§ 5.5  Module 5 — The Hydraulic Profile

Drawing It So a Reviewer Believes It

A drawing nobody can recompute is not a design. It is a drawing.

5.5.1A grade line is a claim until it names its case

Six declarations turn a line on a sheet into something a stranger can check: the datum, the vertical exaggeration, the flow, the level condition, the pipe condition assumed, and the loss method used. Miss one and the drawing still looks like a hydraulic profile; it stops being evidence, because there is no longer a calculation anyone could repeat and land on the same grade line.

The last four of those six are a case. A case is not a flow: it is a flow and a wet well level and a receiving level and an assumed roughness. Different checks are governed by different corners of that space, which is why one profile is never enough (§5.1). The set is complete when every check you intend to make has, somewhere in it, the case that is worst for that check.

Here is the set for the station this module has been building — §1.5's survey: 1 200 m of 250 mm cement-lined ductile iron from the wet well at 0+000 to a submerged discharge at 27.30 m. As-new roughness 0.10 mm; the year-thirty 0.40 mm is what §3.5 defends for a lining that holds. The flows are stated, not derived: what a pump delivers against this main is §7.2.

Read the head column first. Total dynamic head ranges from 25.00 m to 38.31 m across this set — 13.31 m of spread, more than half the static lift — and no single drawing is honest about that. Then note that two of the five cases fail a check: case A has the summit crown 1.50 m above a dead-level grade line, and case E runs at 0.917 m/s against the 1.05 m/s sewage practice commonly asks daily to scour a main — a figure US sources write as 3.5 ft/s, which is strictly 1.07 m/s, so quote one or the other and never the pair (§3.5). Those two failures are what specify an air valve at 0+760 and a duty schedule that scours. A set in which nothing fails was assembled to pass.

5.5.2The schedule and the drawing are one document

A profile sheet carries a picture and a table, and what makes them trustworthy is that every row of the table is keyed to a callout on the picture, and every callout is keyed to a row. A row with no callout is a loss nobody can point at; a callout with no row is a fitting nobody costed. Same defect, seen from two ends.

Case C's schedule, in sheet order. The fittings are Module 4's — ΣK = 0.70 on the 300 mm suction side, ΣK = 4.60 on the 250 mm discharge pipework — and every loss row is Darcy-Weisbach with a Colebrook friction factor at 15 °C.

key  item                                              metres
---  ------------------------------------------------  -------
E1   wet well water surface, this case                   2.300
E2   receiving water surface at the discharge            27.300
S    static lift, E2 − E1                               25.000
L1   suction fittings, SigmaK = 0.70 on 300 mm            0.026
L2   suction pipe, 6 m of 300 mm                          0.013
L3   station pipework fittings, SigmaK = 4.60 on 250 mm   0.350
L4   station pipework, 12 m of 250 mm                     0.065
L5   force main, 1 200 m of 250 mm                        6.504
L6   residual velocity head at the outlet, K = 1.0        0.076
---  ------------------------------------------------  -------
     total dynamic head, S + L1..L6                     32.034
     head shown by the drawn EGL jump at the pump        32.034
     CLOSURE                                             +0 mm

Case C · 60 L/s · wet well 2.30 m · as-new main · Darcy-Weisbach, ε = 0.10 mm

The last line does the work. Closure sets the schedule's total against the head the picture shows the pump producing — the vertical jump of the energy grade line across it — printed in millimetres, because metres hide the errors worth catching. Declare a tolerance beside it: ±10 mm is reasonable on a station this size, and it has an arithmetic consequence. Six loss rows each rounded to the nearest 10 mm can be 30 mm out between them before anyone has made a mistake, so a sheet closing to 10 mm must tabulate to the millimetre and round only the total.

The exaggeration note is not decoration either. The main climbs 23.70 m over 1 200 m, a mean grade of 1.98%, so at true scale the whole hydraulic story is a pencil line; at 10:1 it is readable and every slope on the sheet is a lie of a known size. Exaggeration multiplies the tangent of a grade, never the angle. §1.5's steepest surveyed reach, 0+520 to 0+760, is a true 4.50% — 2.5766° on the ground — and plots at 24.2277°. Divide that apparent angle by ten and you get 2.4228°, low by 6.0%; on a 12% grade the same shortcut returns 5.02° against a true 6.84°, low by 27%. Take the tangent first, divide that by the stated exaggeration, then convert back — the exercise below is that calculation.

5.5.3The checks, and which errors each one can actually see

Run these in this order on your own sheet, before anyone else does. Each has a number and a margin, and each exists because something specific gets past the others.

