solve the example, then play or scrub the timeline and select the tank to read its level-versus-time plot. The duty cycle is right there: how long the pump runs, how long it rests, and how the period depends on the tank area and the leak-line size. Shrink the tank area or widen the leak and the pump cycles faster. Time simulation is included on every plan, so this example is free to run and explore. The method behind it is described on the how it works page.

Open this example in FNS and shrink the tank area to see the pump cycle faster.