Hazen williams headloss
hazen_williams_headloss_m
RM-06-RISING-MAIN-01 Hazen-Williams headloss at design flow
Scores if within ±3% of the reference value.
LIVEdataset aec-bench@releasetasks 552models 18disciplines 5last submission … · built …
mechanicalwith-tool
Pump Station Duty Power Npsh Feeder Package
Calculates source-bound pump station duty metrics from a deterministic SSC-06 task-owned source pack. The template combines rising-main Hazen-Williams headloss, minor losses, total dynamic head, pump curve head margin, hydraulic and shaft power, motor schedule margin, NPSH available, feeder current, feeder voltage drop, and an overall synthetic pass score.
with-tool: The model is given an executable Python calculator script.
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
23 inputs
Always given
Included directly in every task prompt.
Show 23 inputs
Design flow
design_flow_l_s
CASE-SSC06-PUMP-DUTY-001 design flow for EQUIP-06-PUMP-01
72 L/sStatic lift
static_lift_m
WW-06-WETWELL-01 static lift to the rising-main discharge boundary
18.4 mRising main length
rising_main_length_m
RM-06-RISING-MAIN-01 pipe length
540 mRising main diameter
rising_main_diameter_mm
RM-06-RISING-MAIN-01 internal diameter
250 mmHazen williams c
hazen_williams_c
RM-06-RISING-MAIN-01 Hazen-Williams C factor
130Minor loss coefficient
minor_loss_coefficient
RM-06-RISING-MAIN-01 aggregate minor-loss coefficient
5.2Pump curve head at duty
pump_curve_head_at_duty_m
CURVE-06-PUMP-01 selected pump curve head at design flow
25.6 mFluid density
fluid_density_kg_m3
WW-06-WETWELL-01 source-owned fluid density
998 kg/m3Pump efficiency pct
pump_efficiency_pct
CURVE-06-PUMP-01 pump efficiency at design duty
74 %Motor efficiency pct
motor_efficiency_pct
MOTOR-06-SCHED-01 motor efficiency
94 %Motor service factor
motor_service_factor
MOTOR-06-SCHED-01 source-owned motor service factor
1.15Selected motor
selected_motor_kw
MOTOR-06-SCHED-01 selected motor size
30 kWAtmospheric pressure
atmospheric_pressure_kpa_abs
NPSH-06-SUCTION-01 atmospheric pressure
101.3 kPa absVapor pressure
vapor_pressure_kpa_abs
NPSH-06-SUCTION-01 vapor pressure
2.3 kPa absWetwell min level above pump
wetwell_min_level_above_pump_m
WW-06-WETWELL-01 minimum water level above pump centerline
2.1 mSuction loss
suction_loss_m
NPSH-06-SUCTION-01 suction-side loss at design duty
0.42 mNpsh required
npsh_required_m
CURVE-06-PUMP-01 NPSHr at design duty
7.4 mFeeder voltage
feeder_voltage_v
FEEDER-06-480V-01 nominal three-phase feeder voltage
480 VFeeder length
feeder_length_km
FEEDER-06-480V-01 feeder length
0.36 kmFeeder resistance ohm per km
feeder_resistance_ohm_per_km
FEEDER-06-480V-01 conductor resistance
0.386 ohm/kmFeeder reactance ohm per km
feeder_reactance_ohm_per_km
FEEDER-06-480V-01 conductor reactance
0.083 ohm/kmMotor power factor
motor_power_factor
MOTOR-06-SCHED-01 source-owned motor power factor
0.86Max voltage drop percent
max_voltage_drop_percent
FEEDER-06-480V-01 maximum allowed voltage drop
4 %
Scored outputs
18 outputs
Flow velocity m s
flow_velocity_m_s
RM-06-RISING-MAIN-01 flow velocity at design flow
Scores if within ±3% of the reference value.
Minor loss
minor_loss_m
RM-06-RISING-MAIN-01 aggregate minor loss
Scores if within ±3% of the reference value.
