Background reading #

When water turns at a sump, we expect some head loss and a rise in water level against the outer wall. How much do these affect a detention drain? In this article we will use the model from Detention Drain Design With Dynamic Routing to examine the results from MiTS, including what happens when we change the chamber dimensions.

We have covered the theory in two earlier articles. What a One-Dimensional Drainage Model Can Tell Us About Flow Turning in a Sump explains the bend-loss coefficient K and the limits of a 1D routing model. The Superelevation Equation for Flow Through Curved Conduits derives the local water-level rise, explains the curvature ratio R/B , and sets out when we can use the estimate.

Conclusion first: the turning of pipes will introduce a bend loss, represented by K and this affects the centreline hydraulic grade line (HGL) and it doesn’t depend on the chamber size. Superelevation, on the other hand, is affected by the chamber size and the connection between the pipes.

The model and how we modified it #

We use the detention drain with orifice control calibrated in the earlier article. We keep its pipes, storms and routing settings, including the calibration of discharge, velocity and depth at the outfall.

The pipe alignment turns at four junctions. MiTS calculates their deflection angles from the drawn geometry:

Node	Pipe path	Deflection angle
A02	L01 → L02	47.3°
A03	L02 → L03	76.9°
S01	L03 → L05	78.3°
B03	L07 → L08	7.9°

S01 is the project’s discharge control sump, a 1400mm chamber ahead of the orifice and outfall. We keep this chamber as built and change the dimensions at A02, A03 and B03, which are ordinary bends along the pipe run.

To reproduce the comparison, prepare two copies of the project file. In the first copy, open the Node Profile of A02, A03 and B03 in turn and set each rectangular chamber to 100mm wide by 100mm long. In the second copy, set the same three nodes to 900mm by 900mm. Keep S01 at 1400mm in both copies. The three modified nodes remain connected to their 450mm pipes.

Copy of the model	A02, A03, B03 rectangular chamber (width × length)
100mm configuration	100 × 100mm
900mm configuration	900 × 900mm

We change only the chamber dimensions so that we can see which results depend on them. Run both copies with Sump Bend Effects switched on, using the same storms: 5-, 50- and 100-year ARI, with eight durations each.

Bend loss and the centreline HGL #

MiTS obtains the bend-loss coefficient K from the HEC-22 angle-only table described in the first background article. Switching on Sump Bend Effects applies it at all four nodes:

Node	Deflection	Resolved K	Head loss
A02	47.3°	0.765	0.099 m
A03	76.9°	0.935	0.055 m
S01	78.3°	0.942	0.022 m
B03	7.9°	0.256	0.002 m

We compare the peak centreline HGL with and without Sump Bend Effects below. These are the 5-year ARI results; the 50- and 100-year runs follow the same pattern.

Node	Duration (min)	Peak HGL, without (m)	Peak HGL, with (m)	Change
A02	10	4.488	4.492	+4 mm
A02	20	4.485	4.493	+7 mm
A02	50	4.703	4.703	0 mm
A03	10	3.798	3.830	+31 mm
A03	20	3.912	3.925	+13 mm
S01	10	3.776	3.774	−2 mm
S01	50	3.914	3.913	−1 mm
B03	20	3.936	3.919	−17 mm
B03	30	3.934	3.918	−16 mm

At A02 and A03, the peak level rises by a few millimetres to about 3cm, and generally more at the higher ARIs. However, S01 has the largest K (0.942) and its peak level changes by no more than ±2mm. The extra loss at S01 does not control the backwater there.

What about B03, where the peak level goes down? The added losses upstream change the timing and attenuation of flow through the network, so less water arrives at B03 at the same moment. Its own local loss is only 2mm. Thus, we need the routing results to assess the water level at each node; the size of K alone does not tell us how much it will change.

