Halve the temperature difference between flow and return and you double the flow rate for the same heat. That single sentence is why a low temperature system's pipework and pump cannot be inherited from the design that came before it.
This article covers Module 6 of the PlumbMate low temperature heating course: the mass flow rate calculation, velocity limits, pressure drop and the index circuit, reading a pump curve, and sizing the expansion vessel. There is a 10-question mock test at the end.
The flow rate the design creates
mass flow (kg/s) = Q (kW) ÷ (4.18 × ΔT)
For water, kg/s and l/s are near enough the same. Our house: 4.34 kW at a system ΔT of 5 K.
4.34 ÷ (4.18 × 5) = 0.208 l/s
Now the same house at three different design ΔTs:
| System ΔT | Flow rate | Relative to 20 K |
|---|---|---|
| 20 K (old style) | 0.052 l/s | ×1 |
| 10 K | 0.104 l/s | ×2 |
| 5 K (typical heat pump) | 0.208 l/s | ×4 |
Four times the flow. And because pressure drop rises roughly with the square of velocity, four times the flow through the same pipe is around sixteen times the pressure drop. This is why a system converted to low temperature without re-checking the pipework ends up starved at the far end, with a pump running flat out and still not delivering.
Why the narrow ΔT at all? Because a heat pump wants it. A wide ΔT means a hot flow or a cold return; the appliance is designed around a specific ΔT, usually 5 K, and its stated minimum flow rate comes from that. Fall below it and the unit faults out or short-cycles.
Velocity, and the two limits
Copper pipe carrying capacities at practical velocities:
| Size | Bore | Max flow at 1.0 m/s | Max flow at 1.5 m/s |
|---|---|---|---|
| 10 mm | 8.0 mm | 0.050 l/s | 0.075 l/s |
| 15 mm | 13.6 mm | 0.145 l/s | 0.218 l/s |
| 22 mm | 20.2 mm | 0.320 l/s | 0.481 l/s |
| 28 mm | 26.2 mm | 0.539 l/s | 0.808 l/s |
| 35 mm | 32.6 mm | 0.835 l/s | 1.252 l/s |
Our 0.208 l/s needs 22 mm, at 0.65 m/s. Through 15 mm it would be 1.43 m/s — just under the erosion limit, so it would run, but it is well past the noise threshold and its pressure drop is roughly five times that of 22 mm over the same length. On a system with no spare pump head, that matters.
There are two separate limits and they are often conflated.
The noise limit, around 1.0 m/s, is about comfort. Above it, water is audible in the pipe, particularly at night and particularly in a bedroom.
The erosion limit, around 1.5 m/s for copper, is about the pipe's survival. Above it, turbulence strips the protective oxide layer from the bore, especially at bends and fittings, and the wall thins. This is a slow failure that shows up years later as a pinhole in a bend.
Below roughly 0.3 m/s there is a third problem: too slow to carry air and debris along, so air pockets form at high points and sludge settles at low ones. Oversized pipework is not the safe option here either.
Pressure drop and the index circuit
Pressure drop is expressed in Pa/m (or mbar/m), read from a copper pipe sizing chart against flow rate and pipe size. A common design target is 100 to 250 Pa/m.
Fittings are accounted for by equivalent length: each elbow, tee or valve is expressed as the length of straight pipe with the same resistance. An elbow in 22 mm is about 0.8 m; a gate valve about 0.3 m; a branch tee about 1.5 m. Where fittings are not counted individually, adding 10 to 20% to the measured length is the conventional allowance — but on a low temperature system with a tight head budget, count them.
The index circuit is the circuit with the greatest total pressure drop. Usually the longest, but not always — a shorter run with a large flow and many fittings can beat it. The pump has to satisfy the index circuit; every other circuit then has surplus head, which is what the balancing valves absorb.
Worked
The index circuit of our semi: 18 m of pipework, fittings counted in as equivalent length, at about 240 Pa/m. Then the components, each read at its own design flow: the radiator, TRV and lockshield 5.0 kPa, the heat pump heat exchanger 29.7, the magnetic filter 4.8 and the zone valve 3.6.
Pipe loss = 18 × 240 = 4,320 Pa = 4.3 kPa. Plus 43.1 kPa of components = 47.4 kPa. The heat pump alone is 63% of it.
Pumps are catalogued in metres head, so divide by 9.81: 4.8 m.
And the flow in m³/h: 0.208 × 3.6 = 0.75 m³/h.
The duty point is 0.75 m³/h at 4.8 m.
Reading a pump curve
The curve plots head against flow, and the two ends are the parts people misread.
