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

Pump Head Calculation

Calculates total dynamic head for a pump duty point by converting suction and discharge pressure difference, pipe losses, and static elevation difference into metres of fluid head. The template also calculates hydraulic power from flow, fluid density, gravitational acceleration, and total dynamic head.

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

Standards

Hydraulic Institute Standards

Tags

deterministichydraulic-powermechanicalpump-hydraulicstotal-dynamic-head

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

  • Flow rate

    flow_rate_m3_h

    Pump flow rate

    1 – 5000 m3/h

  • Suction pressure

    suction_pressure_kpa

    Suction pressure at pump inlet

    -80 – 1000 kPa

  • Discharge pressure

    discharge_pressure_kpa

    Discharge pressure at pump outlet

    -50 – 3000 kPa

  • Elevation difference

    elevation_difference_m

    Discharge elevation minus suction elevation

    -20 – 200 m

  • Pipe friction losses

    pipe_friction_losses_kpa

    Pipe friction and minor losses

    0 – 1000 kPa

  • Fluid density

    fluid_density_kg_m3

    Fluid density

    600 – 1300 kg/m3

Scored outputs

5 outputs

Static head

static_head_m

Static elevation head

Scores if within ±3% of the reference value.

Pressure head differential

pressure_head_differential_m

Pressure head differential

Scores if within ±3% of the reference value.

Friction head

friction_head_m

Friction loss head

Scores if within ±3% of the reference value.

Total dynamic head

total_dynamic_head_m

Total dynamic head

Scores if within ±3% of the reference value.

Hydraulic power

hydraulic_power_kw

Hydraulic power

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 water transfer pump
medium:
All parameters given for water and process liquid pumps
hard:
All parameters given for higher-head pump duties

Task bundle

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

/workspace

  • instruction.md
  • pump-head-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 pump hydraulics.2 3## Problem4 5Calculate the total dynamic head required for a pump installation and the corresponding hydraulic power.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Flow rate | {{ flow_rate_m3_h }} | m3/h |12| Suction pressure | {{ suction_pressure_kpa }} | kPa |13| Discharge pressure | {{ discharge_pressure_kpa }} | kPa |14| Elevation difference | {{ elevation_difference_m }} | m |15| Pipe friction losses | {{ pipe_friction_losses_kpa }} | kPa |16| Fluid density | {{ fluid_density_kg_m3 }} | kg/m3 |17 18{% if archetype_description is defined %}19### Pump Duty Context20 21{{ archetype_description }}22{% endif %}23 24{% if tool_available %}25## Available Tool26 27A pump head 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. Static elevation head (m)412. Pressure head differential (m)423. Friction loss head (m)434. Total dynamic head (m)445. Hydraulic power (kW)45 46## Constraints47 48- No internet access is available. Work from engineering knowledge and the provided tool.49- Use g = 9.81 m/s2.50- Convert flow from m3/h to m3/s by dividing by 3600.51- Convert pressure difference to head using head = delta pressure x 1000 / (density x g).52- Convert pipe losses to head using the same pressure-to-head relationship.53- Use total dynamic head = static head + pressure head differential + friction head.54- Use hydraulic power = density x g x flow x total dynamic head / 1000.55 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 "static_head_m": <numeric_value>,63 "pressure_head_differential_m": <numeric_value>,64 "friction_head_m": <numeric_value>,65 "total_dynamic_head_m": <numeric_value>,66 "hydraulic_power_kw": <numeric_value>67}68```69 70Write your complete solution to `/workspace/output.md`.71

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.

Water transfer pump

water_transfer_pump

Water transfer pump with moderate pressure rise

water-treatment-transferreservoir-booster
Parameter ranges
flow_rate_m3_h
30 – 500
suction_pressure_kpa
0 – 150
discharge_pressure_kpa
200 – 900
elevation_difference_m
5 – 60
pipe_friction_losses_kpa
20 – 200
fluid_density_kg_m3
990 – 1000

Process liquid pump

process_liquid_pump

Industrial process liquid pump

industrial-process-skidchemical-transfer-loop
Parameter ranges
flow_rate_m3_h
10 – 300
suction_pressure_kpa
-20 – 300
discharge_pressure_kpa
300 – 1500
elevation_difference_m
-5 – 80
pipe_friction_losses_kpa
30 – 400
fluid_density_kg_m3
800 – 1200

High head booster

high_head_booster

High-head booster pump

mine-water-boosterdistrict-pressure-zone
Parameter ranges
flow_rate_m3_h
100 – 1500
suction_pressure_kpa
50 – 600
discharge_pressure_kpa
800 – 3000
elevation_difference_m
30 – 180
pipe_friction_losses_kpa
100 – 800
fluid_density_kg_m3
950 – 1050

Example task

industrial-process-skid-process-liquid-pump-preview — hard difficulty, all inputs given.

Industrial process liquid pump. industrial-process-skid. Required outputs: static_head_m, pressure_head_differential_m, friction_head_m, total_dynamic_head_m, hydraulic_power_kw

The model sees

Scenario context and visible inputs.

flow_rate_m3_h
10 to 300 m3/h
suction_pressure_kpa
-20 to 300 kPa
discharge_pressure_kpa
300 to 1500 kPa
elevation_difference_m
-5 to 80 m
pipe_friction_losses_kpa
30 to 400 kPa
fluid_density_kg_m3
800 to 1200 kg/m3

Executable tool: pump-head-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.

{
  "static_head_m": <number>,
  "pressure_head_differential_m": <number>,
  "friction_head_m": <number>,
  "total_dynamic_head_m": <number>,
  "hydraulic_power_kw": <number>
}
  • static_head_m · scored within ±3%
  • pressure_head_differential_m · scored within ±3%
  • friction_head_m · scored within ±3%
  • total_dynamic_head_m · scored within ±3%
  • hydraulic_power_kw · scored within ±3%