The Profile Through the Station

5.3.1The sheet, and where it stops

A hydraulic profile through a pump station is two lines drawn over a section: the hydraulic grade line, which is where water would stand in a standpipe tapped into the pipe, and the energy grade line, which stands one velocity head above it. Module 2 established both. This lesson does the bookkeeping: start at a surveyed water surface, step the line down once for every element the water passes, jump once at the pump, and land on another surveyed water surface. If it lands somewhere else, the drawing is wrong — and that closure is the only reason a reviewer believes any of the numbers on it.

Two facts about the sheet before any arithmetic. First, a station profile has two fixed ends and nothing fixed in between. The upstream end is the water surface in the wet well, which is a control setting, not a survey. The downstream end is not the station boundary: it is the water surface in the receiving structure 1 200 m away, and the HGL at the flange where the station sheet stops is that surface plus every metre the force main will spend getting there. The station sheet therefore imports a number from §5.4 and cannot be drawn without it.

Second, the two sheets are drawn at different horizontal scales and meet at one station. This station occupies 15.20 m of pipe between the wet well wall and the force main flange; the main beyond it is 1 200 m (3 937 ft), at whose scale the whole station is a tick mark. The station sheet here is drawn 1 : 1 — no vertical exaggeration at all, which is a consequence rather than a choice: inside a station the energy is taller than the station is long, so there is nothing to stretch. State the exaggeration anyway, on every sheet, every time (§1.5) — a reader who assumes 1 : 1 on a 10 : 1 sheet will believe a 1% grade is a hill.

The station: wet well floor at 0.00 m on the drawing datum, finished grade at 8.20 m, invert of the arriving 300 mm concrete gravity sewer at 3.20 m on a 0.40% grade, high water alarm at 2.75 m, lead pump on at 2.60 m and off at 1.35 m. A dry-well pump takes suction through a 300 mm line and discharges into 250 mm pipework, through a check valve, an isolating valve, a meter and a tee into the common header, to a force main flange at 6.68 m — and then 1 200 m of 250 mm cement-lined ductile iron to a receiving water surface at 27.30 m. The duty is 60 L/s (951 gpm, 1.369 MGD) per pump.

5.3.2The first loss is the one nobody itemises

The water does not arrive at rest. At the catchment's peak of 60 L/s the arriving 300 mm sewer runs at a normal depth of y/D = 0.803 by Manning — 0.241 m (0.79 ft) deep, at 0.986 m/s (3.24 ft/s) — so its water surface at the wall is 3.20 + 0.241 = 3.441 m and its energy grade line stands one velocity head above that, at 3.491 m. In a free-surface pipe the HGL is the water surface; that is the whole difference between the left-hand end of this drawing and the rest of it.

With the well drawn down to the off level at 1.35 m, the water then falls into it. Everything between 3.491 m and 1.35 m — the fall, and the entire velocity head the sewer arrived with — is destroyed in the well as turbulence. That is 2.141 m (7.02 ft), and it is the largest single energy drop anywhere inside this station: 3.7 times the 0.581 m spent by every fitting and every metre of station pipework put together. It appears on no loss schedule, because the pump is never charged for it — total dynamic head is measured from the wet well water surface, which is where the water has already finished falling.

No design avoids it: it is the price of cutting a gravity system and restarting it at a different elevation, and it is why a wet well is a plunge pool full of entrained air (§8.1). Raise the well level and the drop shortens metre for metre — and so, exactly, does the head the pump must produce, because both are measured from the same surface.

The check that goes with it is the first one a reviewer runs, and it is subtraction: the wet well water surface must sit below the arriving invert. At the alarm level of 2.75 m the freeboard is 0.45 m; at lead-on, 2.60 m, it is 0.60 m. Lose it and the station is backing water up the sewer it was built to relieve.

5.3.3Element by element, bell to flange

Now the pumped path, in the order the water meets it. Two velocity heads carry the whole schedule: at 60 L/s the 300 mm suction line runs at 0.849 m/s (2.79 ft/s) for v²/2g = 0.0367 m, and the 250 mm discharge pipework at 1.222 m/s (4.01 ft/s) for 0.0762 m. Each minor loss is K velocity heads of whichever bore its K is referenced to; each pipe run is Darcy-Weisbach over its own length (§3.2). The suction pipe is 4.75 m long and the station discharge pipework 13.88 m, both cement-lined ductile iron at 0.10 mm roughness.

Read the third column before the fourth. The reducer sits at the end of the 300 mm suction run, but its K is referenced by convention to the smaller, faster bore, and at fixed flow velocity head goes as D^-4, so the two candidate velocity heads differ by exactly (300/250)⁴ = 2.0736. Charge the reducer on the suction side and you book 5.5 mm where 11.4 mm belongs. Six millimetres is nothing here; the habit is not, because the same confusion on the check valve's K = 2.00 is 79 mm, and on a whole suction header at a low-lift drainage station it is the design. Write the reference bore beside every K and the question stops being a question.

The totals: static lift 25.95 m (85.14 ft), station losses 0.581 m, force main 6.702 m — 6.504 m of friction plus 0.198 m for four 45° bends and a submerged exit — giving 33.233 m (109.03 ft, 326 kPa, 47.3 psi) across the pump. As shares of that: static 78.1%, force main 20.2%, the station's discharge side 1.5%, the suction side 0.21%. The station's own pipework is a rounding error against 1 200 m of main — which is what §4.1 means by "minor": it describes a long force main, not a pump station. Shorten the main to 100 m and the same 0.581 m is 44% of the loss budget; push the flow to 110 L/s (1 744 gpm) and the station reaches 3.9% while the main takes 43.6%.

