Datum, Stationing and Elevations

5.2.1The datum, and the one case where it bites

A hydraulic profile is a drawing made of subtractions. Static lift is one elevation minus another; cover is one elevation minus another; the clearance between the grade line and the pipe is one elevation minus another. Almost nothing on the sheet is an elevation in its own right — which is why the datum matters much less than beginners fear, and much more than experienced engineers remember.

Restate every elevation on the drawing on a datum that reads 0.42 m higher. The wet well surface, the ground, the crown, the invert, the receiving water surface, the grade line — all of them move together, and not one hydraulic quantity changes. The static lift on this station is 27.30 − 2.75 = 24.55 m before the restatement and 27.72 − 3.17 = 24.55 m after it. The offset appears twice, with opposite signs, and cancels exactly. Even the picture does not move, because the sheet's bottom gridline is a printed elevation too and gets restated with everything else. Rung 2 of the instrument below is that experiment: turn the datum knob and watch a screenful of printed numbers change while every readout that means anything holds still.

Now take one number from somewhere else. The wet well level comes off the station survey; the receiving water surface is lifted off the downstream authority's record drawing, which is on a different vertical datum that happens to read 0.42 m high at this site. Subtract, and the offset appears once. The static lift comes out as 24.97 m instead of 24.55 m — and that is the benign half of the damage. The hydraulic grade line is anchored on that same receiving water surface, so the whole line is 0.42 m too high along the entire main, and every high-point check on the sheet is 0.42 m too generous.

Name the failure, because it is specific. On this alignment with a 300 mm main, the summit at 0+760 is genuinely 0.546 m short of the grade line at the stated flow: the crown stands above it and air will collect there. A discharge sheet reading 0.60 m high draws that same summit with 0.054 m to spare. The drawing is internally consistent, the arithmetic on it closes, the reviewer's slope check passes — and the station gets built with an air pocket at 0+760 that nobody looked for. Nothing in the picture is capable of announcing this. The only tell is the datum note on the sheet the number came from.

1. Choose one datum for the whole set and print it on every sheet, not just the profile. If any source is on another datum, convert it once, note the conversion and the value used, and never carry the original number forward.
2. Tie it to a benchmark you can find again. An assumed datum is legitimate on a small job — "site benchmark, assumed elevation 100.00" keeps every number positive — but write the word assumed on the sheet, because the day someone extends the force main is the day it has to be connected to a real one.
3. Set the stationing origin at a structure, not at a property line. 0+000 at the wet well centre survives a change of easement; 0+000 at a fence does not.
4. Station in the direction of flow for a force main, so that increasing station means increasing distance from the pump and the grade line falls left to right, the way every other profile in the set reads.
5. Fix the two scales and state the exaggeration before plotting anything, because the vertical scale decides which of your results the drawing is physically able to show.

5.2.2Stationing: the plus sign means two different things

Stationing is the horizontal axis: distance measured along the alignment from a chosen origin, written with a plus. The trap is that the plus is scaled differently in the two systems in use. In US customary practice a station is 100 ft, so 12+50 is 12 × 100 + 50 = 1 250 ft, which is 381.000 m exactly. In metric practice a station is 1 km, so 12+50 is 12 000 + 50 = 12 050 m. The same five characters, read on the wrong convention, are out by a factor of 31.6 — and a drawing rarely says which convention it is using, because inside one office nobody needs telling.

The same point therefore carries two labels. The summit on this alignment is 760 m from the wet well: 0+760 metric, and 24+93.4 in 100-foot stations. Rung 1 of the instrument prints both for whatever point you drag the cursor to, which is worth doing until the conversion stops feeling like arithmetic and starts feeling like a smell you can detect on a drawing.

5.2.3One pipe, four elevations

"Pipe elevation" is not a quantity. A pipe has four elevations that matter, and they are a diameter apart from top to bottom.

Usage is not uniform between offices — some drawings say crown for the outside top of the barrel, and obvert or soffit for the inside — so the discipline is not to memorise one vocabulary but to write which surface each number belongs to. On this course, crown and soffit both mean the inside top.

Cover is measured to the outside top of the pipe. To keep the geometry visible without tying the exercise to one wall-thickness standard, this course's worked profile deliberately treats that outside top as coincident with its inside crown; the result is conservative for HGL clearance by one wall thickness, and a real drawing must carry outside diameter and wall thickness separately. With that stated simplification, the crown is the elevation the survey fixes and the rest follow from the diameter. At the summit on this alignment the surveyed ground is 30.20 m and the cover is 1.40 m, so the crown is 28.80 m — and in a 250 mm main the centreline is 28.675 m and the invert is 28.55 m. Change the diameter and the crown does not move at all; the invert drops away beneath it. That is rung 4 of the instrument, and it is worth watching because the instinct is that a bigger pipe sits higher.

