Flow velocity m per s
flow_velocity_m_per_s
Pipe flow velocity V (m/s)
Scores if within ±3% of the reference value.
Computes the hydraulic grade line (HGL) at the upstream pit of a single stormwater pipe reach using Manning's equation for friction loss and a pit loss coefficient for junction losses. Checks whether the HGL remains below the pit surface level with adequate clearance to prevent surcharging, following ARR 2019 and local council DCP methods.
with-tool: The model is given an executable Python calculator script.
Standards
One template produces many comparable benchmark tasks while keeping the scoring contract fixed.
01
The reusable contract shown on this page.
02
An archetype and site context are sampled.
03
Inputs may be hidden at harder tiers.
04
The model responds with the declared outputs.
Inputs the model receives, and the outputs it is scored on.
8 inputs
Included directly in every task prompt.
Design flow m3 per s
design_flow_m3_per_s
Design peak flow Q at the pipe reach
Pipe diameter
pipe_diameter_mm
Nominal internal pipe diameter DN
Pipe length
pipe_length_m
Pipe reach length L between pits
Tailwater level m
tailwater_level_m
HGL at the downstream pit (tailwater condition)
Surface level m
surface_level_m
Surface level at the upstream pit
Sampled from the scenario and inferable from its description.
Mannings n
mannings_n
Manning's roughness coefficient n for the pipe material
Derived from the archetype scenario. Hidden at hard difficulty.
Pit loss coefficient
pit_loss_coefficient
Pit/junction loss coefficient K (dimensionless)
Derived from the archetype scenario. Hidden at hard difficulty.
Used only when the sampled task needs this part of the contract.
Minimum clearance
minimum_clearance_mm
Minimum required clearance between HGL and surface level
Optional input.
7 outputs
flow_velocity_m_per_s
Pipe flow velocity V (m/s)
Scores if within ±3% of the reference value.
friction_loss_m
Friction head loss h_f through the pipe (m)
Scores if within ±3% of the reference value.
pit_loss_m
Pit/junction head loss h_pit (m)
Scores if within ±3% of the reference value.
hgl_upstream_m
HGL elevation at the upstream pit (m AHD)
Scores if within ±3% of the reference value.
clearance_mm
Clearance between surface level and HGL (mm), positive = below surface
Scores if within ±1000% of the reference value.
surcharge_ratio
HGL to surface level ratio (> 1.0 indicates surcharging)
Scores if within ±3% of the reference value.
pass_fail
Surcharge compliance (1.0 = pass, clearance adequate; 0.0 = fail)
Scores if within ±1% of the reference value.
Each template is sampled at three tiers. Harder tiers may hide inputs, forcing the model to infer them from the scenario description.
All inputs given
Small pipe, straight pit, all parameters given including Manning's n and pit loss K
Pipe diameter restricted to: 225, 300, 375, 450
All inputs given
Any pipe size and pit configuration, all parameters given
Some inputs hidden
Manning's n and pit loss K hidden, agent must infer from pipe material and junction description
Hidden inputs
Prompt replacement text
The pipe is {{ archetype.description }} installed at {{ archetype.site_context }}
The exact instruction and parameter contract used to generate this task, pinned to the published library source.
