Worked examples
All 20 built-in example networks, across every solve mode. Each card shows what the network actually solves to, so you can see the answer before you open anything. Open any of them in the Studio to re-solve and explore it - building and running the built-in examples is always free.
Every figure below is solver output from the example itself, produced by solving it the way the Studio does rather than worked by hand for the page. Each example page reproduces it with the full table of flows, heads, temperatures or pressures behind it.
Incompressible liquids
Worked example: the three-reservoir junction
Solve the classic three-reservoir problem in your browser. Three tanks at different heads feed one junction - the solver finds each pipe flow and direction.
Solved result: The junction settles at a head of 83.71 m, which is 819.5 kPa gauge at the ground-level junction.
Open in the Studio →Worked example: a looped water distribution network
A looped water distribution network solved in the browser: a pump station feeds two mains with three demands and a throttle valve, balanced against a storage tower.
Solved result: The pump settles at 62.89 L/s and 49.03 m, which is 7.89 L/s more than the demands take, so the tower fills.
Open in the Studio →Worked example: a single-loop network
Solve a single-loop pipe network in your browser. Flow divides between two parallel branches of different diameter so head loss around the loop balances.
Solved result: The reservoir delivers 78.43 L/s, and it divides 53.47 L/s down the 200 mm branch against 24.96 L/s down the 150 mm one.
Open in the Studio →Worked example: pump and system curve
Find a pump operating point in your browser, where the pump curve meets the system curve as it lifts water between reservoirs. Power and BEP reported too.
Solved result: The two curves cross at 40.93 L/s and 33.87 m of pump head.
Open in the Studio →Worked example: a supply line with an in-line fitting
See minor losses in action in your browser. A supply line with a 90 degree elbow draws a demand - the solver separates fitting loss, friction and elevation.
Solved result: The demand fixes the flow at 20 L/s, so the velocity in the 150 mm bore is 1.132 m/s and every loss follows from it.
Open in the Studio →Worked example: a branched distribution main
Check pressures across a branched distribution main in your browser. One reservoir feeds three demands at different ground levels - find every pressure.
Solved result: The worst pressure is at demand two, 251.7 kPa, and it is not the demand furthest from the source.
Open in the Studio →Worked example: a Hazen-Williams water main
A branched water main solved with Hazen-Williams in the browser: a 65 m reservoir feeds three demands, every pipe at C = 130, switchable to Darcy-Weisbach.
Solved result: The governing 20 m demand holds 412.8 kPa of residual pressure.
Open in the Studio →Worked example: a PE100 diesel rising main
A pump lifting diesel up a 250 m PE100 rising main, in the browser: static lift dominates and the diesel preset reports NPSHa for a suction-margin check.
Solved result: The pump settles at 6.880 L/s and 38.96 m of head, of which 35 m is pure lift.
Open in the Studio →
Heat transfer
Worked example: an insulated hot water main
See what insulation saves on a hot water main in your browser. The solver compares insulated and bare segments and tracks the temperature drop on each.
Solved result: Water enters at 80 degrees Celsius and arrives at 71.34 degrees, and the single bare segment is responsible for 6.90 of the 8.66 degrees lost.
Open in the Studio →Worked example: a hot and cold mixing tee
Find a blended temperature in your browser. A hot and a cold water stream mix at a tee by enthalpy, then the flow cools along a pipe to a cold ambient.
Solved result: The tee blends to 37.00 degrees Celsius and the outlet delivers 34.78 degrees.
Open in the Studio →Worked example: a glycol cooling loop
A 30% glycol cooling loop with heat transfer: a pump circulates coolant through a heat exchanger and an 8 kW load, and a bare return line sheds the heat to ambient.
Solved result: The pump settles at 6.363 L/s and 16.89 m, and the 8 kW load raises the glycol by 0.33 K.
Open in the Studio →
Compressible gas
Compressed air line, a worked pressure-drop example
Worked compressed air example, a line at about 6 bar gauge feeding a 1.15 kg/s draw-off through two pipe sizes, solved in pressure-squared form.
Solved result: The run passes 1.151 kg/s of air, and the pressure profile is strongly lopsided.
Open in the Studio →Fan and duct, a worked operating-point example
Worked fan and duct example, a fan pushing air through a 60 m duct to atmosphere. The operating point is where the fan curve meets the duct resistance.
Solved result: The fan and the duct meet at 37.37 L/s and 221.4 Pa.
Open in the Studio →Worked example: a circular air-duct run
An inline fan driving air through 40 m of DN250 spiral duct: the operating point is where the fan curve meets the duct resistance and a balancing damper.
Solved result: The fan delivers 164.8 L/s against 25.61 Pa, and the whole run is remarkably cheap in pressure.
Open in the Studio →Compressor and line, a worked set-ratio example
Worked compressor example, a set-ratio compressor raising 200 kPa air to 400 kPa down a 150 m line. Reports discharge temperature and shaft power.
Solved result: The system settles at 0.3716 kg/s, and the air leaves the compressor at 99.15 degrees Celsius.
Open in the Studio →Air blow-down, a worked high-velocity example
Worked high-velocity air example, a short line dumping 300 kPa air to 120 kPa and reaching about 210 m/s, firing the solver's high-velocity advisory.
Solved result: The 20 m line passes 0.6021 kg/s and the air reaches 211.4 m/s at the outlet.
Open in the Studio →Hot air line, a worked cooling example
Worked hot gas example, 0.18 kg/s of 127 C air cooling along a bare 300 m line. As the gas cools, its density rises and its velocity falls off.
Solved result: The air enters at 126.9 degrees Celsius and arrives at 15.78 degrees, within a degree of the ambient, and the density and the velocity move the wrong way on the way there.
Open in the Studio →
Non-Newtonian fluids
Power-law fluid network, a worked non-Newtonian example
Worked non-Newtonian example, a shear-thinning power-law fluid fed from three reservoirs into a junction. Shows the Metzner-Reed Reynolds number.
Solved result: The junction settles at 31.79 m, above the middle reservoir, so only the top reservoir supplies and the other two receive.
Open in the Studio →Bingham line, a worked yield-stress example
Worked Bingham-plastic example, a yield-stress sludge pumped down a 100 m line. Shows the laminar to turbulent regime via the Hanks transition.
Solved result: The 100 m line costs 4.773 m of head to pass 2 L/s, and it is running laminar with an unsheared plug filling 74.3 per cent of the bore.
Open in the Studio →
Time simulation
Worked example: a tank filled by a pump on level control
A time simulation of a pump filling a tank on level control: it starts below 2 m and stops above 5 m as a leak drains the tank, and the level cycles in the deadband.
Solved result: A time simulation has no single steady answer to publish, because the heads and flows change at every one of the 101 recorded timesteps. What it does have is a duty cycle, and that settles into a clean repeating pattern: the pump runs 140 seconds in every 500.
Open in the Studio →