1. Datum, here and on every sheet this one borrows from. Compare the tabulated E2 against the survey. First, because it is the only error that corrupts the static term — the largest number in the schedule.
2. Closure. Schedule total against the drawn jump at the pump, in millimetres, against a declared tolerance. Here, ±10 mm.
3. Fitting audit. ΣK on the schedule against the fittings drawn on the pipework, item by item — 4.60 against 4.60 — not total against total.
4. Every local maximum, at the lowest flow. Not the highest point: the shorter high point at 1+050 has only 150 m of main beneath it and governs above 60.6 L/s (§2.2). At the lowest flow, because friction downstream of a summit is what lifts the grade line over it — this summit goes subatmospheric below about 47 L/s on new pipe and 42 L/s at year thirty.
5. Freeboard at the wet well. Arriving invert minus water surface at the highest level in the set: 3.20 − 2.75 = 0.45 m in case D. Being a difference between two elevations on one sheet, it survives a datum change that static lift does not.
6. Velocity, at both ends of the set. 1.732 m/s in case D against whatever maximum the authority sets; 0.917 m/s in case E against 1.05 m/s. In a 250 mm main 51.5 L/s is the flow that reaches it — continuity, not friction.
7. The energy grade line falls, everywhere. The hydraulic grade line may legitimately rise across a diameter increase; the energy line may not, and one that does was drawn rather than computed.
8. Method and condition, named — Darcy or Hazen-Williams, and which roughness or C — for the picture and the table.

Now the part that matters more than the list. The checks divide errors into three classes, and only two of the classes can be seen by comparing the two documents to each other.

A transcription error reaches one document. Take the discharge water surface off a sheet drawn on a datum 0.42 m lower while the profile is plotted on the survey: the schedule totals 31.614 m against a drawn 32.034 m, so closure reads −420 mm. Better than the number is where it appears. The two documents agree through the suction rows, part company at the pump, and never meet again — so the table's own march finishes 0.42 m below the surveyed water surface. That signature names the row.

A method mismatch also reaches one document, but it hides. Plot the grade line by Hazen-Williams at C = 140 while the schedule totals Darcy-Weisbach: on the as-new case that is 6.341 m against 6.504 m, closure +164 mm, which a hurried reviewer reads as rounding. Draw the same sheet for year thirty and it becomes +2 023 mm, because the assumed condition moves Darcy and does not touch C = 140 at all. The signature differs too: the gap opens at the pump and closes again at the outlet, both lines being anchored on the same water surface with only the slope between them disagreeing. A gap that heals downstream is a slope error; one that persists is a level error.

5.5.4Reading the failures as requirements

A failing check is not necessarily an error. Case A puts the summit crown 1.50 m above the grade line whenever the pumps are off, and no redesign changes it: water surface 27.30 m, crown 28.80 m, and with no flow nothing to lift the line. The check is not asking you to fix it. It says this station requires an air valve at 0+760, and that the vacuum it must tolerate is 1.50 m against a column-separation limit of about 10.13 m at that elevation and 15 °C — comfortable, and worth writing on the sheet (§5.4).

Case E is the same kind of statement. 0.917 m/s clears the roughly 0.6 m/s (2 ft/s) minimum but not the 1.05 m/s daily scour figure, so the sheet owes an answer: a smaller main, a control strategy that runs two pumps briefly each day, or a deviation with the authority's name on it. What it must not do is omit the case. An omitted case is the only profile error that leaves no trace at all — every drawing present is correct, and the missing one governed.

So present the set, not the drawing: one sheet per case, or one sheet whose case block names all of them, with a schedule and a closure line on each. Beside them one summary table — case, flow, levels, condition, TDH, velocity, worst clearance, worst freeboard — because that is what a reviewer reads first and what tells them which sheet to check hardest. The pump is bought against the largest head asked of one machine, case B at 35.32 m, not against case C's 32.03 m however tidy that sheet looks.

5.5.5What is still not on this sheet

Every number here is steady-state, and the sheet is silent about the two most dangerous minutes in a station's day. There is no pump curve: the flows were stated, and that a pump delivers whatever the crossing of two curves says is §6.2 and §7.2. There is no transient — the pressure envelope during a power failure or a check valve slam can dwarf every head here, and it gets its own profile in §8.5. The arriving sewer runs part-full, so its grade line is a water surface rather than a piezometric line, and is not drawn. Temperature is pinned at 15 °C. And the minor losses counted are the ones on the list: an unlisted strainer is not hiding in a coefficient, it is absent.

Take one habit from this module rather than a template. Before issuing it, hand your profile to someone with the survey, the fitting list and a calculator, and ask them to reproduce your total dynamic head. Inside 10 mm, and the sheet is a design. If they cannot tell which flow, which level, which roughness or which method you used, the reviewer's first mark will not be arithmetic — it will be a circle around the empty space where the case block should be.