How Much Will 8 m of Head Actually Discharge? 62.1 L/s or 96.5 L/s

Siphonic roof drainage is the default answer for long-span steel roofs: no pipe gradient, fewer downpipes, smaller diameters. But its capacity is not copied from a product brochure. It is bounded by the few metres of head the building gives you. The drop from gutter to discharge point is fixed by the architecture; the diameter is chosen by the designer. When the two do not match, the surplus rain does not disappear - it stays on the roof.

This article works one project end to end. A 24 m x 60 m metal roof in central Guangzhou carries 74.9 L/s under the design storm, with 8.0 m of head from outlet face to the transition point. Under that identical head, DN100 suspended mains with a DN125 stack pass 62.1 L/s; DN125 mains with a DN150 stack pass 96.5 L/s. One step in diameter is worth 34.4 L/s.

Step 1 - Size the rain, not the pipe

Scope of the calculation. This example uses the Guangzhou central-district short-duration intensity-duration-frequency relationship in its 1-to-10-year return-period branch, a runoff coefficient of 0.9 for a metal roof, a catchment of 1440 m2, a design water depth over the outlet of 0.06 m, an absolute equivalent roughness of 0.015 mm for solution-annealed 304 stainless, and water at 20 C. Local loss coefficients are taken as 2.0 for the outlet, 0.3 per 90-degree bend and 0.5 for a converging tee. Included: friction loss via Colebrook, local loss, exit velocity head, stack-top negative pressure, external-pressure buckling of thin-wall tube, and thermal expansion of 304. Not included: the manufacturer's tested flow-versus-depth curve for the outlets (the only legitimate source per CECS 183:2015 Annex A.2), the air-water two-phase priming transient, the knock-down of buckling pressure from initial ovality, and the attenuation from roof falls and gutter storage. All diameters are thin-wall stainless tube with the bore taken as outside diameter minus twice the wall.

The standard form of the design storm relationship follows GB 50014 (Standard for design of outdoor wastewater engineering) and the companion technical specification for deriving IDF curves:

Guangzhou folds the (1 + C·log P) term into A and publishes parameters per return-period band. For P between 1 and 10 years:

At P = 10 a and t = 5 min:

With Q = psi · q · F, psi = 0.9 and F = 1440 m2 = 0.144 ha:

Values are L/(s·ha) over mm/h; 1 L/(s·ha) = 0.36 mm/h. The 93 mm/h at one hour and 208 mm/h at five minutes for a ten-year event are consistent with the measured Guangzhou hyetograph, and this consistency is the cheapest self-check that you are using the right local curve.

Step 2 - One energy equation holds the whole physics

In a conventional gravity downpipe, water spirals down the wall around a continuous central air core and the pipe never runs more than about one-third full. A 100 mm downpipe therefore uses a third of its section. A siphonic system changes that at the outlet: an anti-vortex baffle shuts the air out once roughly 50 mm of water covers the outlet, the pipe runs full, and the full drop is converted into velocity.

The design calculation then collapses to a single statement: the available head must be exactly consumed by friction loss, local loss and the exit velocity head. Referenced to the roof free surface and taken to the transition section where the siphon breaks:

Written in the pressure convention of CECS 183:2015, the Chinese technical specification for siphonic roof drainage systems (clauses 3.7.12 to 3.7.14):

The causal loop is worth stating plainly: head is fixed, diameter sets velocity, velocity sets loss, and loss eats the head. Lambda moves with Reynolds number as well, so nothing here scales linearly. Every estimate of the form "one size up gives proportionally more flow" is wrong, and the table further down shows how badly.

Example basis

The 8.0 m drop satisfies clause 3.7.8, which asks for more than 5 m where the stack is DN90 or larger.

Step 3 - Pipe sizing: case A is 3.56 m short, case B has 3.15 m to spare

Every velocity in case A sits inside the code envelope of clause 3.7.9 (mains and connector pipes not below 1.0 m/s, stacks not below 2.2 and not above 10 m/s). Judged on velocity alone it passes. Judged on the head ledger it fails: it needs 11.62 m and the site has 8.06 m.

