§ 1.4  Module 1 — The Station in One Picture

Flows, Firm Capacity and Redundancy

Installed capacity is what the nameplates add up to. Firm capacity is what the station can still do on the day one of them is on the back of a truck.

A pump station is sized against a flow it will see for a few hours a year, with one of its pumps missing. Both halves of that sentence are this lesson. The flow is not the average, and the capacity is not the sum of the nameplates — and an engineer who quotes either of those two comfortable numbers has described a station that does not exist.

1.4.1Four flows, and which one sizes what

A station has one inflow and four numbers for it. Keeping them apart is most of the discipline in this part of the subject, because three of the four are routinely quoted as though they were the fourth.

• Average day flow — a year of volume divided by the days in it. It sizes nothing. It is what you cost energy against, what loads a treatment works, and what every peaking factor is a multiple of.
• Peak hour flow — the highest hourly average the station sees in dry weather. For a sanitary station this is the design peak, and it is the flow that must be moved with the largest unit out of service.
• Peak wet-weather flow — peak hour plus whatever the collection system admits through cracked joints, roof leaders plumbed into the sanitary sewer, and manhole covers under water. In an old system it dwarfs everything else. It is a measurement, not a formula.
• Minimum flow — the small hours. It sizes nothing and governs behaviour: how long sewage sits in the wet well before it turns septic, and how often the motors start.

Take a subdivision of 4,800 people with no industry and a separate sewer system. The Ten State Standards' familiar basis is 100 US gallons per capita per day; that is 379 L, and we will use 380 L/person/day so the arithmetic stays checkable by hand. Read what the standard actually says about that figure, because it is usually quoted as half of itself: the 100 gpcd is to be used in conjunction with a peaking factor from its Figure 1, and it is the two together that are intended to cover normal infiltration in a system built with modern construction techniques — with an additional allowance where conditions are unfavourable. The per-capita figure alone covers nobody's groundwater. Then 4,800 × 380 = 1,824,000 L/day = 1,824 m³/day, and dividing by the 86,400 seconds in a day gives an average day flow of 21.1 L/s (0.48 MGD). Nothing in the station is sized on that number.

The peaking factor converts it into one that sizes something. Harmon, with P = 4.8 thousand: PF = 1 + 14/(4 + 2.191) = 3.26, so the design peak hour flow is 21.1 × 3.26 = 68.9 L/s (1,090 gpm, 1.57 MGD). Babbitt returns 3.65 for the same population and so 77.1 L/s, twelve per cent higher. Both formulas agree about the structure of the thing: small populations peak hard. At 100,000 people Harmon returns exactly 2.0, because √100 = 10 and 14/14 = 1. At 200 people Harmon returns 4.15 and Babbitt 6.90 — 66% apart, and the disagreement is not symmetrical. Babbitt printed a range with his fit: not below 1,000 people and not above 1,000,000 (Sewerage and Sewage Treatment, 1922, p. 36). At 200 people his formula is being read well outside the range its own author allowed, which is why 6.90 should be treated as an artefact rather than a second opinion. Harmon states no range at all, which is not the same as being valid everywhere. Inside Babbitt's range the two are closer and still not close: at 1,000 people, 3.80 against 5.00. Where a flow record exists, the record wins; where it does not, say in the calculation which formula you used and what it gave, because the reviewer will check.

Two things are still missing from 68.9 L/s, and both are collection-system questions this course takes as given. What the peaked figure covers, on the standard's own terms, is normal infiltration. What it does not cover is inflow — roof leaders plumbed into the sanitary sewer, yard drains, a manhole cover under water — or infiltration beyond normal in an old system with tributary development already in the ground. Those are added to the peaked flow rather than multiplied by the peaking factor, because groundwater seeping through a cracked joint does not keep a diurnal schedule, and because a per-capita rate that has already been peaked cannot be asked to peak a second time. The standard expects that allowance to be evaluated where conditions are unfavourable, not assumed away. And the population is the one at the end of the design life, not today's: a station commissioned for 4,800 people in a district zoned for 9,000 has been designed for the wrong decade.

