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civilwith-tool

Spillway Weir Capacity

Calculates spillway discharge capacity using the weir equation Q = C*L_eff*H_e^1.5 with pier and abutment contraction corrections to effective crest length and approach velocity head adjustments per USBR Design Standard No. 14 and USACE EM 1110-2-1603. Supports ogee and broad-crested weir types for dam safety and flood routing assessments.

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

Standards

USACE EM 1110-2-1603 USBR Design Standard No. 14

How this task is generated

One template produces many comparable benchmark tasks while keeping the scoring contract fixed.

01
Template
The reusable contract shown on this page.
02
Scenario
An archetype and site context are sampled.
03
Difficulty tier
Inputs may be hidden at harder tiers.
04
Task prompt
The model responds with the declared outputs.

Parameters

Inputs the model receives, and the outputs it is scored on.

Inputs

8 inputs

Always given

Included directly in every task prompt.

Crest length
crest_length_m
Gross crest length of the spillway L
3 – 120 m
Design head
design_head_m
Design head over the spillway crest H
0.3 – 8 m

Derived from scenario

Sampled from the scenario and inferable from its description.

Discharge coefficient
discharge_coefficient
Weir discharge coefficient C (SI metric)
Derived from the archetype scenario. Hidden at hard difficulty.
1.4 – 2.25

Optional

Used only when the sampled task needs this part of the contract.

Number of piers
number_of_piers
Number of piers on the spillway crest N
Optional input.
0 – 8
Pier shape
pier_shape
Pier nose geometry for contraction coefficient Kp
Derived from the archetype scenario. Optional input. Hidden at hard difficulty.
squareroundpointed
Abutment shape
abutment_shape
Abutment geometry for contraction coefficient Ka
Derived from the archetype scenario. Optional input. Hidden at hard difficulty.
squareroundedstreamlined
Approach channel width
approach_channel_width_m
Width of the approach channel upstream of the spillway B
Optional input.
5 – 200 m
Approach depth
approach_depth_m
Depth of flow in the approach channel h_approach
Optional input.
0.5 – 15 m

Scored outputs

5 outputs

Effective crest length

effective_crest_length_m

Effective crest length after pier and abutment contraction corrections L_eff (m)

Scores if within ±3% of the reference value.

Approach velocity head

approach_velocity_head_m

Approach velocity head correction Va²/(2g) (m)

Scores if within ±5% of the reference value.

Total energy head

total_energy_head_m

Total energy head over crest He = H + Va²/(2g) (m)

Scores if within ±3% of the reference value.

Discharge

discharge_m3_s

Total spillway discharge capacity Q (m³/s)

Scores if within ±3% of the reference value.

Unit discharge m3 s per

unit_discharge_m3_s_per_m

Unit discharge per metre of effective crest q (m³/s/m)

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

Simple ogee spillway, no piers, all parameters given

Number of piers restricted to: 0

Pier shape restricted to: round

Abutment shape restricted to: rounded

medium

All inputs given

All parameters given, includes pier and abutment corrections across both types

hard

Some inputs hidden

Discharge coefficient, pier shape, and abutment shape hidden; agent infers from site context

Hidden inputs

Discharge coefficientdischarge_coefficient
Pier shapepier_shape
Abutment shapeabutment_shape

Prompt replacement text

The spillway 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
spillway-weir-capacity_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/dams engineer specializing in spillway hydraulics and dam safety.2 3## Problem4 5Calculate the discharge capacity of a spillway weir using the standard weir equation with pier and abutment contraction corrections.6 7## Given8 9| Parameter | Value | Unit |10|-----------|-------|------|11| Gross crest length (L) | {{ crest_length_m }} | m |12| Design head over crest (H) | {{ design_head_m }} | m |13{% if discharge_coefficient is defined %}14| Discharge coefficient (C) | {{ discharge_coefficient }} | - |15{% endif %}16{% if number_of_piers is defined %}17| Number of piers (N) | {{ number_of_piers }} | - |18{% endif %}19{% if pier_shape is defined %}20| Pier nose shape | {{ pier_shape }} | - |21{% endif %}22{% if abutment_shape is defined %}23| Abutment shape | {{ abutment_shape }} | - |24{% endif %}25{% if approach_channel_width_m is defined %}26| Approach channel width (B) | {{ approach_channel_width_m }} | m |27{% endif %}28{% if approach_depth_m is defined %}29| Approach flow depth (h_approach) | {{ approach_depth_m }} | m |30{% endif %}31{% if archetype_description is defined %}32 33### Site Conditions34 35{{ archetype_description }}36{% endif %}37 38{% if tool_available %}39## Available Tool40 41A spillway discharge calculation tool is available at `/workspace/spillway-weir-capacity_calc.py`. Run it with:42 43```bash44python3 /workspace/spillway-weir-capacity_calc.py --help45```46 47You may use this tool to verify your calculations or compute values directly.48{% endif %}49 50## Required51 52Calculate the following:53 541. Effective crest length after pier and abutment contraction corrections L_eff (m)552. Approach velocity head correction Va²/(2g) (m)563. Total energy head over crest He (m)574. Total spillway discharge capacity Q (m³/s)585. Unit discharge per metre of effective crest q (m³/s/m)59 60## Applicable Standards61 62- USBR Design Standard No. 14 — Spillway design criteria63- USACE EM 1110-2-1603 — Hydraulic Design of Spillways64 65## Constraints66 67- No internet access is available. Work from engineering knowledge and the provided tool.68- Use the standard weir discharge equation:69  - **Q = C × L_eff × H_e^(3/2)**70  - Where C is the weir discharge coefficient in SI metric units71- Compute effective crest length with pier and abutment corrections:72  - **L_eff = L − 2 × (N × Kp + Ka) × H**73  - Pier contraction coefficients Kp: square = 0.02, round = 0.01, pointed = 0.0074  - Abutment contraction coefficients Ka: square = 0.20, rounded = 0.10, streamlined = 0.0075- Apply approach velocity head correction:76  - **Va = Q_initial / (B × h_approach)**77  - **Velocity head = Va² / (2g)**78  - **H_e = H + Va² / (2g)**79  - First compute Q_initial = C × L_eff × H^(3/2) without velocity head, then apply correction80- Use g = 9.81 m/s²81- Typical discharge coefficients (SI metric):82  - Ogee spillway: C ≈ 2.10–2.2083  - Broad-crested weir: C ≈ 1.50–1.8084- If no pier shape is given, assume round-nosed piers (Kp = 0.01)85- If no abutment shape is given, assume rounded abutments (Ka = 0.10)86- If no number of piers is given, assume N = 087- Unit discharge: q = Q / L_eff88 89## Output Format90 91Show 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:92 93```json94{95  "effective_crest_length_m": <numeric_value>,96  "approach_velocity_head_m": <numeric_value>,97  "total_energy_head_m": <numeric_value>,98  "discharge_m3_s": <numeric_value>,99  "unit_discharge_m3_s_per_m": <numeric_value>100}101```102 103Write your complete solution to `/workspace/output.md`.104