Total dynamic head
total_dynamic_head_m
Static lift plus rising-main headloss plus minor losses
Scores if within ±3% of the reference value.
Pump curve head margin
pump_curve_head_margin_m
CURVE-06-PUMP-01 head at duty minus total dynamic head
Scores if within ±3% of the reference value.
Hydraulic power
hydraulic_power_kw
Hydraulic power at the selected pump duty point
Scores if within ±3% of the reference value.
Shaft power
shaft_power_kw
Pump shaft power after pump efficiency
Scores if within ±3% of the reference value.
Motor input power
motor_input_power_kw
Motor electrical input power after motor efficiency
Scores if within ±3% of the reference value.
Required motor power
required_motor_power_kw
Required motor power after applying source-owned service factor
Scores if within ±3% of the reference value.
Motor size margin
motor_size_margin_kw
Selected motor size minus required motor power
Scores if within ±3% of the reference value.
Npsh available
npsh_available_m
NPSH available at minimum wet-well level
Scores if within ±3% of the reference value.
Npsh margin
npsh_margin_m
NPSH available minus NPSH required
Scores if within ±3% of the reference value.
Npsh margin ratio
npsh_margin_ratio
NPSH available divided by NPSH required
Scores if within ±3% of the reference value.
Load reactive power kvar
load_reactive_power_kvar
Reactive load derived from motor input power and power factor
Scores if within ±3% of the reference value.
Feeder current
feeder_current_a
FEEDER-06-480V-01 three-phase feeder current
Scores if within ±3% of the reference value.
Feeder voltage drop
feeder_voltage_drop_percent
FEEDER-06-480V-01 source-owned voltage-drop percentage
Scores if within ±3% of the reference value.
Voltage drop margin
voltage_drop_margin_percent
Maximum allowed voltage drop minus calculated voltage drop
Scores if within ±3% of the reference value.
Overall pass score
overall_pass_score
1.0 when curve, NPSH, motor size, and voltage-drop margins are non-negative
Scores if within ±0.1% 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 source-pack values given for the SSC-06 pump station duty package
- medium:
- All source-pack values given for the SSC-06 pump station duty package
- hard:
- All source-pack values given for the SSC-06 pump station duty package
Task bundle
The exact instruction and parameter contract used to generate this task, pinned to the published library source.
/workspace
- instruction.md
- pump-station-duty-power-npsh-feeder-package_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 pump station design engineer checking a task-owned synthetic SSC-06 pump station duty, power, NPSH, and feeder package.2 3Use only the task-owned synthetic source pack values shown below for numeric grading. EPA EPANET, Datacor Fathom, PIPE-FLO, PUMP-FLO, vendor pump-selection, and Hydraulic Institute style workflows shape the context only; this instance does not run those tools or parse a real vendor curve export.4 5## Scene6 7- Pump duty case: `CASE-SSC06-PUMP-DUTY-001`8- Equipment tag: `EQUIP-06-PUMP-01`9- Wet-well schedule: `WW-06-WETWELL-01`10- Rising main: `RM-06-RISING-MAIN-01`11- Pump curve table: `CURVE-06-PUMP-01`12- Motor schedule: `MOTOR-06-SCHED-01`13- NPSH basis: `NPSH-06-SUCTION-01`14- Feeder schedule: `FEEDER-06-480V-01`15- Selection memo: `MEMO-06-SELECTION-01`16 17## Hydraulic Duty Basis18 19| Item | Value |20|------|-------|21| Design flow | {{ design_flow_l_s }} L/s |22| Static lift | {{ static_lift_m }} m |23| Rising-main length | {{ rising_main_length_m }} m |24| Rising-main diameter | {{ rising_main_diameter_mm }} mm |25| Hazen-Williams C | {{ hazen_williams_c }} |26| Minor-loss coefficient | {{ minor_loss_coefficient }} |27| CURVE-06-PUMP-01 head at duty | {{ pump_curve_head_at_duty_m }} m |28 29Hydraulic checks:30 31- Convert design flow to m3/s as `design_flow_l_s / 1000`.32- Convert pipe diameter to m as `rising_main_diameter_mm / 1000`.33- Hazen-Williams headloss equals `10.67 x length_m x flow_m3_s^1.852 / (C^1.852 x diameter_m^4.87)`.34- Flow velocity equals `flow_m3_s / (pi x diameter_m^2 / 4)`.35- Minor loss equals `minor_loss_coefficient x velocity^2 / (2 x 9.81)`.36- Total dynamic head equals static lift plus Hazen-Williams headloss plus minor loss.37- Pump curve head margin equals `pump_curve_head_at_duty_m - total_dynamic_head_m`.38 39## Motor, NPSH, And Feeder Basis40 41| Item | Value |42|------|-------|43| Fluid density | {{ fluid_density_kg_m3 }} kg/m3 |44| Pump efficiency | {{ pump_efficiency_pct }} % |45| Motor efficiency | {{ motor_efficiency_pct }} % |46| Motor service factor | {{ motor_service_factor }} |47| Selected motor size | {{ selected_motor_kw }} kW |48| Atmospheric pressure | {{ atmospheric_pressure_kpa_abs }} kPa abs |49| Vapor pressure | {{ vapor_pressure_kpa_abs }} kPa abs |50| Wet-well minimum level above pump | {{ wetwell_min_level_above_pump_m }} m |51| Suction loss | {{ suction_loss_m }} m |52| NPSH required | {{ npsh_required_m }} m |53| Feeder voltage | {{ feeder_voltage_v }} V |54| Feeder length | {{ feeder_length_km }} km |55| Feeder resistance | {{ feeder_resistance_ohm_per_km }} ohm/km |56| Feeder reactance | {{ feeder_reactance_ohm_per_km }} ohm/km |57| Motor power factor | {{ motor_power_factor }} |58| Maximum voltage drop | {{ max_voltage_drop_percent }} % |59 60Motor, NPSH, and feeder checks:61 62- Hydraulic power equals `fluid_density_kg_m3 x 9.81 x flow_m3_s x total_dynamic_head_m / 1000`.63- Shaft power equals hydraulic power divided by pump efficiency as a decimal.64- Motor input power equals shaft power divided by motor efficiency as a decimal.65- Required motor power equals shaft power times motor service factor.66- Motor size margin equals selected motor size minus required motor power.67- NPSH available equals `(atmospheric_pressure_kpa_abs - vapor_pressure_kpa_abs) x 1000 / (fluid_density_kg_m3 x 9.81) + wetwell_min_level_above_pump_m - suction_loss_m`.68- NPSH margin equals NPSH available minus NPSH required.69- NPSH margin ratio equals NPSH available divided by NPSH required.70- Load reactive power equals `motor_input_power_kw x tan(acos(motor_power_factor))`.71- Apparent power equals `sqrt(motor_input_power_kw^2 + load_reactive_power_kvar^2)`.72- Feeder current equals `apparent_power_kva x 1000 / (sqrt(3) x feeder_voltage_v)`.73- Feeder voltage drop percent equals `sqrt(3) x feeder_current_a x feeder_length_km x (feeder_resistance_ohm_per_km x motor_power_factor + feeder_reactance_ohm_per_km x reactive_factor) / feeder_voltage_v x 100`, where `reactive_factor = load_reactive_power_kvar / apparent_power_kva`.74- Voltage drop margin equals maximum voltage drop percent minus feeder voltage drop percent.75- Overall pass score is `1.0` only when pump curve head margin, NPSH margin, motor