1.4.2Firm capacity: the flow you can promise

Installed capacity is the sum of the nameplates. Firm capacity is what the station can still deliver with its largest unit out of service. Only the second number means anything, because the largest unit is precisely what a burnt winding, a rag ball across the impeller, a seal rebuild or a scheduled inspection takes away. There is no version of the asset's thirty-year life in which one pump is never out; designing as though there were is the failure this whole rule exists to prevent, and the way it presents itself is a manhole lid lifting three streets upstream.

The Ten State Standards asks one thing of the pump set, and it asks it of every station regardless of how many units there are: with any unit out of service, the remaining units must have capacity to handle the design peak hourly flow. There is no separate clause for a duplex. The single rule is what forces each of a duplex's two pumps to carry the whole peak alone — remove one of two and one is left — and the one thing the standard does add for a two-unit station is that the two units be of the same size, which stops a designer from meeting the letter of the rule with one real pump and one token. Potable practice asks the same question with a different flow: maximum day demand plus the fire flow the local fire authority requires, with the largest pump out. The hydraulics is identical. The flow is a fire-protection decision and comes from outside the hydraulics.

The premium in the sixth column is n/(n−1) and nothing else — an identity, not an estimate. A duplex buys twice the capacity it can promise; a five-unit station pays 25% over. That is the argument for many small units, and it is why large stations have five or six of them. Against it: each unit is smaller, so the shared main runs slower when only one is going, which the last column makes plain; more units means more control complexity and more starts to distribute; and, as the next section shows, the arithmetic that makes the small units look free is not true.

1.4.3Sizing the set, and where the arithmetic breaks

The duplex is trivial to size and expensive to buy. Each pump must move the whole 68.9 L/s, so we specify two at 70 L/s: firm capacity 70 L/s, installed 140 L/s, and 1.1 L/s of margin over the design peak. The triplex looks obviously better. Three units at 34.4 L/s give an arithmetic firm capacity of 68.9 L/s for 103 L/s installed — the same promise for a quarter less pump.

Now give the station its pipe: 18 m of static lift, and 900 m of 250 mm ductile iron carrying a check valve, an isolation valve, two elbows and a discharge into the receiving structure. A unit rated 34.4 L/s on that system is honest — running alone it delivers 34.4 L/s. Two of them together deliver 53.5 L/s, not 68.9: one and a half times a single unit, and 78% of the arithmetic firm capacity. Nothing is broken. Parallel pumps add flow at equal head, and on a system curve that rises with the square of flow, more flow costs more head — so the second unit climbs the curve instead of extending it. How far short it lands depends on how steep the pump curve is: the 53.5 L/s above is for a shutoff head 35% above the duty head, an ordinary radial curve, and across the steepnesses in common use two units land between 1.4 and 1.7 times one — never at 2. §7.3 does this properly, with the curves drawn.

Size the triplex against that result instead of against division, and each unit needs 48.8 L/s rather than 34.4 — 42% bigger — for 146 L/s installed. The duplex specified two paragraphs up installs 140 L/s. On a main with real friction the saving from splitting the duty can be negative, and the engineer who promised a cheaper station on the strength of the (n−1) arithmetic now owns the difference.

population                                    4 800 people
average day     4800 × 380 L/d ÷ 86 400 s   =   21.11 L/s
Harmon PF       1 + 14/(4 + √4.8)           =    3.261
design peak     21.11 × 3.261               =   68.85 L/s   (1 090 gpm)

duplex    2 × 70.0 L/s    firm  70.0 L/s    installed  140.0 L/s
triplex   3 × 34.4 L/s    firm  68.9 L/s    installed  103.3 L/s   ← on paper

same triplex on 900 m of 250 mm main, 18 m static lift:
  two units running together                =   53.5 L/s          ← 22% short
  unit needed so that two make 68.85 L/s    =   48.8 L/s
  triplex installed, sized honestly         =  146.5 L/s          ← above the duplex

Every figure computed through src/core/hydraulics.js; the parallel results are operating points of two identical units on one system curve, not multiples.

