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

Wave Speed Calculation

Calculates pressure wave propagation speed in an elastic pipe from fluid bulk modulus, fluid density, pipe elastic modulus, diameter, wall thickness, and restraint condition. The template separates the fluid-only wave speed from the pipe flexibility reduction used in first-pass water hammer screening.

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

Standards

AWWA M11

Tags

deterministicmechanicaltransient-analysiswater-hammerwave-speed

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

6 inputs

Always given

Included directly in every task prompt.

6

  • Fluid bulk modulus

    fluid_bulk_modulus_gpa

    Fluid bulk modulus K

    0.8 – 2.4 GPa

  • Fluid density

    fluid_density_kg_m3

    Fluid density rho

    700 – 1300 kg/m3

  • Pipe elastic modulus

    pipe_elastic_modulus_gpa

    Pipe material elastic modulus E

    0.5 – 220 GPa

  • Pipe diameter

    pipe_diameter_mm

    Pipe internal diameter D

    50 – 2500 mm

  • Pipe wall thickness

    pipe_wall_thickness_mm

    Pipe wall thickness e

    2 – 80 mm

  • Restraint condition

    restraint_condition

    Pipe restraint condition factor

    fully_restrainedanchored_with_expansionunrestrained

Scored outputs

4 outputs

Fluid only wave speed m s

fluid_only_wave_speed_m_s

Wave speed considering fluid compressibility only

Scores if within ±3% of the reference value.

Flexibility factor

flexibility_factor

Pipe flexibility reduction factor

Scores if within ±3% of the reference value.

Wave speed m s

wave_speed_m_s

Pressure wave speed in the pipe

Scores if within ±3% of the reference value.

Pipe flexibility ratio

pipe_flexibility_ratio

Dimensionless pipe flexibility contribution

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.

All inputs remain visible at every tier

For this template, difficulty scales through parameter and scenario ranges rather than hidden information.

easy:
All parameters given for a stiff steel water main
medium:
All parameters given across steel and ductile iron water mains
hard:
All parameters given across stiff and flexible pipe systems

Task bundle

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

/workspace

  • instruction.md
  • wave-speed-calculation_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 mechanical engineer specializing in hydraulic transients.2 3## Problem4 5Calculate pressure wave propagation speed in a pipe, accounting for both fluid compressibility and pipe-wall flexibility.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Fluid bulk modulus K | {{ fluid_bulk_modulus_gpa }} | GPa |12| Fluid density rho | {{ fluid_density_kg_m3 }} | kg/m3 |13| Pipe elastic modulus E | {{ pipe_elastic_modulus_gpa }} | GPa |14| Pipe internal diameter D | {{ pipe_diameter_mm }} | mm |15| Pipe wall thickness e | {{ pipe_wall_thickness_mm }} | mm |16| Restraint condition | {{ restraint_condition }} | - |17 18{% if archetype_description is defined %}19### Pipe Context20 21{{ archetype_description }}22{% endif %}23 24{% if tool_available %}25## Available Tool26 27A wave speed calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:28 29```bash30python3 /workspace/{{ meta.name }}_calc.py --help31```32 33You may use this tool to verify your calculations or compute values directly.34{% endif %}35 36## Required37 38Calculate the following:39 401. Fluid-only wave speed (m/s)412. Pipe flexibility factor423. Pressure wave speed in the pipe (m/s)434. Pipe flexibility ratio44 45## Constraints46 47- No internet access is available. Work from engineering knowledge and the provided tool.48- Convert GPa to Pa by multiplying by 10^9.49- Convert mm to m by dividing by 1000.50- Use fluid-only speed a0 = sqrt(K / rho).51- Use pipe flexibility ratio = K x D / (E x e x restraint factor).52- Use restraint factors: fully_restrained = 1.0, anchored_with_expansion = 0.85, unrestrained = 0.7.53- Use flexibility factor = sqrt(1 + pipe flexibility ratio).54- Use wave speed = fluid-only speed / flexibility factor.55 56## Output Format57 58Show your step-by-step working in Markdown. At the end of your solution, include a JSON block with your final answers in exactly this format:59 60```json61{62 "fluid_only_wave_speed_m_s": <numeric_value>,63 "flexibility_factor": <numeric_value>,64 "wave_speed_m_s": <numeric_value>,65 "pipe_flexibility_ratio": <numeric_value>66}67```68 69Write your complete solution to `/workspace/output.md`.70

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.

Steel water main

steel_water_main

Steel water main with high wall stiffness

trunk-water-mainraw-water-pipeline
Parameter ranges
fluid_bulk_modulus_gpa
2 – 2.25
fluid_density_kg_m3
990 – 1000
pipe_elastic_modulus_gpa
190 – 210
pipe_diameter_mm
300 – 1800
pipe_wall_thickness_mm
6 – 30

Ductile iron main

ductile_iron_main

Ductile iron water main with cement lining

urban-distribution-mainregional-transfer-main
Parameter ranges
fluid_bulk_modulus_gpa
2 – 2.25
fluid_density_kg_m3
990 – 1000
pipe_elastic_modulus_gpa
150 – 180
pipe_diameter_mm
150 – 1000
pipe_wall_thickness_mm
5 – 25

Hdpe rising main

hdpe_rising_main

Flexible HDPE rising main

sewer-rising-mainirrigation-transfer-line
Parameter ranges
fluid_bulk_modulus_gpa
1.8 – 2.2
fluid_density_kg_m3
990 – 1000
pipe_elastic_modulus_gpa
0.8 – 1.5
pipe_diameter_mm
90 – 800
pipe_wall_thickness_mm
6 – 60

Example task

urban-distribution-main-ductile-iron-main-preview — hard difficulty, all inputs given.

Ductile iron water main with cement lining. urban-distribution-main. Required outputs: fluid_only_wave_speed_m_s, flexibility_factor, wave_speed_m_s, pipe_flexibility_ratio

The model sees

Scenario context and visible inputs.

fluid_bulk_modulus_gpa
2 to 2.25 GPa
fluid_density_kg_m3
990 to 1000 kg/m3
pipe_elastic_modulus_gpa
150 to 180 GPa
pipe_diameter_mm
150 to 1000 mm
pipe_wall_thickness_mm
5 to 25 mm
restraint_condition
fully_restrained

Executable tool: wave-speed-calculation_calc.py

The model must infer

Inputs withheld at this difficulty.

Nothing. All inputs are supplied.

The model must produce

The scored JSON answer schema.

{
  "fluid_only_wave_speed_m_s": <number>,
  "flexibility_factor": <number>,
  "wave_speed_m_s": <number>,
  "pipe_flexibility_ratio": <number>
}
  • fluid_only_wave_speed_m_s · scored within ±3%
  • flexibility_factor · scored within ±3%
  • wave_speed_m_s · scored within ±3%
  • pipe_flexibility_ratio · scored within ±3%