Worked example: a PE100 diesel rising main

A rising main is a pump lifting a fluid up an elevation, and its character is different from a long flat pipe: most of the pump head goes into raising the fluid, not into friction. This worked example transfers diesel up a PE100 main, and it also shows the suction-side check that matters whenever a pump lifts a fuel.

The setup

A pump draws diesel from a low tank at 2 m of head and lifts it up a 250 m PE100 rising main to an elevated day tank at 37 m, so the static lift is 35 m. The fluid is the diesel preset (density 840 kg/m3, kinematic viscosity 3.5 x 10^-6 m2/s), which carries a vapour pressure, so the solver can report the available net positive suction head. The pipe is PE100 OD110 SDR11, a 90 mm bore, with a very low roughness of 0.003 mm, so it is hydraulically smooth. The pump curve runs from 40 m at shut-off to 22 m at about 37.5 L/s, at 75 per cent efficiency, with a required net positive suction head of 3 m.

The physics and the method

Fluid Network Studio solves the network for the flow where the pump curve meets the system curve. The system curve here is dominated by the 35 m of static lift: of the head the pump develops at its operating point, the great majority is spent raising the diesel, and only a small part on friction, because the smooth PE bore loses little. That is the signature of a rising main, and the numbers below put figures on it.

Because the diesel preset carries a vapour pressure, the solver computes the available net positive suction head at the pump inlet from the suction static head and the friction to that point, and compares it against the required net positive suction head of 3 m. If the available margin falls below the required value, the pump would cavitate, and the model flags it. This is the check that a flat-pipe friction calculation cannot give you.

The solved result

The pump settles at 6.880 L/s and 38.96 m of head, of which 35 m is pure lift:

The head split is the signature of a rising main. Only 3.962 m of the 38.96 m the pump develops is friction, and the other 35.00 m is the elevation the diesel has to climb. That means the duty point on this system barely moves when you change the pipe: double the riser length and you add about four metres to a duty that is already thirty-nine, whereas on a flat transfer line the same change would halve the flow. It also means there is little to gain from upsizing the bore. A smooth PE100 wall at 1.081 m/s is already cheap to push fluid through.

The suction side is the check the friction calculation cannot give you. NPSHa comes out at 14.24 m against a required 3.00 m, a margin of 11.24 m, so this pump is nowhere near cavitating. Nearly all of that margin is atmospheric pressure acting on a fluid whose vapour pressure is only 0.5 kPa, and the tank contributes just 2 m of static head. Drop the supply tank and the margin falls with it, roughly metre for metre, which is the experiment the example is set up for.

Everything here is solver output rather than a hand calculation. Open the example, press Solve, and check the head split and the suction margin for yourself.

What you learn

Solving the example shows how a rising main splits its head between elevation and friction, the low friction of a smooth PE bore, and the suction margin between available and required net positive suction head. Lower the tank level or lengthen the suction side and re-solve to watch the available margin fall towards the required value. The wider pump-sizing workflow, including the operating point against a system curve, is on the pump system design page.

Open this example in FNS and lower the supply tank to watch the suction margin shrink.