The missing 3.56 m cannot be conjured. The system can only raise the water level over the outlets, and gutters are typically 0.2 to 0.3 m deep. Case A therefore passes 62.1 L/s at full flow, and the remaining 12.8 L/s becomes water standing on the roof:

Over a 30-minute ten-year burst that is 16.0 mm of standing water, or 0.16 kN/m2 of extra load; over 60 minutes, 32.0 mm and 0.32 kN/m2. Not structurally alarming for a light steel roof, but the moment it overtops the gutter upstand it is indoors - and all of it was avoided by one step up in main diameter.

Step 4 - Three caps on capacity, take the smallest

The most counter-intuitive reading is the last two rows. Raising the head from 8 m to 20 m lifts case A only from 62.1 to 80.3 L/s, still below the 96.5 L/s that case B delivers on 8 m. Twelve extra metres of drop, 16.8 percent less capacity.

The second cap explains it. More head drives more flow, and more flow pulls the stack-top pressure further down; once it falls below the vapour pressure of water the siphon breaks and the system oscillates between full-bore and broken flow. On 20 m of head, case A's energy solution is 99.0 L/s, but the stack-top pressure that goes with it is −123.3 kPa gauge, and the absolute pressure would be 100.7 − 123.3 = −22.6 kPa, which does not exist. Cavitation clamps the flow to 88.7 L/s and the code's −80 kPa floor clamps it again to 80.3.

Head is only realised through diameter. That is why tall buildings need their siphonic systems re-derived from the actual drop instead of inheriting the 17.5 to 30.0 L/s per DN100 outlet figure printed in a catalogue.

Step 5 - Negative pressure: the lowest point is the top of the stack

Intuition says the bottom. It is the opposite. The bottom has the whole drop feeding pressure back in, whereas the top of the stack is where all upstream loss has been paid and none of the drop has been collected. Per clause 3.7.12:

For case B at design flow, the stack top sits 0.56 m below the free surface, the suspended main has already spent 2.64 m, and the stack velocity is 3.97 m/s:

At the full-flow condition (96.5 L/s) it reaches −50.0 kPa, an absolute pressure of 100.7 − 50.0 = 50.7 kPa, still 48.4 kPa above the 2.3 kPa vapour pressure of water at 20 C. The clause 3.7.15 limits are:

The two small tables behind this are routinely skipped. Atmospheric pressure P_a is 100.7, 94.9 and 90.0 kPa at 0, 500 and 1000 m; vapour pressure P_vp is 2.3, 3.2 and 4.2 kPa at 20, 25 and 30 C. At 1000 m the basic limit becomes 15 − 90.0 = −75.0 kPa, tighter than the −80 floor, so upland projects cannot simply copy a coastal judgment. The cavitation boundary itself is P_vp − P_a = 2.3 − 100.7 = −98.4 kPa; the code's −80 kPa leaves 18.4 kPa of margin in front of it.

Step 6 - Will the vacuum suck a thin-wall stainless tube flat

The −80 kPa floor has a second meaning for thin-wall stainless: the pipe is working under external pressure. Elastic buckling of a long thin cylinder under uniform external pressure, in the n = 2 ovalisation mode, is:

With E = 193 GPa and nu = 0.29 for 304, on DN150 (159 mm outside diameter):

Doubling the wall from 1.0 to 2.0 mm multiplies external-pressure resistance by 8.1 times. That is the cubic law, and bending stiffness I = t³/12 follows exactly the same cubic law, rising eightfold as well. What rises only fourfold is the section modulus W = t²/6 - added wall buys stability and stiffness long before it buys static strength. A 1.0 mm DN150 sits only 1.34 times above the −80 kPa limit; large-diameter siphonic duty cannot inherit the thin walls chosen for plumbing tube.

In fairness, negative pressure is rarely what actually flattens a pipe on site. It is initial ovality from over-wide support spacing, plus foot traffic and impact during construction. The buckling equation assumes a true circle; a real tube with ovality of even a percent loses a noticeable slice of its critical pressure. Negative-pressure control and support spacing belong in the same specification clause.

Step 7 - Same nominal size, different bore: stainless versus HDPE

Clause 4.1.1 permits HDPE, stainless, plastic-coated steel, galvanised steel and cast iron. But the real bore behind the same nominal size differs enormously:

Thin-wall stainless carries a sixth to a seventh of the HDPE wall thickness, which hands it 18 to 62 percent more flow area for free. The two directions of error are not symmetric: applying an HDPE hydraulic table to stainless under-predicts capacity by 18 to 62 percent, which is merely wasteful; applying a stainless table to HDPE over-predicts it, and that is the direction that leaks.