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.

Small ogee dam

small_ogee_dam

Small ogee spillway dam with low head and no piers

tasmania-small-hydrovictoria-farm-dam

Parameter ranges

crest_length_m: 5 – 20
design_head_m: 0.5 – 1.5
discharge_coefficient: 2.1 – 2.18
number_of_piers: 0
approach_channel_width_m: 8 – 30
approach_depth_m: 1 – 3

Medium ogee gated

medium_ogee_gated

Medium ogee spillway with gated bays and piers

nsw-water-supply-damqueensland-irrigation-dam

Parameter ranges

crest_length_m: 20 – 60
design_head_m: 1.5 – 4
discharge_coefficient: 2.12 – 2.2
number_of_piers: 1 – 4
approach_channel_width_m: 25 – 80
approach_depth_m: 3 – 8

Large ogee flood

large_ogee_flood

Large ogee flood spillway with multiple pier bays

snowy-mountains-flood-damnorth-queensland-major-dam

Parameter ranges

crest_length_m: 50 – 120
design_head_m: 3 – 8
discharge_coefficient: 2.15 – 2.22
number_of_piers: 2 – 8
approach_channel_width_m: 60 – 200
approach_depth_m: 5 – 15

Broad crested weir

broad_crested_weir

Broad-crested weir spillway on low-head dam or diversion structure

south-australia-diversion-weirwestern-australia-creek-crossing

Parameter ranges

crest_length_m: 5 – 40
design_head_m: 0.3 – 2.5
discharge_coefficient: 1.5 – 1.75
number_of_piers: 0 – 2
approach_channel_width_m: 8 – 60
approach_depth_m: 0.5 – 5

Broad crested large

broad_crested_large

Large broad-crested spillway with piers for multi-bay structure

northern-territory-barragecanberra-lake-overflow

Parameter ranges

crest_length_m: 30 – 80
design_head_m: 1 – 3.5
discharge_coefficient: 1.55 – 1.8
number_of_piers: 1 – 5
approach_channel_width_m: 40 – 120
approach_depth_m: 2 – 8

Example task

snowy-mountains-flood-dam-large-ogee-flood-preview — hard difficulty, some inputs hidden.

Large ogee flood spillway with multiple pier bays. snowy-mountains-flood-dam. Required outputs: effective_crest_length_m, approach_velocity_head_m, total_energy_head_m, discharge_m3_s, unit_discharge_m3_s_per_m

The model sees

Scenario context and visible inputs.

crest_length_m: 50 to 120 m
design_head_m: 3 to 8 m
number_of_piers: 2 to 8
approach_channel_width_m: 60 to 200 m
approach_depth_m: 5 to 15 m

Executable tool: spillway-weir-capacity_calc.py

The model must infer

Inputs withheld at this difficulty.

Abutment shape
abutment_shape
Pier shape
pier_shape
Discharge coefficient
discharge_coefficient

Stand-in text in the prompt

The spillway is a {{ archetype.description }} ({{ archetype.site_context }})

The model must produce

The scored JSON answer schema.

{
  "effective_crest_length_m": <number>,
  "approach_velocity_head_m": <number>,
  "total_energy_head_m": <number>,
  "discharge_m3_s": <number>,
  "unit_discharge_m3_s_per_m": <number>
}

effective_crest_length_m · scored within ±3%
approach_velocity_head_m · scored within ±5%
total_energy_head_m · scored within ±3%
discharge_m3_s · scored within ±3%
unit_discharge_m3_s_per_m · scored within ±3%

Spillway Weir Capacity

How this task is generated

Template

Scenario

Difficulty tier

Task prompt

Parameters

Inputs

Scored outputs

Effective crest length

Approach velocity head

Total energy head

Discharge

Unit discharge m3 s per

Difficulty

easy

medium

hard

Task bundle

Scenario archetypes

Small ogee dam

Medium ogee gated

Large ogee flood

Broad crested weir

Broad crested large

Example task

The model sees

The model must infer

The model must produce