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

Weir Outlet Design

Sizes a sharp-crested rectangular weir for detention basin emergency overflow using the Francis formula Q = Cw * (L - 0.1*n*H) * H^1.5, where Cw = Cd * sqrt(2g). Solves for the required crest length given design flow, head, discharge coefficient, and end contractions, supporting stormwater detention and flood control design.

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

Standards

Francis formula (1883)Hydraulics textbooks

Tags

civildetentionhydraulicsspillwaystormwaterweir

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

4 inputs

Always given

Included directly in every task prompt.

1

  • Design flow

    design_flow_m3_s

    Design overflow discharge Q

    0.01 – 10 m³/s

Derived from scenario

Sampled from the scenario and inferable from its description.

1

  • Head over weir

    head_over_weir_m

    Head of water over the weir crest H

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.05 – 1.5 m

Optional

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

2

  • Discharge coefficient

    discharge_coefficient

    Weir discharge coefficient Cd

    Derived from the archetype scenario. Optional input. Hidden at hard difficulty.

    0.55 – 0.7

  • Number of contractions

    number_of_contractions

    Number of end contractions n (0 = suppressed, 1 or 2 = contracted)

    Derived from the archetype scenario. Optional input.

    0 – 2

Scored outputs

2 outputs

Required weir length

required_weir_length_m

Required weir crest length L (m)

Scores if within ±3% of the reference value.

Unit discharge m3 s per

unit_discharge_m3_s_per_m

Unit discharge per metre of weir crest q (m³/s/m)

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

All parameters given, suppressed weir with standard coefficient

Number of contractions restricted to: 0

Discharge coefficient restricted to: 0.62

medium

All inputs given

All parameters given, variable coefficient and end contractions

hard

Some inputs hidden

Discharge coefficient and head hidden, agent must infer from site context

Hidden inputs

  • Discharge coefficientdischarge_coefficient
  • Head over weirhead_over_weir_m

Prompt replacement text

The detention basin has a {{ archetype.description }} ({{ 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
  • weir-outlet-design_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 stormwater management and detention basin design.2 3## Problem4 5Size an emergency spillway weir to safely pass the design overflow from a detention basin using the Francis weir discharge formula.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Design overflow discharge (Q) | {{ design_flow_m3_s }} | m³/s |12{% if head_over_weir_m is defined %}13| Head over weir crest (H) | {{ head_over_weir_m }} | m |14{% endif %}15{% if discharge_coefficient is defined %}16| Discharge coefficient (Cd) | {{ discharge_coefficient }} | - |17{% endif %}18{% if number_of_contractions is defined %}19| Number of end contractions (n) | {{ number_of_contractions }} | - |20{% endif %}21{% if archetype_description is defined %}22 23### Site Conditions24 25{{ archetype_description }}26{% endif %}27 28{% if tool_available %}29## Available Tool30 31A weir sizing calculation tool is available at `/workspace/weir-outlet-design_calc.py`. Run it with:32 33```bash34python3 /workspace/weir-outlet-design_calc.py --help35```36 37You may use this tool to verify your calculations or compute values directly.38{% endif %}39 40## Required41 42Calculate the following:43 441. Required weir crest length L (m)452. Unit discharge per metre of weir crest q (m³/s/m)46 47## Applicable Standards48 49- Standard hydraulics textbook weir flow equations50- Francis formula (1883) for sharp-crested rectangular weirs51 52## Constraints53 54- No internet access is available. Work from engineering knowledge and the provided tool.55- Use the Francis weir discharge formula:56 - **Q = Cw × (L − 0.1 × n × H) × H^(3/2)**57 - Where the weir coefficient **Cw = Cd × √(2g)**58 - Rearranged for length: **L = Q / (Cw × H^(3/2)) + 0.1 × n × H**59 - Unit discharge: **q = Q / L**60- Use g = 9.81 m/s²61- If no discharge coefficient is given, use Cd = 0.62 (sharp-crested rectangular weir)62- If no number of contractions is given, assume n = 0 (suppressed weir)63- The weir is assumed to be a sharp-crested rectangular weir with free overflow64 65## Output Format66 67Show 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:68 69```json70{71 "required_weir_length_m": <numeric_value>,72 "unit_discharge_m3_s_per_m": <numeric_value>73}74```75 76Write your complete solution to `/workspace/output.md`.77

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.

Small urban basin

small_urban_basin

Small urban detention basin with low-level spillway weir

sydney-infill-residentialmelbourne-suburban-subdivision
Parameter ranges
head_over_weir_m
0.05 – 0.3
discharge_coefficient
0.6 – 0.64
number_of_contractions
0

Medium commercial basin

medium_commercial_basin

Medium commercial development detention basin spillway

brisbane-commercial-parkadelaide-retail-precinct
Parameter ranges
head_over_weir_m
0.2 – 0.6
discharge_coefficient
0.58 – 0.63
number_of_contractions
0 – 2

Large regional basin

large_regional_basin

Large regional stormwater detention facility with emergency spillway

perth-regional-wetlandgold-coast-flood-control
Parameter ranges
head_over_weir_m
0.4 – 1.2
discharge_coefficient
0.6 – 0.65
number_of_contractions
0

Channel diversion weir

channel_diversion_weir

Channel diversion weir with end contractions

canberra-drainage-diversiontownsville-channel-control
Parameter ranges
head_over_weir_m
0.1 – 0.5
discharge_coefficient
0.58 – 0.62
number_of_contractions
1 – 2

Example task

sydney-infill-residential-small-urban-basin-preview — hard difficulty, some inputs hidden.

Small urban detention basin with low-level spillway weir. sydney-infill-residential. Required outputs: required_weir_length_m, unit_discharge_m3_s_per_m

The model sees

Scenario context and visible inputs.

design_flow_m3_s
0.01 to 10 m³/s
number_of_contractions
0 to 0

Executable tool: weir-outlet-design_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Head over weir

    head_over_weir_m

  • Discharge coefficient

    discharge_coefficient

Stand-in text in the prompt

The detention basin has a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "required_weir_length_m": <number>,
  "unit_discharge_m3_s_per_m": <number>
}
  • required_weir_length_m · scored within ±3%
  • unit_discharge_m3_s_per_m · scored within ±3%