LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …

civilwith-tool

Mannings Pipe Capacity

Computes the flow capacity, velocity, flow area, and hydraulic radius of circular drainage pipes using Manning's equation Q = (1/n) * A * R^(2/3) * S^(1/2), supporting both full and partially full pipe flow via the central angle geometry method. Used in stormwater and sewer pipe sizing per HEC-22 and QUDM to verify that pipe capacity meets the design discharge.

with-tool: The model is given an executable Python calculator script.

Standards

HEC-22 PUB Code of Practice QUDM

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

4 inputs

Always given

Included directly in every task prompt.

Pipe diameter
pipe_diameter_m
Internal pipe diameter D
0.15 – 3 m
Slope m per m
slope_m_per_m
Longitudinal pipe slope S
0.001 – 0.1 m/m

Derived from scenario

Sampled from the scenario and inferable from its description.

Mannings n
mannings_n
Manning's roughness coefficient n
Derived from the archetype scenario. Hidden at hard difficulty.
0.009 – 0.025

Optional

Used only when the sampled task needs this part of the contract.

Flow depth ratio
flow_depth_ratio
Flow depth to diameter ratio d/D (1.0 = full)
Optional input.
0.1 – 1

Scored outputs

4 outputs

Flow area m2

flow_area_m2

Flow cross-sectional area A (m²)

Scores if within ±3% of the reference value.

Hydraulic radius

hydraulic_radius_m

Hydraulic radius R (m)

Scores if within ±3% of the reference value.

Flow velocity m s

flow_velocity_m_s

Flow velocity V (m/s)

Scores if within ±3% of the reference value.

Flow capacity

flow_capacity_m3_s

Flow capacity Q (m³/s)

Scores if within ±3% of the reference value.

Difficulty

Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.

easy

All inputs given

Full pipe flow, all parameters given

Flow depth ratio restricted to: 1

medium

All inputs given

Partially full flow, all parameters given

hard

Some inputs hidden

Partially full flow, roughness coefficient hidden

Hidden inputs

Mannings nmannings_n

Prompt replacement text

The pipe is {{ archetype.description }} installed at {{ archetype.site_context }}

Task bundle

The exact instruction and parameter contract used to generate this task, pinned to the published library source.

/workspace

instruction.md
mannings-pipe-capacity_calc.py

Teal lines show Jinja input conditions, not task visibility policy. A line renders only when that input or tool is visible.

1You are a senior civil engineer specializing in hydraulic design and stormwater drainage.2 3## Problem4 5Calculate the flow capacity and velocity in a circular pipe using Manning's equation.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Pipe diameter (D) | {{ pipe_diameter_m }} | m |12{% if mannings_n is defined %}13| Manning's roughness (n) | {{ mannings_n }} | - |14{% endif %}15| Pipe slope (S) | {{ slope_m_per_m }} | m/m |16{% if flow_depth_ratio is defined %}17| Flow depth ratio (d/D) | {{ flow_depth_ratio }} | - |18{% endif %}19{% if archetype_description is defined %}20 21### Pipe Conditions22 23{{ archetype_description }}24{% endif %}25 26{% if tool_available %}27## Available Tool28 29A pipe flow calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:30 31```bash32python3 /workspace/{{ meta.name }}_calc.py --help33```34 35You may use this tool to verify your calculations or compute values directly.36{% endif %}37 38## Required39 40Calculate the following:41 421. Flow cross-sectional area A (m²)432. Hydraulic radius R (m)443. Flow velocity V (m/s)454. Flow capacity Q (m³/s)46 47## Applicable Standards48 49- HEC-22: Urban Drainage Design Manual50- QUDM: Queensland Urban Drainage Manual51- PUB Code of Practice on Surface Water Drainage52 53## Constraints54 55- No internet access is available. Work from engineering knowledge and the provided tool.56- Use Manning's equation (SI units):57  - **Velocity:** V = (1/n) × R^(2/3) × S^(1/2)58  - **Flow capacity:** Q = V × A59- For circular pipe geometry using the central angle method:60  - Central angle: θ = 2 × arccos(1 − 2 × d/D)61  - Flow area: A = (D² / 8) × (θ − sin(θ))62  - Wetted perimeter: P = (D / 2) × θ63  - Hydraulic radius: R = A / P64- For full pipe (d/D = 1.0): A = π×D²/4, P = π×D, R = D/465 66## Output Format67 68Show your step-by-step working in Markdown, including formulas and intermediate calculations. At the end of your solution, include a JSON block with your final answers in exactly this format:69 70```json71{72  "flow_area_m2": <numeric_value>,73  "hydraulic_radius_m": <numeric_value>,74  "flow_velocity_m_s": <numeric_value>,75  "flow_capacity_m3_s": <numeric_value>76}77```78 79Write your complete solution to `/workspace/output.md`.80

Scenario archetypes

Each generated task is drawn from one of these realistic scenario bands.

Site contexts ground each scenario in a real locale the model can use to infer hidden values.

Concrete pipe

concrete_pipe

Concrete stormwater pipe

brisbane-suburban-drainagesydney-trunk-stormwater

Parameter ranges

mannings_n: 0.011 – 0.015

Pvc pipe

pvc_pipe

PVC or HDPE smooth-wall pipe

perth-residential-drainagemelbourne-subdivision

Parameter ranges

mannings_n: 0.009 – 0.011

Corrugated metal pipe

corrugated_metal_pipe

Corrugated metal pipe (CMP)

darwin-rural-crossingcairns-temporary-diversion

Parameter ranges

mannings_n: 0.019 – 0.025

Vitrified clay pipe

vitrified_clay_pipe

Vitrified clay sewer pipe

adelaide-heritage-sewerhobart-infill-drainage

Parameter ranges

mannings_n: 0.011 – 0.015

Example task

brisbane-suburban-drainage-concrete-pipe-preview — hard difficulty, some inputs hidden.

Concrete stormwater pipe. brisbane-suburban-drainage. Required outputs: flow_area_m2, hydraulic_radius_m, flow_velocity_m_s, flow_capacity_m3_s

The model sees

Scenario context and visible inputs.

pipe_diameter_m: 0.15 to 3 m
slope_m_per_m: 0.001 to 0.1 m/m
flow_depth_ratio: 1

Executable tool: mannings-pipe-capacity_calc.py

The model must infer

Inputs withheld at this difficulty.

Mannings n
mannings_n

Stand-in text in the prompt

The pipe is {{ archetype.description }} installed at {{ archetype.site_context }}

The model must produce

The scored JSON answer schema.

{
  "flow_area_m2": <number>,
  "hydraulic_radius_m": <number>,
  "flow_velocity_m_s": <number>,
  "flow_capacity_m3_s": <number>
}

flow_area_m2 · scored within ±3%
hydraulic_radius_m · scored within ±3%
flow_velocity_m_s · scored within ±3%
flow_capacity_m3_s · scored within ±3%

Mannings Pipe Capacity

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Flow area m2

Hydraulic radius

Flow velocity m s

Flow capacity

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Concrete pipe

Pvc pipe

Corrugated metal pipe

Vitrified clay pipe

Example task

The model sees

The model must infer

The model must produce