Two other stainless numbers matter. Its roughness was taken as 0.015 mm, slightly higher than HDPE at 0.007 mm but far better than galvanised steel. Its coefficient of thermal expansion is 17.3 × 10⁻⁶ per K. Note that EN 1991-1-5 Annex C lists 16 × 10⁻⁶ per K for stainless, and the spread between 16.0 and 17.3 is exactly where published figures diverge. The Chinese specification for press-fit thin-wall stainless tube requires pipe and fittings in roof drainage duty to be no less corrosion resistant than S30408, to be solution annealed, and to withstand −80 kPa of negative pressure.

Step 8 - Three checks that are usually skipped

Self-cleansing velocity (3.7.18)

The code asks for the suspended main to be checked at the one-year, five-minute flow. Here that is q = 386.8 L/(s·ha) and Q = 50.1 L/s. Case B runs at 1.89 m/s, comfortably above the 1.0 m/s floor. Case C, with its DN150 main, drops to 1.33 m/s. Bigger is not automatically better: past a point, light rain no longer scours the pipe.

Loss of one outlet (3.7.17)

Four outlets share 74.9 L/s at 18.7 L/s each. With one blocked, three carry 25.0 L/s each, still inside the 17.5 to 30.0 L/s band for a DN100 outlet, so the clause is met. But more outlets is not more safety: at five outlets the share falls to 15.0 L/s, below the lower end of the manufacturer's curve. The pipes never run full, the siphon degrades to gravity flow, and the capacity you thought you had disappears.

Velocity downstream of the transition (3.7.10)

The code asks for no more than 1.8 m/s below the transition, with energy dissipation where it is exceeded. At 74.9 L/s, DN150 gives 3.97 m/s and DN200 (219 x 2.0, bore 215.0 mm) gives 2.06 m/s. You have to go to DN250 (273 x 2.0, bore 269.0 mm) to reach 1.32 m/s. The instinct that makes the siphon section as small as possible has to be reversed after the transition: the discharge line runs two sizes larger than the stack.

Step 9 - A 24 m 304 main needs 14.1 mm of expansion room

A 24 m suspended main moves 14.1 mm over a 34 K annual swing, 20.8 mm over 50 K, and 28.2 mm at 48 m length with 34 K. The press-fit stainless tube specification calls for expansion compensation where ambient temperature varies significantly, preferably by natural means. A long straight horizontal main rarely offers the leg length for a natural offset, so the practical answer is segmented anchoring plus proprietary compensators.

Cross-checking against other standards

The criteria above are not self-invented. Here is how they sit against the mainstream international sources:

Two criteria that are routinely mixed up

The first is that the criteria are the same equation with a coefficient twice as large. SR654 and CECS 183 are both writing the minimum absolute pressure as a velocity term plus the vapour pressure. CECS uses 0.3 kPa per (m/s)²; SR654 uses 0.061 m of head, which is 0.061 x 9.81 = 0.598 kPa per (m/s)², 1.99 times the CECS figure. At v = 6 m/s and 25 C, the SR654 velocity term is 0.061 x 36 = 2.196 m and the vapour pressure head is 3.2 / 9.81 = 0.326 m; their sum gives h_min = 2.522 m absolute. Subtracting the atmospheric head of 100.7 / 9.81 = 10.265 m leaves -7.74 m gauge, that is -75.96 kPa, within 0.7 percent of the -7.8 m that BS 8490 states outright. CECS, at v at or below 6 m/s, is floored at -80 kPa. The two sit 3.5 to 4.0 kPa apart in the low-velocity range and close to a factor of two apart once velocity climbs, so an overseas project cannot borrow one for the other.

The second is that one criterion does not travel across materials. HDPE has far lower ring stiffness than thin-wall stainless, and suppliers usually cap system negative pressure at 50 kPa, 30 kPa tighter than the -80 kPa the code allows for metal tube. Substituting stainless for HDPE makes negative pressure the relaxed item; putting HDPE into a system designed against -80 kPa means going back and re-checking at 50 kPa.

SR654 also carries two checks that CECS 183 does not state in its main text but that matter on site: a 10 percent safety factor added to the design runoff, which applies to gutter sizing as well, and a system filling time not greater than 60 s. The second governs whether full-bore flow can establish before the peak of the storm arrives, a priming criterion that CECS covers only through its steady-state hydraulics.

