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civilwith-tool

Npsh Calculation

Calculates the Net Positive Suction Head Available (NPSHa) at a pump inlet from atmospheric pressure, vapour pressure, static suction head, and friction losses using the Hydraulics Institute formula NPSHa = (P_atm - P_vap)/(rho*g) + h_s - h_f. Determines the NPSH margin and margin ratio against the pump's required NPSHr to verify cavitation-free operation per ANSI/HI 9.6.1.

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

Standards

ANSI/HI 9.6.1Hydraulics Institute

Tags

cavitationcivildeterministicnpshpump-stationsuction-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.

4

  • Atmospheric pressure

    atmospheric_pressure_kpa

    Atmospheric pressure at the site elevation

    70 – 101.325 kPa

  • Static suction head

    static_suction_head_m

    Static suction head (positive = pump below liquid surface, negative = pump above)

    -8 – 15 m

  • Friction loss

    friction_loss_m

    Total friction losses in the suction piping

    0.1 – 5 m

  • Npsh required

    npsh_required_m

    NPSH required by the pump (from manufacturer data)

    1 – 12 m

Derived from scenario

Sampled from the scenario and inferable from its description.

2

  • Vapour pressure

    vapour_pressure_kpa

    Vapour pressure of the fluid at pumping temperature

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.6 – 50 kPa

  • Specific gravity

    specific_gravity

    Specific gravity of the fluid relative to water

    Derived from the archetype scenario. Hidden at hard difficulty.

    0.8 – 1.3

Scored outputs

4 outputs

Pressure head

pressure_head_m

Net pressure head contribution (P_atm - P_vap) / (rho * g) (m)

Scores if within ±3% of the reference value.

Npsh available

npsh_available_m

Net Positive Suction Head Available NPSHa (m)

Scores if within ±3% of the reference value.

Npsh margin

npsh_margin_m

NPSH margin: NPSHa - NPSHr (m)

Scores if within ±3% of the reference value.

Npsh margin ratio

npsh_margin_ratio

NPSH margin ratio: NPSHa / NPSHr (dimensionless)

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, flooded suction or elevated tank with comfortable NPSH margin

medium

All inputs given

All parameters given, any suction arrangement including suction lift and high-temperature

hard

Some inputs hidden

Vapour pressure and specific gravity hidden, agent must infer from fluid type and temperature

Hidden inputs

  • Vapour pressurevapour_pressure_kpa
  • Specific gravityspecific_gravity

Prompt replacement text

The pump station is 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
  • npsh-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 civil engineer specializing in water infrastructure and pump station design.2 3## Problem4 5Calculate the Net Positive Suction Head Available (NPSHa) for a pump station suction system. Determine the pressure head, NPSHa, NPSH margin, and margin ratio to assess whether the pump will operate without cavitation.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Atmospheric pressure (P_atm) | {{ atmospheric_pressure_kpa }} | kPa |12{%- if vapour_pressure_kpa is defined %}13| Vapour pressure (P_vap) | {{ vapour_pressure_kpa }} | kPa |14{%- endif %}15{%- if specific_gravity is defined %}16| Specific gravity (SG) | {{ specific_gravity }} | - |17{%- endif %}18| Static suction head (h_s) | {{ static_suction_head_m }} | m |19| Friction losses (h_f) | {{ friction_loss_m }} | m |20| NPSH required (NPSHr) | {{ npsh_required_m }} | m |21{% if archetype_description is defined %}22 23### Site Conditions24 25{{ archetype_description }}26{% endif %}27 28{% if tool_available %}29## Available Tool30 31A NPSH calculation tool is available at `/workspace/npsh-calculation_calc.py`. Run it with:32 33```bash34python3 /workspace/npsh-calculation_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. Net pressure head contribution (P_atm - P_vap) / (rho x g) in metres452. NPSHa -- Net Positive Suction Head Available (m)463. NPSH margin: NPSHa - NPSHr (m)474. NPSH margin ratio: NPSHa / NPSHr (dimensionless)48 49## Applicable Standards50 51- Hydraulics Institute -- pump NPSH definitions and methodology52- ANSI/HI 9.6.1 -- NPSH margin guideline (recommends margin ratio > 1.35)53 54## Constraints55 56- No internet access is available. Work from engineering knowledge and the provided tool.57- Use the following formulas:58 - Fluid density: rho = 998 x SG (kg/m^3)59 - Pressure head: h_p = (P_atm - P_vap) x 1000 / (rho x g) where pressures are in kPa, converted to Pa by multiplying by 100060 - NPSHa = h_p + h_s - h_f61 - NPSH margin = NPSHa - NPSHr62 - Margin ratio = NPSHa / NPSHr63- Physical constants: g = 9.81 m/s^2, rho_water = 998 kg/m^364- Static suction head h_s is positive when the pump is below the liquid surface (flooded suction) and negative when the pump is above the liquid surface (suction lift)65- If vapour pressure or specific gravity is not provided, estimate from the site description, fluid type, and temperature66 67## Output Format68 69Show your step-by-step working in Markdown, including the density calculation, pressure head calculation, NPSHa calculation, and margin assessment. At the end of your solution, include a JSON block with your final answers in exactly this format:70 71```json72{73 "pressure_head_m": <numeric_value>,74 "npsh_available_m": <numeric_value>,75 "npsh_margin_m": <numeric_value>,76 "npsh_margin_ratio": <numeric_value>77}78```79 80Write your complete solution to `/workspace/output.md`.81

