What Series Operation Buys and What It Costs

Why this matters

Putting one pump's discharge into another pump's suction is the standard answer when a single machine cannot make the head, and it works. What gets people is the bill. A series pair pushes both machines to the right on their curves, toward more flow than either was selected for, which is where required suction head and shaft power both climb fastest; it puts the sum of both pressures on the second casing, its seal, and everything downstream to the next relief; and it welds the two machines into one, because they must pass identical flow and neither can usefully run without the other. This article states one gate and runs it against two jobs that give opposite answers, one where series is the right arrangement and one where it works perfectly and is still the wrong fix.

Isolate the second machine for what it actually holds

The second pump in a series pair sits at the sum of both pressures, and the pipe between the two machines is at the first pump's discharge pressure even when only the first pump is running. Before either machine is opened: close and lock the isolation valves on both sides of the pump being worked on, lock and tag both driver disconnects and prove them dead against a known live source (29 CFR 1910.333(b)(2); NFPA 70E-2021, 120.5), then relieve and drain the section to a routed drain with nobody at the outlet and confirm zero on a gauge, all under 29 CFR 1910.147. Note the specific trap: locking out only the pump you are opening leaves its casing connected to the other machine, and starting the other machine, or a check valve leaking back off the header, re-pressurises the one you are inside. On a hot service let the casing cool below 140 F, read with a non-contact infrared thermometer, before a joint is broken.

Series is built by adding head at constant flow

Pick a flow. Read the head each pump makes at that flow. Add the heads. That is one point on the combined curve. It is the exact opposite construction to the parallel case, where flows are added at constant head, and getting the two mixed up is the most common arithmetic mistake in this subject.

Two identical pumps in series therefore have twice the shutoff head and the same flow range: a taller curve, not a wider one. A multistage pump is this arrangement built into one casing, which is why a multistage machine's head is roughly its stage count times a single stage.

The folk rule needs a condition attached

"Parallel for flow, series for head" is a good mnemonic and it is not a prediction. Which arrangement actually delivers more flow depends on how steep the system curve is relative to how much the pump curve droops between shutoff and duty.

Using the field model where a pump's head is its shutoff head minus a droop coefficient times flow squared, and the system's head is a friction coefficient times flow squared: the two arrangements deliver the same flow when the friction coefficient is about 1.5 times the droop coefficient. Steeper systems than that favour series; flatter ones favour parallel. That break-even is a property of this two-parameter model and not a law, so the honest use of it is as a warning that the mnemonic has a hinge in it. The real answer is always to construct both curves and cross them against the actual system curve.

What the mnemonic gets right is the thing series is uniquely capable of. A system whose static head exceeds a single pump's shutoff head cannot be served by any number of pumps in parallel, at any flow, ever. It can only be served by series or by a bigger machine. That is the one case with no argument in it.

The three costs

One: series pushes both machines toward higher flow, and the first pump pays for it in suction. Series raises the flow through both machines. Required net positive suction head rises steeply with flow, and it is the first pump that has the real suction condition, because the second pump's suction is the first one's discharge. So the suction margin that mattered at the selection flow is not the margin you have at the series flow, and it has to be re-read off the curve at the new flow rather than assumed to carry over. Power rises with flow too.

Two: the second casing and everything after it sees the sum. The second pump's casing working pressure rating, its seal chamber pressure and its seal's pressure rating, the discharge piping, the flanges, and every fitting up to the next relief device are now specified by the total, not by one pump's rise. A seal chamber sitting at the first pump's discharge pressure is a different specification problem from one sitting near suction pressure, and the flush arrangement has to suit it.

Three: the two machines are one machine. They pass identical flow, so run the second alone and it is fed at whatever the stopped first pump's flow path allows, which without a bypass is nothing. A series set needs an interlock, a starting order, and usually a bypass around each machine if the service has to survive one of them being down.

The gate

Is the head deficit a designed requirement, or is it a symptom of something that got worse?

Series is a legitimate machine arrangement for the first. For the second it will still work, hydraulically, and that is exactly what makes it dangerous.

Outcome one: the deficit is designed in

A transfer duty needs to lift liquid 150 ft, with 25 ft of friction at the required flow, so 175 ft total. The available pump makes 90 ft at that flow with a shutoff head of 120 ft off the curve sheet. One pump cannot reach this duty at any flow, because 175 ft is above its shutoff. Parallel changes nothing about that. Series is the arrangement.

Curve models. One pump: head = 120 - 30 x (flow fraction) squared, from the 30 ft between shutoff and the 90 ft duty point at a flow fraction of 1.0. Two in series: head = 240 - 60 x (flow fraction) squared. System: head = 150 + 25 x (flow fraction) squared.

The crossing. 240 - 60 q squared = 150 + 25 q squared, so 90 = 85 q squared, q squared = 1.0588, q = 1.029. Flow lands at 103 percent of the single-pump design flow, at a head of 150 + 25 x 1.0588 = 176.5 ft. Each pump contributes 120 - 30 x 1.0588 = 88.2 ft, and 2 x 88.2 = 176.4 ft, which closes.

