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mechanicalwith-tool

Pressure Loss Calculation

Calculates water pipe pressure loss using the Hazen-Williams equation for straight-pipe friction and a total K value for fittings and valves. The template reports pipe velocity, friction loss, fitting loss, and total pressure loss in kPa.

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

Standards

AS/NZS 3500.1Hazen-Williams

Tags

deterministichydraulicsmechanicalpipepressure-loss

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_l_s

    Water flow rate

    0.01 – 1000 L/s

  • Pipe internal diameter

    pipe_internal_diameter_mm

    Internal pipe diameter

    10 – 1000 mm

  • Pipe length

    pipe_length_m

    Pipe length

    0.1 – 5000 m

  • Hazen williams c

    hazen_williams_c

    Hazen-Williams roughness coefficient

    40 – 160

  • Total fitting k

    total_fitting_k

    Total fitting and valve K value

    0 – 100

  • Fluid density

    fluid_density_kg_m3

    Fluid density

    900 – 1200 kg/m3

Scored outputs

4 outputs

Velocity m s

velocity_m_s

Pipe flow velocity

Scores if within ±3% of the reference value.

Friction loss

friction_loss_kpa

Straight-pipe friction pressure loss

Scores if within ±3% of the reference value.

Fitting loss

fitting_loss_kpa

Fitting and valve pressure loss

Scores if within ±3% of the reference value.

Total pressure loss

total_pressure_loss_kpa

Total pipe pressure loss

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 building water service
medium:
All parameters given across water pipe contexts
hard:
All parameters given for a site water main

Task bundle

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

/workspace

  • instruction.md
  • pressure-loss-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 building water hydraulics.2 3## Task4 5Calculate the pressure loss through the water pipework in {{ site_context }}.6 7## Given8 9| Parameter | Value | Unit |10| --- | ---: | --- |11| Flow rate | {{ flow_rate_l_s }} | L/s |12| Internal pipe diameter | {{ pipe_internal_diameter_mm }} | mm |13| Pipe length | {{ pipe_length_m }} | m |14| Hazen-Williams C value | {{ hazen_williams_c }} | - |15| Total fitting K value | {{ total_fitting_k }} | - |16| Fluid density | {{ fluid_density_kg_m3 }} | kg/m3 |17 18## Constraints19 20- No internet access is available.21- Use `h_f = 10.67 L Q^1.852 / (C^1.852 d^4.871)` with Q in m3/s and d in m.22- Use `h_k = K v^2 / (2g)` for fittings and valves.23- Use `g = 9.81 m/s2`.24- Convert pressure losses from head using `delta_p = rho g h`.25 26{% if tool_available %}27## Available Tool28 29A 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:41 42- Pipe velocity (`velocity_m_s`)43- Straight-pipe friction pressure loss (`friction_loss_kpa`)44- Fitting and valve pressure loss (`fitting_loss_kpa`)45- Total pipe pressure loss (`total_pressure_loss_kpa`)46 47## Output Format48 49Show 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:50 51```json52{53 "velocity_m_s": <numeric_value>,54 "friction_loss_kpa": <numeric_value>,55 "fitting_loss_kpa": <numeric_value>,56 "total_pressure_loss_kpa": <numeric_value>57}58```59 60Write your complete solution to `/workspace/output.md`.61

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.

Building water service

building_water_service

Building water service pressure-loss check

building-water-servicedomestic-water-riser
Parameter ranges
flow_rate_l_s
0.5 – 50
pipe_internal_diameter_mm
25 – 150
pipe_length_m
5 – 200
hazen_williams_c
100 – 150
total_fitting_k
2 – 30
fluid_density_kg_m3
990 – 1030

Site water main

site_water_main

Site water main pressure-loss check

site-water-maincampus-water-ring-main
Parameter ranges
flow_rate_l_s
10 – 300
pipe_internal_diameter_mm
100 – 600
pipe_length_m
50 – 1500
hazen_williams_c
100 – 150
total_fitting_k
1 – 20
fluid_density_kg_m3
990 – 1030

Example task

site-water-main-site-water-main-preview — hard difficulty, all inputs given.

Site water main pressure-loss check. site-water-main. Required outputs: velocity_m_s, friction_loss_kpa, fitting_loss_kpa, total_pressure_loss_kpa

The model sees

Scenario context and visible inputs.

flow_rate_l_s
10 to 300 L/s
pipe_internal_diameter_mm
100 to 600 mm
pipe_length_m
50 to 1500 m
hazen_williams_c
100 to 150
total_fitting_k
1 to 20
fluid_density_kg_m3
990 to 1030 kg/m3

Executable tool: pressure-loss-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.

{
  "velocity_m_s": <number>,
  "friction_loss_kpa": <number>,
  "fitting_loss_kpa": <number>,
  "total_pressure_loss_kpa": <number>
}
  • velocity_m_s · scored within ±3%
  • friction_loss_kpa · scored within ±3%
  • fitting_loss_kpa · scored within ±3%
  • total_pressure_loss_kpa · scored within ±3%