Which brings the two halves of the lesson together. An air-collection high point cannot be checked by drawing it; it is checked by subtracting the crown elevation from the grade line elevation at that station, and the answer has to be positive at the lowest flow the station will run, not the highest. Here is that subtraction written out as a schedule, which is how it belongs on a sheet.

STATION 0+760   summit, governing high point
  surveyed ground                          30.20  m   (station datum, BM-3)
  cover to crown                        -   1.40  m
  crown / soffit                           28.80  m
  inside diameter                           0.250 m
    centreline                             28.675 m   <- NOT the check
    invert                                 28.550 m

  receiving water surface at 1+200          27.30  m
  friction still to spend, 440 m
    at 0.5420 m per 100 m               +   2.38  m   (60 L/s, Module 3)
  HGL at 0+760                             29.68  m

  HGL - crown, at 60 L/s                +   0.88  m   pressurised
  HGL - crown, at 47 L/s                    0.00  m   the crossing
  HGL - crown, pumps off                -   1.50  m   vacuum: air collects
  same check to the centreline          +   1.01  m   wrong by D/2 = 0.125 m

Summit check at 0+760 — the governing high point on this alignment

Two things in that schedule are worth stopping on. The first is that the worst case is pump-off: the grade line is pinned at the receiving water surface and rises above it only by the friction still to be spent, so less flow means a lower grade line at every high point. The second is the last line. The same check made to the centreline gives 1.01 m, comfortably positive, on a summit that at 47 L/s has nothing to spare. Being wrong by half a diameter is enough to lose an air valve you needed. §5.4 takes the high point apart properly; this lesson is about getting the elevations into it correctly.

5.2.4Vertical exaggeration, stated honestly

This station's ground climbs 19.60 m in 1 200 m — an overall grade of 1.63%. Plot the length at 1:3 000 and it fills 400 mm of paper; plot the rise at the same 1:3 000 and it is 6.5 mm. The wet well, the two high points, the grade line and the whole hydraulic argument would be one thick pencil line. So the vertical scale is stretched — 1:300 here, ten times the horizontal — and the same 19.60 m becomes 65.3 mm and the drawing becomes readable. Every profile you are ever handed is vertically exaggerated. Rung 5 of the instrument opens at 1:1 so you can see why nobody draws them that way.

The price is that every angle on the sheet is now false, and falsified in a way a reader cannot undo by eye. Exaggeration multiplies the tangent of a grade, because it stretches the rise and leaves the run alone. The steepest reach here, 0+520 to 0+760, climbs 10.80 m in 240 m: a true 4.50%, which is 2.58° above horizontal. At 10:1 it plots as 45.0%, an apparent 24.23°. At 20:1 it plots at 41.99°. Note what did not happen: ten times the true angle would be 25.77°, which is not the apparent angle and never will be. The distortion is not a scaling of the slopes a reader sees; it is a different function of them.

So the exaggeration must be stated on the drawing, beside both scales, every time — H 1:3 000 · V 1:300 · vertical exaggeration 10:1. Without it, no slope on the sheet can be recovered, and a reader who scales one off gets an answer that is wrong by the ratio nobody told them.

The vertical scale also decides what the drawing is physically capable of showing, which is a result and not a limitation. At 60 L/s the velocity in this 250 mm main is 1.22 m/s and the velocity head — the entire gap between the energy grade line and the hydraulic grade line (§2.2) — is 0.076 m. At 1:300 that plots as 0.254 mm: thinner than the line used to draw it. The clearance at the summit, 0.885 m, plots as 2.9 mm. Double the exaggeration and it becomes 5.9 mm: twice as reassuring, and no clearer. Which is why a profile carries a schedule of numbers as well as a picture, and why the instrument charts the clearance in metres against station rather than leaving it to the eye.

5.2.5What the sheet still does not carry

Everything above is bookkeeping, and it is now consistent: one datum, one stationing, four named elevations per pipe, two stated scales and a stated exaggeration. Four things were borrowed. The friction gradient of 0.5420 m per 100 m is Darcy-Weisbach with a Colebrook friction factor (Module 3) — 6.504 m over the whole 1 200 m. The two grade lines and the 0.076 m between them are §2.2. The 60 L/s was asserted, and where a stated flow comes from is §7.2. And the losses inside the station itself — the ones that turn a wet well level into a discharge flange pressure — are §5.3, which is the next thing this profile needs.

One habit, and it is cheap. On a profile you are about to draw or to review, check one elevation you can derive two ways — a crown against its own ground shot and its cover — and check that every elevation on it came from one datum. Those two checks cost a minute and catch the error class this whole lesson is about, which is the one class of error that leaves the drawing looking right.