One line, two curves. The EGL runs through the numbers above; the HGL runs 0.0762 m below it in the 250 mm pipework and 0.0367 m below it in the 300 mm suction line. So the HGL falls 0.0509 m across the reducer where the EGL falls only 0.0114 m, the difference being kinetic energy borrowed rather than spent — and run the same fitting the other way, as an increaser, and the HGL rises with no energy created at all. That is why "does the grade line fall in the direction of flow?" has to be asked of the energy grade line. On a 34 m sheet the gap is a third of a pixel, so the instrument magnifies it twenty times and says so; never let a drawing exaggerate silently.

5.3.4The suction column, and the lowest pressure in the station

Put the pump's centreline at 1.00 m and ask what happens if you raise it. The answer surprises almost everybody: nothing happens to the head the pump must produce. Static lift is measured between the two water surfaces (§2.3) and the pump sits between them, so raising it lengthens the suction column by exactly what it shortens off the discharge column. Move it 2.00 m up and the head goes from 33.2329 m to 33.2264 m — 6.5 mm, and even that is not elevation: it is 2 m of 300 mm suction pipe gained in exchange for 2 m of 250 mm discharge pipe, which is cheaper per metre because the bore is bigger.

What the move does change is on the other axis. The HGL on the suction side is fixed by the wet well: at 60 L/s it leaves the surface at 1.35 m and arrives at the pump's suction nozzle at 1.2025 m, having spent 0.0713 m on the bell, the elbow, the valve, the reducer and 4.75 m of pipe. The pressure there is that grade line minus the elevation of the nozzle. At 1.00 m it is +0.20 m of water (+2.0 kPa, +0.29 psi). At 3.00 m it is −1.80 m (−17.7 kPa, −2.56 psi): the same duty, the same flow, the same fittings, 2.00 m less pressure at the nozzle. Elevation does not change what the pump must produce. It changes whether the pump can stand where you put it.

Which brings the high-point check inside the station, and it must be a check against the grade line, not a shape someone drew. The highest point of the suction line is the horizontal run at the pump's own elevation, and the governing spot on it is its downstream end, past the isolating valve, where 0.0599 m of the suction loss has already been spent; its crown sits 0.150 m above the centreline. Set crown equal to HGL and the answer is linear in elevation: z* = 1.103 m. Below that the whole suction line lies under its grade line — at a centreline of 1.00 m the crown is 0.103 m (0.34 ft) clear. Above it the crown is above the grade line: at 3.00 m it stands 1.901 m (6.24 ft) above, at sub-atmospheric pressure. The pipe does not empty — it is a closed pipe with water in it — but air comes out of solution at the lowest pressure and collects at the local maximum, shrinking the effective bore, and a large enough pocket breaks the column and the pump loses prime. That is why suction lines are laid with a continuous rise to the pump and no intermediate high points, and why a pump on a genuine suction lift needs a priming system rather than good intentions.

The discharge side gets the same check and passes by inspection, which is a result and not a reason to skip it. The HGL at the flange is 33.93 m, the highest pipe inside the station is the header crown at 6.805 m, and the margin is 27.12 m (88.98 ft); with the pumps off it is still 20.50 m. Inside a station the discharge side is never where a grade line falls below a pipe. Out on the force main, where the ground climbs to 30.20 m and the static grade line is 27.30 m, it is — and that is §5.4.

5.3.5Which case governs

Everything above was drawn for one case. Four levels and one flow can move independently, and no single profile covers them, so the honest deliverable is a small set of profiles and a statement of which question each one answers.

• Maximum head — lowest wet well level, highest receiving level, highest flow. On this station: 51.83 m (170.04 ft) at 110 L/s with the well at 1.20 m and the receiving structure surcharged to 29.50 m. This is the case the pump is bought against.
• Minimum head — highest wet well level, lowest receiving level, lowest flow: 23.10 m (75.79 ft), pure static lift with the pumps just off. The pump must be tolerable here too, 28.73 m away on the head axis, because this is where it runs out to the right of its curve (§7.2).
• Surcharge of the arriving sewer — highest wet well level, and the flow is irrelevant. Governed by the alarm level against the invert at 3.20 m, not by anything the pump does.
• Lowest pressure at the pump — lowest wet well level and highest flow, because suction losses grow as Q².
• Air at a high point — lowest wet well level and lowest flow. Lowest flow, because on the force main the grade line above a summit is the discharge level plus the friction still to be spent downstream of it, so less flow means a lower line (§1.5). Checking everything at maximum flow gets this one exactly backwards.
• Self-cleansing — at the pumping rate, not at rest. 0.6 m/s (2 ft/s) in a 250 mm bore is 29.45 L/s (467 gpm), so any duty below that fails the usual minimum. The figure is common practice and the governing standard — Ten States Standards, or your local authority — sets the real number.

Notice how little of that list is about flow. Between lead-off at 1.35 m and lead-on at 2.60 m the head travels exactly 1.25 m (4.10 ft) at every flow, because nothing but the static term follows the level — a closed form worth checking your own arithmetic against. The band a specification must cover here is 28.73 m wide, and 3.0 m of that comes from a receiving structure which surcharges in wet weather precisely when the inflow is highest.

What this lesson borrowed and did not pay for: the friction came from Darcy-Weisbach with a Colebrook factor, which Module 3 earned, and the K values from the course table, which Module 4 earned. The pump supplied 33.233 m because the ledger demanded it, which is all a profile is entitled to assume; whether a real pump produces that head at that flow is Module 6. And the ground beyond the flange has not been looked at once — 1 200 m of it, with a summit at 30.20 m that this station's static grade line cannot reach. That is the next lesson, and it is where the high-point check stops being arithmetic you can do by inspection.