LIVEdataset aec-bench@releasetasks 552models 18last submission … · built …
civilwith-tool

Open Channel Capacity

Computes flow area, wetted perimeter, hydraulic radius, velocity, discharge capacity, and Froude number for trapezoidal or rectangular open channels using Manning's equation V = (1/n)*R^(2/3)*S^(1/2). Used in drainage and flood conveyance design per HEC-22 and Australian Rainfall and Runoff (ARR) standards.

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

Standards

ARRHEC-22

Tags

civildeterministicdrainagehydraulicsmanningsopen-channel

How this task is generated

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

  1. 01

    Template

    The reusable contract shown on this page.

  2. 02

    Scenario

    An archetype and site context are sampled.

  3. 03

    Difficulty tier

    Inputs may be hidden at harder tiers.

  4. 04

    Task prompt

    The model responds with the declared outputs.

Parameters

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

Inputs

5 inputs

Always given

Included directly in every task prompt.

4

  • Bottom width

    bottom_width_m

    Channel bottom width b

    0.3 – 10 m

  • Flow depth

    flow_depth_m

    Flow depth y

    0.1 – 5 m

  • Side slope z

    side_slope_z

    Side slope ratio z (horizontal:vertical, 0 for rectangular)

    0 – 4

  • Channel slope m per m

    channel_slope_m_per_m

    Longitudinal channel slope S

    0.0005 – 0.1 m/m

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Mannings n

    mannings_n

    Manning's roughness coefficient n

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.01 – 0.06

Scored outputs

6 outputs

Flow area m2

flow_area_m2

Flow cross-sectional area A (m²)

Scores if within ±3% of the reference value.

Wetted perimeter

wetted_perimeter_m

Wetted perimeter P (m)

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.

Froude number

froude_number

Froude number Fr (dimensionless)

Scores if within ±5% 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

Rectangular channel (z = 0), all parameters given

Side slope z restricted to: 0

medium

All inputs given

Trapezoidal channel, all parameters given

hard

Some inputs hidden

Trapezoidal channel, roughness coefficient hidden

Hidden inputs

  • Mannings nmannings_n

Prompt replacement text

The channel is {{ archetype.description }} 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
  • open-channel-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 open channel flow.2 3## Problem4 5Calculate the flow capacity and velocity in an open channel using Manning's equation.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Bottom width (b) | {{ bottom_width_m }} | m |12| Flow depth (y) | {{ flow_depth_m }} | m |13| Side slope (z H:V) | {{ side_slope_z }} | - |14{% if mannings_n is defined %}15| Manning's roughness (n) | {{ mannings_n }} | - |16{% endif %}17| Channel slope (S) | {{ channel_slope_m_per_m }} | m/m |18{% if archetype_description is defined %}19 20### Channel Conditions21 22{{ archetype_description }}23{% endif %}24 25{% if tool_available %}26## Available Tool27 28An open channel flow calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:29 30```bash31python3 /workspace/{{ meta.name }}_calc.py --help32```33 34You may use this tool to verify your calculations or compute values directly.35{% endif %}36 37## Required38 39Calculate the following:40 411. Flow cross-sectional area A (m²)422. Wetted perimeter P (m)433. Hydraulic radius R (m)444. Flow velocity V (m/s)455. Flow capacity Q (m³/s)466. Froude number Fr (dimensionless)47 48## Applicable Standards49 50- HEC-22: Urban Drainage Design Manual51- ARR: Australian Rainfall and Runoff52 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 trapezoidal channel geometry (side slope z, horizontal:vertical):60 - Flow area: A = (b + z × y) × y61 - Wetted perimeter: P = b + 2 × y × √(1 + z²)62 - Hydraulic radius: R = A / P63 - Top width: T = b + 2 × z × y64- For rectangular channel (z = 0): A = b × y, P = b + 2y, R = A / P, T = b65- Froude number: Fr = V / √(g × D_h) where D_h = A / T and g = 9.81 m/s²66 67## Output Format68 69Show 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:70 71```json72{73 "flow_area_m2": <numeric_value>,74 "wetted_perimeter_m": <numeric_value>,75 "hydraulic_radius_m": <numeric_value>,76 "flow_velocity_m_s": <numeric_value>,77 "flow_capacity_m3_s": <numeric_value>,78 "froude_number": <numeric_value>79}80```81 82Write your complete solution to `/workspace/output.md`.83

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 lined

concrete_lined

Concrete-lined trapezoidal channel

brisbane-trunk-drainagesydney-stormwater-channel
Parameter ranges
mannings_n
0.012 – 0.018

Grassed channel

grassed_channel

Grassed or turfed drainage swale

melbourne-suburban-swaleperth-bioretention-swale
Parameter ranges
mannings_n
0.025 – 0.045

Riprap lined

riprap_lined

Riprap or rock-lined channel

darwin-creek-stabilisationcairns-erosion-control
Parameter ranges
mannings_n
0.03 – 0.05

Natural earth

natural_earth

Unlined natural earth channel

adelaide-rural-drainhobart-farm-channel
Parameter ranges
mannings_n
0.02 – 0.035

Gabion lined

gabion_lined

Gabion-lined channel

gold-coast-creek-workstownsville-flood-channel
Parameter ranges
mannings_n
0.025 – 0.04

Example task

brisbane-trunk-drainage-concrete-lined-preview — hard difficulty, some inputs hidden.

Concrete-lined trapezoidal channel. brisbane-trunk-drainage. Required outputs: flow_area_m2, wetted_perimeter_m, hydraulic_radius_m, flow_velocity_m_s, flow_capacity_m3_s, froude_number

The model sees

Scenario context and visible inputs.

bottom_width_m
0.3 to 10 m
flow_depth_m
0.1 to 5 m
side_slope_z
0 to 4 -
channel_slope_m_per_m
0.0005 to 0.1 m/m

Executable tool: open-channel-capacity_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Mannings n

    mannings_n

Stand-in text in the prompt

The channel is {{ archetype.description }} at {{ archetype.site_context }}

The model must produce

The scored JSON answer schema.

{
  "flow_area_m2": <number>,
  "wetted_perimeter_m": <number>,
  "hydraulic_radius_m": <number>,
  "flow_velocity_m_s": <number>,
  "flow_capacity_m3_s": <number>,
  "froude_number": <number>
}
  • flow_area_m2 · scored within ±3%
  • wetted_perimeter_m · scored within ±3%
  • hydraulic_radius_m · scored within ±3%
  • flow_velocity_m_s · scored within ±3%
  • flow_capacity_m3_s · scored within ±3%
  • froude_number · scored within ±5%