Splitting the duty has a second consequence a sanitary designer has to check before signing anything. The duplex's single pump puts 1.40 m/s through the 250 mm main, above the 1.05 m/s (3.4 ft/s) that practice commonly asks for to scour settled solids — the figure US sources quote as 3.5 ft/s, which is 1.07 m/s, so treat the pair as near equivalents and not as one number; this course uses the rounded 1.05 m/s throughout, as §1.3 set it. The triplex's single unit puts 0.70 m/s through the same pipe, and one unit of a four-unit set only 0.47 m/s — under the 0.6 m/s (2 ft/s) that Ten State Standards asks be maintained. Read the condition before calling that a failure, though: the standard asks for it at the design pumping rate, and at the design rate the main is carrying the whole 68.9 L/s at 1.40 m/s whichever set is delivering it — three units of 23 L/s move the same water as one of 69. So splitting the duty does not breach the velocity rule. What it does is leave the main below scouring velocity for most of the day, when a single small unit is cycling against the night and shoulder flows, and the solids that settle there are still there when the peak arrives. That is why designers stagger pump sizes, or bring a second unit on for a flushing cycle, rather than accept the slowest condition as normal. §1.3 introduced self-cleansing velocity; this is the first place it constrains a decision that looked purely economic.

1.4.4Why installed capacity overstates what a station can be relied on to do

Firm capacity is a better number than installed capacity and it is still an optimistic one. It removes exactly one pump and assumes everything else in the station is perfect. Five things it does not remove:

1. The things there is only one of. One wet well, one suction arrangement, one discharge header, one force main, one control panel, one level transducer, one power feed. A fouled level float stops a station whose pumps are all in perfect health, and no capacity arithmetic anywhere notices.
2. Concurrency. Pumps fail in storms. The water that raises the inflow is the water that floods the site, trips the feeder and blocks the access road. Firm capacity assumes the failure and the peak are independent events; they are correlated ones.
3. Degradation without failure. A rag-wrapped impeller, a worn wear ring, a check valve that never fully opens: the unit is still "available" and 20% short. The nameplate is unchanged.
4. Overlap. The largest unit out for a rebuild is out for weeks, not hours, and the chance that a second unit goes down inside those weeks is not small.
5. Whether the pump reaches its duty point at all. Cavitation from a poor intake, a vortex from too little submergence, air carried under the suction bell — each costs real capacity the nameplate still claims. Those are §6.5 and §8.3.

Which is why the standards ask for more than pumps: provision for emergency operation — standby power, a second feed, or storage — and alarms that tell somebody before the manhole does. Storage is the honest backstop. A station that is short of firm capacity for two hours a year needs volume, not another pump, and volume is cheap while the excavator is still on site and ruinous to retrofit. That trade is §8.6.

Notice what this lesson did, and did not, do. It computed one head without explaining it: the 53.5 L/s in §1.4.3 is a pump curve crossing a system curve, that crossing sits at about 22.8 m of total head, and both curves are Module 7's subject — taken here on trust, because the only thing you needed from them was the sign of the error in the arithmetic. What this lesson never did was prove a capacity. The design peak is a demand, firm capacity is a claim about meeting it, and neither is proved until a pump curve crosses a system curve at the flow you promised, at the wet well level you promised it, on the pipe you will actually have in year thirty. Module 2 assembles the head, Modules 3 and 4 the losses, Module 5 the profile that displays them, Module 7 the crossing. Carry these two numbers forward, because they are the first two a reviewer asks for: the design peak flow, and the firm capacity with the largest unit out.

¶Field quirks

What the specifications say, and what the browsers actually do, are two different documents. These are the divergences that cost production teams their weekends.