Aging: Designing for Year Thirty

3.5.1The one term you forecast rather than specify

Look at what Darcy-Weisbach asks you for. Length is surveyed and staked. Diameter is ordered and inspected. Flow is whatever the catchment sends. Those three you write down, and what you wrote is what you get. The wall roughness is the only term you forecast, and the only one you cannot measure, because the pipe does not exist yet. Be honest about the limit of that framing: on unlined ferrous pipe the diameter moves too, as corrosion nodules eat into the bore — an effect ε cannot represent and this lesson does not model, and one that matters because h_f goes as D⁻⁵.

Roughness grows for a few specific physical reasons, and knowing which applies to your main is most of the work. Tuberculation — iron corrosion nodules on an unlined ferrous wall — is the classic and the worst, because it roughens the wall and narrows the bore at once. Scale is calcium carbonate out of hard water, which is why the same pipe ages differently in two towns forty kilometres apart. Biofilm and grease is the sanitary case: a slime layer with grease bound into it builds a soft, wavy wall that is hydraulically rough although nothing has corroded. Sulphide attack belongs to septic sewage, where hydrogen sulphide oxidises to sulphuric acid and eats cementitious linings from inside.

Notice what is not on that list. A pipe does not roughen because it is old; it roughens because a chemistry or a biology acts on a material. So "how much should I allow?" is a question about water quality and lining, not about years — and materials that offer those mechanisms nothing to work on barely age at all.

3.5.2Two ledgers for one wall, and they disagree about time

The profession keeps this forecast in two incompatible sets of books. Darcy-Weisbach wants an absolute roughness ε in millimetres, a physical length. Hazen-Williams wants a coefficient C, dimensionless, higher for smoother, tabulated for aged pipe because that is what its authors had records of. Both appear in specifications, often on one sheet.

You can convert between them, but not the way a table implies. On the worked station this lesson uses — 1 200 m of 250 mm main at its 60 L/s design flow — a C of 120 is worth an ε of 0.415 mm. At 20 L/s the same C of 120 becomes 0.696 mm; at 120 L/s it becomes 0.287 mm. A factor of 2.4 across a flow range the station will genuinely see, from one unchanged C. The reason is structural: Darcy's loss rises very nearly as Q², Hazen-Williams' as Q^1.852, and two power laws with different exponents cannot agree at more than one flow. A C is a statement about a pipe at a flow, not a property of the wall.

The ledgers do not merely differ in units. They disagree about the shape of aging, and the disagreement is invisible until you extrapolate. Take the two anchors the course's C table gives for cast iron: C = 130 new, C = 100 at twenty years. On this pipe at 60 L/s those are ε = 0.202 mm and ε = 1.485 mm, so the linear law implies α = 0.064 mm per year. Now ask both books for year forty. The linear law gives 0.202 + 40 × 0.064 = 2.77 mm; the C table's own year-forty entry, C = 80, corresponds to 5.03 mm. Same anchors, same pipe, a factor of 1.8 between them — at 60 L/s, 14.43 m of friction against 17.87 m.

3.5.3What year thirty does to the curve, and to the water

Hold the flow at 60 L/s and the effect is easy to state and easy to underrate. The main is cement-lined ductile iron, as-new ε = 0.10 mm, at Re = 2.68 × 10⁵ — firmly turbulent, as §3.1 promised a municipal main would be. Then f = 0.01779 and the main costs 6.50 m of friction on top of 18.0 m of static lift, so the pump is asked for 24.50 m. Now age it thirty years at 0.05 mm per year — and read that rate for what it is, an unlined-ferrous rate borrowed as a deliberately severe upper bound, not the allowance a cement lining warrants — and ε reaches 1.60 mm: f = 0.03307, friction 12.09 m, total 30.09 m — friction up by a factor of 1.86 with nothing else changed.

Now stop holding the flow, because nothing in the station holds it. A fixed-speed pump delivers the one flow at which its head output equals what the system curve demands. Take the pump as a catalogue gives it: shutoff 32.0 m, and 24.50 m at 60 L/s, which is exactly the as-new duty point. Where that shape comes from and what its efficiency does is Module 6; here it is a boundary condition and nothing more.

On the as-new main that pump delivers 60.0 L/s at 24.50 m, by construction. On the year-thirty main it delivers 50.70 L/s at 26.65 m — 84.5% of the flow the station was built for, at a head that went up. Nothing has broken and nothing alarms. It has slid up its own pump curve to the left, and it will keep sliding for the rest of its life.

One consequence is obvious: the station needs 18% more running time for the same daily volume, which eats the standby time §1.4's firm capacity was protecting. The unobvious one is velocity. At 60.0 L/s the main runs at 1.222 m/s; at 50.70 L/s, 1.033 m/s. That still clears the roughly 0.6 m/s (2 ft/s) minimum commonly required of a force main, but it has dropped below the 1.05 m/s (3.4 ft/s) often specified for daily scour — a rule you will also see written as 3.5 ft/s, which is 1.07 m/s, the same requirement rounded in the other unit system and 1.6% stricter. Quote one or the other; do not pair 1.05 m/s with 3.5 ft/s, because they are not the same number. Name the failure: the main that roughened stops cleaning itself, solids settle, and the deposits raise the roughness further. The mechanism closes a loop on itself, which is why the allowance must be generous rather than exact.