Does chamber size change the bend loss? #

We obtain identical K , head loss and node HGL time series for the 100mm and 900mm copies, at every node and storm duration:

Node	K , 100mm chamber	K , 900mm chamber	Head loss, 100mm	Head loss, 900mm
A02	0.7655	0.7655	0.099 – 0.599 m	0.099 – 0.599 m
A03	0.9347	0.9347	0.038 – 0.297 m	0.038 – 0.297 m
B03	0.2556	0.2556	0.002 – 0.008 m	0.002 – 0.008 m

This is because the HEC-22 lookup used here depends only on the angle between the inlet and outlet pipes. MiTS uses the chamber plan dimensions in the separate superelevation calculation.

Case studies #

Chamber footprint and the curvature ratio #

For superelevation, we use the chamber footprint to estimate a reference turning radius R and a clear width B . Their ratio, R/B , describes how sharp the bend is relative to the available width.

Does a uniform resize change R/B ? #

We first compare the two square chamber sizes:

Node	R/B (100 × 100mm chamber)	R/B (900 × 900mm chamber)
A02	1.14	1.14
A03	0.63	0.63
B03	7.22	7.22

The ratio stays the same because enlarging a square scales R and B by the same factor. But what if we change the shape? At A02, we also try a 100 × 900mm rectangle and then swap its width and length:

A02 chamber	R	B	R/B
900 × 900 mm (square)	≈ 1.043 m	0.914 m	1.14
100 × 900 mm (tall rectangle)	0.189 m	0.102 m	1.86
900 × 100 mm (wide rectangle)	0.116 m	0.165 m	0.70

Swapping the dimensions changes R/B from 0.70 to 1.86, about 2.6 times, even though the node and pipes are the same. To calculate this ratio, we measure T_{in} and T_{out} from the node to the chamber wall along each pipe centreline. We also measure the full chamber spans B_{in} and B_{out} through the node, perpendicular to those centrelines. We then use the smaller distance and the smaller span:

\displaystyle R=\frac{\min(T_{in},T_{out})}{\tan(\delta/2)},\qquad B=\min(B_{in},B_{out})

These measurements give the chamber scenario, LambdaChamber, illustrated below. As explained in the superelevation article, we use the chamber plan as an approximate way to obtain R and B .

For the square chamber centred on the node, the geometry gives \min(T_{in},T_{out})=B/2 . Using the recorded B=0.914 m and A02’s deflection angle of 47.319°, we obtain R=(0.914/2)/\tan(47.319^\circ/2)\approx1.043 m, and R/B\approx1.14 .

B03 has a much smaller deflection angle, 7.9°, so its reference turning radius is large relative to its width. Its R/B of 7.22 exceeds the handbook’s recommended 3.0 and does not trigger the low-ratio caution.

Why, then, do A02 and A03 report different rises for the two square chamber sizes if their chamber ratios are unchanged? MiTS also evaluates LambdaPipe, which uses the outlet pipe’s top width, limited to the chamber’s clear width:

B_{pipe}=\min(\text{outlet top width},B)

For the 900mm chambers, the pipe top width of up to 0.45m is already narrower than the chamber, so the limit rarely applies. For the 100mm chambers, the chamber width limits B_{pipe} throughout the analysed timesteps. This changes the pipe scenario’s curvature ratio and therefore the reported rise.

How to read the reported rise #

Read each rise together with its status and caution codes. The superelevation article explains the checks in detail; the statuses are summarised below:

Status	Meaning	Typical condition
Not computed	The method is outside its applicability range.	No free surface, invalid chamber geometry, or near-dry outlet depth.
Withheld	A value was calculated but fails the energy-ratio screen.	Raw rise exceeds 1.5 times its energy-conservation ceiling.
Reported with caution	A value is shown together with the reason it needs engineering judgement.	Low R/B , near-critical flow, or an energy cap.
Reported	No applicability or caution condition applies.	Normal free-surface conditions.

The report lists K , maximum head loss, maximum Froude number, rim margin and maximum local rise, together with the caution codes. Rise Scenario identifies the width used (LambdaChamber or LambdaPipe) and the coefficient, C=0.5 or C=1.0. MiTS evaluates both coefficients for near-critical flow; the other regimes use one.