Correction one, the interconnect, printed. The pipe between the two machines is not free. It costs 3 ft at a flow fraction of 1.0 and rises with flow squared, so it comes off the combined curve: 240 - 60 q squared - 3 q squared = 150 + 25 q squared, giving 90 = 88 q squared, q squared = 1.0227, q = 1.011. Flow is 101 percent rather than 103. Small on a short interconnect, and not small where the two machines are rooms apart.

Correction two, suction margin re-read at the new flow, printed. The first pump is running at 101 percent of its design flow, essentially where it was selected, so its required suction head off the curve is unchanged at 12 ft against a measured available 18 ft: margin 6 ft, unchanged. This is the check that is skipped because it is boring when it passes, and it is the same check that fails loudly in the next case.

Correction three, the pressure the second machine sees, printed. Gauge suction at the first pump is 5 psig. Each pump adds 89.3 ft at the CORRECTED crossing, not the 88.2 ft from the crossing correction one already superseded, which on water is 89.3 / 2.31 = 38.7 psi. So the first pump's discharge sits at 5 + 38.7 = 43.7 psig. The interconnect costs 3 x 1.0227 = 3.1 ft, or 1.3 psi, so the second pump's suction and seal chamber sit at 43.7 - 1.3 = 42.4 psig. The second pump adds its own 38.7 psi, so its discharge and everything downstream to the next relief sit at 42.4 + 38.7 = 81.1 psig. Two pumps off the same pallet: the first one's casing tops out near 44 psig and the second one's near 81, and the second one's seal is specified against a 42 psig chamber rather than against 5.

Why this is the right call. The requirement is permanent, no single available machine reaches it, and the arrangement is inside every rating once the pressures above are checked against the casing's rated working pressure and the seal's rating. Series here is not a workaround; it is the machine.

Outcome two: the deficit is a symptom

Same pump, a different job. A heat exchanger has fouled over two seasons. The system's friction coefficient has risen from 90 to 200 in the model's own units, and the pump alone now sits where 120 - 30 q squared = 200 q squared, so q squared = 120 / 230 = 0.5217 and q = 0.722. Flow is down to 72 percent and the plant wants it back.

What series delivers. 240 - 60 q squared = 200 q squared, so q squared = 240 / 260 = 0.923 and q = 0.961. Flow comes back to 96 percent of design. The arrangement works. That is not in dispute and it is why people do it.

Correction, suction margin re-read at the new flow, printed. Measured available suction head on this installation is 14 ft. Required, off the curve: 9 ft at 72 percent flow, so the margin today is 14 - 9 = 5 ft. At the series flow of 96 percent, required rises to 12 ft, so the margin becomes 14 - 12 = 2 ft. The margin has fallen by 60 percent, and 2 ft is below what suction margin guidance asks for on most services. The fouling problem has been traded for a cavitation exposure.

Correction, the power, printed with its efficiency term. Head at the new point is 200 x 0.923 = 184.6 ft against the 90 ft the system needed before it fouled. Power scales with flow times head over efficiency, and both machines are running near best efficiency at 96 percent so the efficiency term is close to unity and is stated rather than silently dropped. Relative to the clean system at 100 percent flow: (0.961 x 184.6) / (1.0 x 90) = 1.97. Roughly twice the shaft power to move slightly less water than the clean system moved with one pump.

What that doubled power is buying. Nothing. All of it is spent across the fouling, as heat, in the exchanger. This article agrees with the one on why a bigger pump does not fix a restriction and adds the arithmetic: the arrangement succeeds hydraulically and the success is the problem, because it removes the symptom that was reporting the fouling while the fouling keeps getting worse, at twice the running power, with the suction margin cut to 2 ft.

What getting it wrong looks like. A booster goes in, the flow complaint closes, and eighteen months later the first pump is cavitating and the exchanger is worse. The tell that should have redirected it is on the record: flow was fine two seasons ago with one pump and nothing about the duty changed. A deficit that appeared is a symptom. A deficit that was always there is a requirement.

How to verify a series pair is behaving

Put a gauge between the two machines. That single reading splits the pair into two measurable pumps and tells you whether each is making its share of the head. A pair where the interstage pressure is far below half the total has one machine underperforming, and without that gauge the set reads as one black box that is a bit down.

Then check the three things the arrangement changed, at the actual operating flow rather than at the selection flow: the first pump's suction margin from the curve at that flow, the second pump's casing and seal against the summed pressure from its own rating, and the flow itself against both machines' allowable operating range. And record the interstage pressure with the other readings, because the next person to look at this set will otherwise have exactly one number for two machines.

References

• Pump manufacturer's curve sheet for each machine, which owns shutoff head, required suction head at any flow, casing rated working pressure and allowable operating range
• Seal manufacturer's pressure rating for the second pump's seal chamber condition
• ANSI/HI 9.6.1, Hydraulic Institute guidance on net positive suction head margin, in the edition your engineering specification adopts
• 29 CFR 1910.147 for isolating a machine that stays connected to the other half of the pair, with 29 CFR 1910.333(b)(2) and NFPA 70E-2021, 120.5 for proving both drivers dead
• See related: What Happens When Two Pumps Run in Parallel; Why a Bigger Pump Does Not Fix a Restriction; What a Seal Flush Plan Is Actually For