The BS 8490 factor of 1.4 deserves a specific warning. It holds only for long runs with few fittings, where friction dominates. In this example the outlet coefficient alone, xi = 2.0, pushes main local loss (1.50 m) above main friction loss (1.14 m); across the whole system local loss is 2.38 m against 1.72 m of friction, and the 1.4 shortcut under-predicts by 41 percent. That is precisely why CECS 183 clause 3.7.14 insists on measured coefficients item by item. In a siphonic system the money is in the local losses.

A bonus calculation: why you split into several suspended mains

Put all four outlets on a single DN125 suspended main with the stack still at DN150, and all 74.9 L/s travels down that one pipe at 5.64 m/s. The head demand becomes 12.48 m, and 8.06 m will not come close. Split into two parallel mains and each carries 37.45 L/s; velocity falls to 2.82 m/s, loss falls with v squared, and the demand drops to 4.91 m. The pipe tonnage barely changes, yet parallel routing saves 7.57 m of head, a 60.7 percent reduction. That is why siphonic layouts multiply branches instead of inflating a single diameter.

Procurement and handover checklist

1. Name the IDF relationship in full - city, district, edition, P and t. "Per the standard" is not an answer; the four return periods above differ by a factor of 1.6.
2. Outlet capacity comes from the tested curve (CECS 183 Annex A.2), not from linear interpolation. The 17.5 to 30.0 L/s band is for scheme-stage triage only.
3. List every loss coefficient. Clause 3.7.14 requires xi to be determined by product testing. In case B the local loss is 1.50 m against 1.14 m of friction - local loss is the larger half of a siphonic budget and cannot be a single allowance.
4. Material conditions: no less corrosion resistant than S30408, solution annealed, negative-pressure capability at least −80 kPa, and pipe and fittings of the same material throughout.
5. Negative-pressure acceptance: computed minimum no lower than −80 kPa, and no lower than −90 kPa in the check case (3.7.16).
6. Computing accuracy: clause 3.7.11 allows each node's head-loss error to be under 10 percent of the geometric drop and no more than 10 kPa.
7. Discharge line two sizes up so that downstream velocity stays at or below 1.8 m/s.
8. Support spacing and ovality belong in the specification, so the pipe is not flattened by something other than vacuum.

Reproduce the calculation

Summary. Siphonic capacity is set by head and diameter together, and it must clear three gates: the energy balance, the cavitation boundary, and the code's −80 kPa floor. In this example, on 8 m of head, DN100 mains with a DN125 stack pass only 62.1 L/s and are 3.56 m short of the head they need; DN125 mains with a DN150 stack reach 96.5 L/s with 28.8 percent to spare. Raising the head to 20 m without touching the diameters buys only 80.3 L/s - because drop is not capacity until the pipe is big enough to spend it.

Frequently asked questions

How much will a siphonic system with 8 m of head discharge?

It depends entirely on diameter. For the 24 m x 60 m roof in this example with a design flow of 74.9 L/s: DN125 suspended mains with a DN150 stack reach 96.5 L/s, 28.8 percent above the design flow. DN100 mains with a DN125 stack manage only 62.1 L/s, leaving a 12.8 L/s shortfall that ponds on the roof at 32.0 mm/h.

How much does one size up on the stack buy?

On 8 m of head, going from DN125 to DN150 takes capacity from 62.1 to 96.5 L/s, a gain of 34.4 L/s or 55.4 percent. Three consequences travel with it: stack velocity drops to 3.97 m/s, still above the 2.2 m/s floor; stack-top negative pressure reaches −50.0 kPa at full flow, still well clear of the −80 kPa limit; and the discharge line downstream of the transition has to become DN250 to stay at 1.8 m/s.

Will −80 kPa of vacuum collapse a thin-wall stainless pipe?

Using p_cr = 3EI / [(1 − nu²)R³] for long-tube elastic buckling, DN150 at 2.0 mm wall gives 871 kPa, 10.89 times the 80 kPa load; at 1.5 mm it is 364 kPa, 4.55 times; at 1.0 mm only 107 kPa, 1.34 times. Large diameters should be specified at 2.0 mm or thicker, with support spacing and initial ovality controlled as well.