Side-by-side results #

The reported rises for the two chamber sizes are:

Node	Duration (min)	Reported rise, 100mm chamber	Reported rise, 900mm chamber
A02	10	(none reported, see the near-dry timestep below)	112 mm
A02	20	41 mm	115 mm
A02	50	33 mm	66 mm
A02	80	33 mm	40 mm
A03	10–80	(none reported at any duration)	92 – 106 mm
B03	10–80	0.6 – 2.9 mm (unchanged)	0.6 – 2.9 mm (unchanged)

Where no rise is reported, check the accompanying reason in MiTS. A blank cell does not mean zero rise– it may only mean that the result is not trustworthy so we just set it blank.

The near-dry timestep at A02 #

For A02’s 10-minute storm in the 100mm configuration, the omitted result is associated with the following near-dry timestep. The values here are from that timestep, whereas the comparison above gives one result per storm:

Node	Result scope	Outlet depth	Outlet velocity	Froude number	Raw rise before the near-dry screen	Reported result
A02	Individual near-dry timestep	24 mm	3.9 m/s	≈ 8	782 mm	Withheld: depth is below the 50 mm minimum

The formula scales with velocity squared. Here, a 24mm depth at 3.9 m/s gives a calculated rise of 782mm, but the depth is below the 50mm minimum for applying the method. MiTS therefore excludes the estimate. It also excludes fully pressurised flow, where there is no free surface to superelevate.

A03 in the 900 × 900mm configuration #

We now calculate the rise at A03 for a 100-year storm and a 5-year storm, using the 900 × 900mm chamber in both cases.

100-year ARI, 10-minute storm #

Quantity	Value
Deflection angle \delta	76.93° (L02 → L03)
Chamber	900 × 900mm rectangular
Applied K	0.935 (HEC-22 angle-only table)
Max head loss	0.080 m
Max Froude number (separate timestep)	1.11
Max node HGL	3.935 m
Min rim margin	0.065 m
Max local rise (superelevation)	0.136 m
Rise scenario	LambdaPipe (C = 0.5)
Cautions	LowRatio, NearCritical, NonpositiveContainmentMargin

The maximum local rise occurs at t = 600 min. We use the hydraulic results at this timestep for the calculations below.

Hydraulic depth and Froude number #

At t = 600 min the outlet reports Q_o = 0.0819 m³/s, |V_o| = 1.292 m/s and top width T = 0.450 m, so

• flow area A = |Q_o/V_o| = 0.0819 / 1.292 = 0.0634 m²
• hydraulic depth D_h = A/T = 0.0634 / 0.450 = 0.141 m
• Fr = |V_o|/\sqrt{g D_h} = 1.292 / √(9.81 × 0.141) = 1.292 / 1.176 = 1.10

Thus, Fr = 1.10 is within the near-critical range, 0.8 ≤ Fr ≤ 1.2. The maximum Fr of 1.11 in the summary table occurs at another timestep. The reported maxima for HGL, Froude number and local rise need not occur together.

Choosing the coefficient C #

For near-critical flow, MiTS evaluates C = 0.5 and C = 1.0 across the storm time series and reports the larger accepted peak rise. At A03, the reported result uses C = 0.5. We need to compare the accepted results over the time series, including the applicability and energy checks; choosing C = 1.0 simply because it is larger would miss these checks.

Curvature ratio R/B #

For A03, T_{in} = 0.462 m and T_{out} = 0.450 m. We use the smaller distance, 0.450 m, to calculate R :

\displaystyle R=\frac{0.450}{\tan(76.93^\circ/2)}=\frac{0.450}{0.795}=0.566\ \text{m}

We use this radius with each of the two widths:

• LambdaChamber: B = chamber clear span = 0.900 m, giving \lambda = 0.566 / 0.900 = 0.629
• LambdaPipe: B = min(outlet top width, chamber width) = min(0.450, 0.900) = 0.450 m, giving \lambda = 0.566 / 0.450 = 1.259

Both ratios are below the recommended R/B \ge 3 and trigger LowRatio. After the applicability and energy checks, LambdaPipe gives the governing rise for this storm.