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.

Wet well flooded

wet_well_flooded

Wet well pump station with flooded suction (submersible or dry-pit pump below water level)

brisbane-sewage-wet-wellsydney-stormwater-wet-well
Parameter ranges
atmospheric_pressure_kpa
99 – 101.325
vapour_pressure_kpa
1.2 – 4.2
specific_gravity
1 – 1.02
static_suction_head_m
1 – 8
friction_loss_m
0.1 – 1.5
npsh_required_m
1.5 – 5

Dry well suction lift

dry_well_suction_lift

Dry well pump station with suction lift (pump above liquid level, negative suction head)

melbourne-dry-well-spsadelaide-dry-well-transfer
Parameter ranges
atmospheric_pressure_kpa
99 – 101.325
vapour_pressure_kpa
1.2 – 4.2
specific_gravity
1 – 1.02
static_suction_head_m
-8 – -1
friction_loss_m
0.5 – 3
npsh_required_m
1.5 – 4

Elevated tank feed

elevated_tank_feed

Pump fed from elevated storage tank with generous static head and long suction pipe

perth-hilltop-reservoirdarwin-elevated-tank
Parameter ranges
atmospheric_pressure_kpa
95 – 101.325
vapour_pressure_kpa
1.2 – 2.5
specific_gravity
0.99 – 1.01
static_suction_head_m
3 – 15
friction_loss_m
0.5 – 3.5
npsh_required_m
2 – 6

High temp process

high_temp_process

High-temperature industrial process pump handling warm fluid with elevated vapour pressure

gladstone-process-plantkwinana-industrial-pump
Parameter ranges
atmospheric_pressure_kpa
99 – 101.325
vapour_pressure_kpa
12 – 50
specific_gravity
0.95 – 1.1
static_suction_head_m
2 – 10
friction_loss_m
0.5 – 3
npsh_required_m
3 – 12

Example task

brisbane-sewage-wet-well-wet-well-flooded-preview — hard difficulty, some inputs hidden.

Wet well pump station with flooded suction (submersible or dry-pit pump below water level). brisbane-sewage-wet-well. Required outputs: pressure_head_m, npsh_available_m, npsh_margin_m, npsh_margin_ratio

The model sees

Scenario context and visible inputs.

atmospheric_pressure_kpa
99 to 101.325 kPa
static_suction_head_m
1 to 8 m
friction_loss_m
0.1 to 1.5 m
npsh_required_m
1.5 to 5 m

Executable tool: npsh-calculation_calc.py

The model must infer

Inputs withheld at this difficulty.

  • Specific gravity

    specific_gravity

  • Vapour pressure

    vapour_pressure_kpa

Stand-in text in the prompt

The pump station is a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "pressure_head_m": <number>,
  "npsh_available_m": <number>,
  "npsh_margin_m": <number>,
  "npsh_margin_ratio": <number>
}
  • pressure_head_m · scored within ±3%
  • npsh_available_m · scored within ±3%
  • npsh_margin_m · scored within ±3%
  • npsh_margin_ratio · scored within ±3%