At zero flow the pump develops its maximum head. A “six metre pump” gives six metres when nothing is moving — the one condition in which it is doing no useful work at all. That headline figure describes the pump's shut-off, not its duty.
At maximum flow the head is near zero.
The duty point sits between the two, and it must be on or just above the selected speed curve. Below the curve, the pump cannot do it.
Two failure modes worth naming. A pump selected far to the left of its best efficiency point is oversized: it runs inefficiently, wears its bearings and generates velocity noise once the balancing valves are throttled to absorb the surplus. A pump selected too far to the right cannot make the head and the far end of the system stays cold.
Modern circulators are variable speed, usually with constant-pressure and proportional-pressure modes. On a system with TRVs, proportional pressure is normally right — as valves close, the pump reduces its head rather than driving the flow through fewer circuits and making noise. Setting it is part of commissioning, not a factory default to leave alone.
Minimum flow rate and system volume
Two manufacturer's figures that are design constraints, not commissioning details.
Minimum flow rate. The heat pump must always see this, whatever the TRVs are doing. It is why some systems need a bypass, a buffer, or — better — a zone left permanently open.
Minimum system volume. Often expressed as litres per kW. Too little water and the appliance has nothing to modulate against: it satisfies its flow temperature within seconds, shuts down, and restarts. Cycling wrecks the seasonal efficiency and wears the compressor.
Both are stated in the installation manual, and both have to be checked at the design stage — because the fix, if you find out later, is a buffer vessel you had not budgeted for.
The expansion vessel
Water expands about 4% between cold and 80 °C. On a low temperature system the temperature swing is smaller, so the expansion is smaller — but the system volume is often larger, because bigger emitters hold more water.
Vvessel = (Vsystem × e) ÷ [1 − ((Pi + 1) ÷ (Pf + 1))]
where e is the expansion coefficient for the temperature reached, Pi is the vessel charge pressure and Pf the safety valve setting, both in bar gauge.
Our system: 145 litres, e = 0.0143 for 55 °C, charge 1.0 bar, safety valve 3.0 bar.
Denominator: 1 − (2.0 ÷ 4.0) = 0.5
V = (145 × 0.0143) ÷ 0.5 = 2.074 ÷ 0.5 = 4.15 litres
Select the next standard size up: an 8 litre vessel. (Take the same system to 80 °C and e becomes 0.0287, giving 8.32 litres and a 12 litre vessel.)
Two points that catch people. The charge pressure must equal the cold fill pressure; a vessel charged at 1.5 bar on a system filled to 1.0 is effectively not connected until the pressure rises past 1.5. And the charge pressure is checked with the system drained or the vessel isolated — measured against a pressurised system it simply reads system pressure and tells you nothing.
Note also what the arithmetic does when a system holds twice the water at half the temperature rise: the two effects very nearly cancel. People expect the low temperature system to need a much smaller vessel, and it usually does not.
📝 10-Question Mock Test
Click an option to see whether you got it right. Explanations appear instantly — no submitting at the end.
Q ÷ (4.18 × ΔT). The same house at a 20 K ΔT would need only 0.052 l/s — a quarter of it.
Pressure drop rises roughly with the square of velocity. It is why a system converted to low temperature without re-checking pipework ends up starved at the far end.
Above it, turbulence strips the protective oxide layer from the bore and the wall thins — a slow failure that shows up years later as a pinhole in a bend. The 1.0 m/s figure is the noise limit, which is about comfort.
Which is why oversized pipework is not the safe option. Air collects at high points and sludge settles at low ones.
22 mm carries 0.320 l/s at 1.0 m/s. Through 15 mm the velocity would be 1.43 m/s — just under the erosion limit, but well past the noise threshold with about five times the pressure drop.
Usually the longest, but not always — a shorter run with a large flow and many fittings can beat it. The pump has to satisfy it; every other circuit then has surplus head for the balancing valves to absorb.
An elbow in 22 mm is about 0.8 m, a branch tee about 1.5 m. A 10 to 20% blanket allowance is conventional, but on a tight head budget, count them.
A 'six metre pump' gives six metres when nothing is moving — the one condition in which it does no useful work. The headline figure describes shut-off, not duty.
It satisfies its flow temperature within seconds, shuts down and restarts. Check it at design stage — the later fix is a buffer vessel you had not budgeted for.
A vessel charged at 1.5 bar on a system filled to 1.0 is effectively not connected until the pressure rises past 1.5. And check it with the system drained or the vessel isolated, or it just reads system pressure.
Four times the flow, sixteen times the pressure drop, and a pump whose headline figure describes the one condition in which it does nothing. Pipework and pump are where a low temperature retrofit quietly fails if nobody re-checks them.