The red arc below has radius R and is tangent to both pipe centrelines. At the outlet, the chamber span is 0.900m and the pipe top width is 0.450m; LambdaPipe uses the latter. We draw both pipes at their 450mm width, but the chamber walls are schematic, positioned from the calculated dimensions rather than traced from the CAD footprint.

The local rise #

The rise is \Delta y = C\,V_{ref}^2/(g\lambda) , capped at \Delta y_{max}=V_{ref}^2/(2g) , with V_{ref} the larger of the inlet and outlet velocities:

• V_{ref} = max(1.832, 1.292) = 1.832 m/s
• \Delta y (uncapped) = 0.5 × 1.832² / (9.81 × 1.259) = 1.678 / 12.35 = 0.136 m
• \Delta y_{max} = 1.832² / (2 × 9.81) = 3.356 / 19.62 = 0.171 m, so no cap applies and \Delta y = 0.136 m, matching the report
• candidate outside water surface = node HGL + \Delta y = 3.875 + 0.136 = 4.011 m (3.875m is the centreline HGL at this timestep; the 3.935m in the summary table is the storm maximum at another timestep)
• containment clearance = containment elevation − candidate water surface = 4.000 − 4.011 = −0.011 m

No separate containment level is defined for this project, so MiTS uses the rim elevation of 4.000m, also reported as A03’s ground level in the Sump Schedule. The calculated outer water surface is 11mm above this level, triggering NonpositiveContainmentMargin.

What the three cautions mean here #

LowRatio: the curvature ratios, 0.629 and 1.259, are below the USACE/USBR recommendation of R/B \ge 3 for a smooth bend. A03’s geometry falls outside that recommendation, so we need engineering judgement when using the rise estimate.

NearCritical: Fr = 1.10 at the governing timestep falls in the range where the formula’s results are least stable. MiTS evaluates both coefficients in this range, as described above.

NonpositiveContainmentMargin: the estimated outer-wall water level exceeds the containment elevation. The centreline HGL alone still gives a minimum rim margin of +0.065m over this storm. However, once we add the local rise to the HGL at its governing timestep, the estimated water surface reaches 4.011m, above the 4.000m rim. Checking only the centreline HGL would miss this local exceedance.

Same node, a milder storm: 5-year ARI, 70-minute #

A03’s outlet is a 450mm box culvert, so its free-surface top width stays constant with depth. Together with the fixed chamber geometry, this keeps R , B and the pipe scenario’s \lambda = 1.259 unchanged across all 24 duration/ARI combinations. LambdaPipe governs in all 24 runs. The storms change the flow conditions, and therefore the Froude number, coefficient choice and local rise.

For the 5-year ARI, 70-minute storm, the governing timestep is t = 1440 min. The outlet velocity is |V_o| = 0.546 m/s, compared with 1.292 m/s in the 100-year example:

• Fr = 0.546 / √(9.81 × 0.101) = 0.548, subcritical (Fr < 0.8), and C = 0.5 applies directly with no two-coefficient evaluation
• V_{ref} = max(1.504, 0.546) = 1.504 m/s, still set by the inlet
• \Delta y (uncapped) = 0.5 × 1.504² / (9.81 × 1.259) = 1.132 / 12.35 = 0.092 m
• \Delta y_{max} = 1.504² / (2 × 9.81) = 2.264 / 19.62 = 0.115 m, no cap
• candidate outside water surface = 3.781 + 0.092 = 3.873 m
• containment clearance = 4.000 − 3.873 = +0.127 m, against −0.011m for the 100-year storm

Only LowRatio applies to this result. At the governing timestep, the flow is subcritical and the estimated outer water surface is 127mm below the rim. The storm does reach a peak Fr of 1.19 at t = 1080 min, but that is earlier than the maximum rise at t = 1440 min.

Conclusion #

For A03, we would review the chamber detailing because the 100-year storm gives an estimated outer water level 11mm above the rim, despite a positive centreline HGL margin. The 5-year example has 127mm clearance with the same chamber geometry. When reviewing your own model, open the Detailed Calculations report and check the HGL, local rise and containment level at the governing timestep, together with the caution codes. Use the chamber dimensions intended for construction: they affect the superelevation estimate even when the routing results remain unchanged.