/workspace
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 drainage design and hydraulic analysis.2 3## Problem4 5Perform a hydraulic grade line (HGL) check for a single stormwater pipe reach between two pits. Determine whether the HGL at the upstream pit remains below the pit surface level with adequate clearance to prevent surcharging.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Design flow (Q) | {{ design_flow_m3_per_s }} | m³/s |12| Pipe diameter (DN) | {{ pipe_diameter_mm }} | mm |13| Pipe length (L) | {{ pipe_length_m }} | m |14{% if mannings_n is defined %}15| Manning's n | {{ mannings_n }} | - |16{% endif %}17{% if pit_loss_coefficient is defined %}18| Pit loss coefficient (K) | {{ pit_loss_coefficient }} | - |19{% endif %}20| Tailwater level (HGL downstream) | {{ tailwater_level_m }} | m AHD |21| Surface level at upstream pit | {{ surface_level_m }} | m AHD |22{% if minimum_clearance_mm is defined %}23| Minimum required clearance | {{ minimum_clearance_mm }} | mm |24{% endif %}25{% if archetype_description is defined %}26 27### Pipe and Pit Conditions28 29{{ archetype_description }}30{% endif %}31 32{% if tool_available %}33## Available Tool34 35A hydraulic grade line calculation tool is available at `/workspace/{{ meta.name }}_calc.py`. Run it with:36 37```bash38python3 /workspace/{{ meta.name }}_calc.py --help39```40 41You may use this tool to verify your calculations or compute values directly.42{% endif %}43 44## Required45 46Calculate the following for the pipe reach:47 481. Flow velocity V in the pipe (m/s)492. Friction head loss h_f through the pipe (m)503. Pit/junction head loss h_pit at the upstream pit (m)514. HGL elevation at the upstream pit (m AHD)525. Clearance between surface level and HGL (mm)536. Surcharge ratio (HGL / surface level)547. Pass/fail assessment (pass if clearance >= minimum clearance)55 56## Applicable Standards57 58- ARR 2019: Australian Rainfall and Runoff59- QUDM: Queensland Urban Drainage Manual60- Local Council Development Control Plans (DCPs)61 62## Constraints63 64- No internet access is available. Work from engineering knowledge and the provided tool.65- Assume the pipe is flowing full (pressure flow assumption for HGL check).66- Use Manning's equation (SI units) for friction loss:67 - **Pipe area:** A = pi x D² / 468 - **Hydraulic radius (full pipe):** R = D / 469 - **Flow velocity:** V = Q / A70 - **Friction slope:** S_f = (V x n / R^(2/3))²71 - **Friction loss:** h_f = S_f x L72- Use the standard minor loss equation for pit losses:73 - **Pit loss:** h_pit = K x V² / (2g), where g = 9.81 m/s²74- **HGL at upstream pit:** HGL_up = HGL_down + h_f + h_pit75- **Clearance:** clearance = (surface_level - HGL_up) x 1000 (in mm)76- **Surcharge ratio:** surcharge_ratio = HGL_up / surface_level77- **Pass/fail:** pass (1.0) if clearance >= minimum clearance, fail (0.0) otherwise78{% if minimum_clearance_mm is not defined %}79- If minimum clearance is not specified, use 150 mm as the default threshold.80{% endif %}81 82## Output Format83 84Show 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:85 86```json87{88 "flow_velocity_m_per_s": <numeric_value>,89 "friction_loss_m": <numeric_value>,90 "pit_loss_m": <numeric_value>,91 "hgl_upstream_m": <numeric_value>,92 "clearance_mm": <numeric_value>,93 "surcharge_ratio": <numeric_value>,94 "pass_fail": <numeric_value>95}96```97 98Write your complete solution to `/workspace/output.md`.99 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.
concrete_pipe_straight
Reinforced concrete pipe through a straight-through pit with benched invert
concrete_pipe_bend
Reinforced concrete pipe through a pit with a change in direction
pvc_pipe_residential
PVC pipe in a residential inter-allotment drainage pit
large_trunk_main
Large reinforced concrete trunk main through a junction pit with multiple inlets
brisbane-suburban-drainage-concrete-pipe-straight-preview — hard difficulty, some inputs hidden.
Reinforced concrete pipe through a straight-through pit with benched invert. brisbane-suburban-drainage. Required outputs: flow_velocity_m_per_s, friction_loss_m, pit_loss_m, hgl_upstream_m, clearance_mm, surcharge_ratio
Scenario context and visible inputs.
Executable tool: hgl-check_calc.py
Inputs withheld at this difficulty.
Mannings n
mannings_n
Pit loss coefficient
pit_loss_coefficient
Stand-in text in the prompt
The pipe is {{ archetype.description }} installed at {{ archetype.site_context }}
The scored JSON answer schema.
{
"flow_velocity_m_per_s": <number>,
"friction_loss_m": <number>,
"pit_loss_m": <number>,
"hgl_upstream_m": <number>,
"clearance_mm": <number>,
"surcharge_ratio": <number>,
"pass_fail": <number>
}