3.5.4Why a single design value answers no question well

It is tempting to settle this by choosing one careful, conservative number and using it everywhere. That fails, and not because the number was badly chosen. It fails because the four questions a station asks want their answers from opposite ends of the range.

1. Will it deliver design flow at end of life? Wants the rough value — here 30.09 m at 60 L/s. A pump that cannot make it will not make design flow in year thirty.
2. What is the highest flow, velocity and pressure it will ever see? Wants the smooth value, on commissioning day, at high water. That is the case that sets surge, thrust, motor loading and suction margin, and the rough value hides it completely.
3. What will it cost to run? Wants neither extreme. At a flat 75% pump efficiency and 95% motor efficiency — 71.25% wire to water, which is the basis every kWh/m³ in this lesson is quoted on — specific energy goes from 0.0936 to 0.1018 kWh/m³ between year zero and year thirty; over 547 500 m³ a year, 51 248 kWh rising to 55 733 kWh.
4. Will it scour? Wants the rough value and the lowest flow together — a combination appearing in neither of the first two checks.

So the design value is not a number but a pair, and the obligation is to run the system curve twice and check both ends. Here the envelope has four corners, because the wet well level swings ±1.75 m as well: as-new pipe at high water gives 63.72 L/s, year-thirty pipe at low water 47.41 L/s. The flow varies by a factor of 1.34 across the station's life with nothing wrong.

That is also the honest answer to why a pump chosen on new-pipe values ends up off its efficiency peak. Best efficiency happens at one flow, and a selection puts the duty point near it. Choose that duty point on the as-new curve — a pump with 32.0 m of shutoff head, on this station — and the pump is at its peak on commissioning day and drifts left for thirty years: 84.5% of duty flow at year thirty, 79.0% at the worst corner. Choose it on the year-thirty curve instead, which on this station is a 38.0 m shutoff, and it is right at the end and wrong at the start: 118.2% of duty on new pipe at mean well level — still inside the band — and 123.3% at the high-water corner, which is outside it. The band is the 70–120% of best-efficiency flow commonly cited as the preferred operating region in the Hydraulic Institute's guideline on operating regions (ANSI/HI 9.6.3). Note what is being assumed to use it that way: the guideline measures percentage of BEP flow, and every figure here is a percentage of design duty flow. They are the same thing only if each catalogue pump's BEP sits at its 60 L/s duty point, which is what a good selection aims at and lands within a few per cent of — the same size as the margins being judged, so treat 118.2% against 120% as a near miss rather than a verdict. What the mismatch costs is §6.5 and §7.4. What belongs here is structural: the pipe moves and the pump does not, so some mismatch is unavoidable.

3.5.5The centred choice, and what is not in this ledger yet

If both ends are wrong, aim between them. Size the pump on a mid-life condition — here ε about 0.80 mm, an equivalent C of about 110, roughly fifteen years in at the severe rate. All three candidate pumps in this comparison are catalogue quadratics through the same 60 L/s duty point, and the only thing that distinguishes them is shutoff head: 32.0 m for the as-new sizing, 35.0 m for the mid-life one, 38.0 m for year thirty. The 35.0 m pump delivers 67.28 L/s on new pipe and 56.49 L/s at year thirty: 112% and 94% of design duty, both inside the 70–120% band, and its worst corner still runs 1.090 m/s, which scours. Neither single-ended choice manages that — the as-new sizing stops scouring at its worst corner, the year-thirty sizing runs its best corner at 123% of duty.

Two honest caveats before you take the centred answer as a rule. The verdict depends on that shutoff head, which is a free parameter nobody has constrained: sweep it on this duty point and the mid-life sizing keeps both corners inside the band only from about 33.5 m upward. At 33.0 m the best corner reads 120.8% and at 32.5 m it reads 121.7%, so a flatter pump of the same nominal sizing fails the check the 35.0 m one passes. And the scour margin is thinner than one threshold makes it look: 1.090 m/s clears 1.05 m/s by 3.8% but clears the stricter 3.5 ft/s form — 1.067 m/s — by only 2.1%. So the centred answer is not a fudge, and on the pumps tabulated here it is the only one of the three that passes every check; it is not a result that survives being quoted without its pump.

Take two habits from this rather than a coefficient. Write the forecast down as an assumption with a rate, a source and a reason for the rate — "ε₀ = 0.10 mm, α = 0.05 mm/yr, linear per Colebrook and White, giving ε₃₀ = 1.60 mm; α is an unlined-ferrous rate taken as an upper bound on a lined main" — because a reviewer can argue with that, and cannot argue with a bare C = 100. And never compute a system curve once: compute it at both ends of the aging range and both ends of the level range, and put all four in the schedule.

What is deliberately missing. Every loss above is straight-pipe friction; the entrance, check valve, meter, elbows and header are Module 4, and inside a station they are frequently larger than the pipe friction they are named as minor beside, so every head figure here is low. Efficiency was pinned flat — 75% at the pump, 95% at the motor — but real pump efficiency falls away from best-efficiency flow, so the true energy penalty exceeds the 8.8% computed here — §7.4 quantifies it. A variable-speed drive helps less than expected, because it cannot move static head (§6.6). And the loop in which deposits lower the velocity, which allows more deposition, is modelled nowhere in this course — it is why field roughness sometimes outruns every forecast.