size margin, and voltage drop margin are all non-negative; otherwise it is `0.0`.76 77## Output Format78 79Write a compact memo to `/workspace/output.md`. Include a source-boundary statement that this is a task-owned synthetic source pack. Explain the calculations briefly, preserve the object IDs above, and state whether the baseline source pack passes the current docs-only checks.80 81Do not claim authority approval, accepted project evidence, software export validity, full standards compliance, executable real source-pack parsing, generated EPANET/Fathom/PIPE-FLO/PUMP-FLO evidence, generated benchmark readiness, or benchmark readiness.82 83Include a fenced JSON block with exactly these numeric keys:84 85```json86{87 "hazen_williams_headloss_m": <numeric_value>,88 "flow_velocity_m_s": <numeric_value>,89 "minor_loss_m": <numeric_value>,90 "total_dynamic_head_m": <numeric_value>,91 "pump_curve_head_margin_m": <numeric_value>,92 "hydraulic_power_kw": <numeric_value>,93 "shaft_power_kw": <numeric_value>,94 "motor_input_power_kw": <numeric_value>,95 "required_motor_power_kw": <numeric_value>,96 "motor_size_margin_kw": <numeric_value>,97 "npsh_available_m": <numeric_value>,98 "npsh_margin_m": <numeric_value>,99 "npsh_margin_ratio": <numeric_value>,100 "load_reactive_power_kvar": <numeric_value>,101 "feeder_current_a": <numeric_value>,102 "feeder_voltage_drop_percent": <numeric_value>,103 "voltage_drop_margin_percent": <numeric_value>,104 "overall_pass_score": <numeric_value>105}106```107 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.
Ssc06 pump station duty case
ssc06_pump_station_duty_case
Pump station duty case with rising main, pump curve, motor schedule, NPSH basis, and feeder schedule
pump-station-duty-selectionpump-npsh-feeder-check
Parameter ranges
- design_flow_l_s
- 72
- static_lift_m
- 18.4
- rising_main_length_m
- 540
- rising_main_diameter_mm
- 250
- hazen_williams_c
- 130
- minor_loss_coefficient
- 5.2
- pump_curve_head_at_duty_m
- 25.6
- fluid_density_kg_m3
- 998
- pump_efficiency_pct
- 74
- motor_efficiency_pct
- 94
- motor_service_factor
- 1.15
- selected_motor_kw
- 30
- atmospheric_pressure_kpa_abs
- 101.3
- vapor_pressure_kpa_abs
- 2.3
- wetwell_min_level_above_pump_m
- 2.1
- suction_loss_m
- 0.42
- npsh_required_m
- 7.4
- feeder_voltage_v
- 480
- feeder_length_km
- 0.36
- feeder_resistance_ohm_per_km
- 0.386
- feeder_reactance_ohm_per_km
- 0.083
- motor_power_factor
- 0.86
- max_voltage_drop_percent
- 4
Example task
pump-station-duty-selection-ssc06-pump-station-duty-case-preview — hard difficulty, all inputs given.
Pump station duty case with rising main, pump curve, motor schedule, NPSH basis, and feeder schedule. pump-station-duty-selection. Required outputs: hazen_williams_headloss_m, flow_velocity_m_s, minor_loss_m, total_dynamic_head_m, pump_curve_head_margin_m, hydraulic_power_kw
The model sees
Scenario context and visible inputs.
- design_flow_l_s
- 72 to 72 L/s
- static_lift_m
- 18.4 to 18.4 m
- rising_main_length_m
- 540 to 540 m
- rising_main_diameter_mm
- 250 to 250 mm
- hazen_williams_c
- 130 to 130
- minor_loss_coefficient
- 5.2 to 5.2
- pump_curve_head_at_duty_m
- 25.6 to 25.6 m
- fluid_density_kg_m3
- 998 to 998 kg/m3
- pump_efficiency_pct
- 74 to 74 %
- motor_efficiency_pct
- 94 to 94 %
- motor_service_factor
- 1.15 to 1.15
- selected_motor_kw
- 30 to 30 kW
- atmospheric_pressure_kpa_abs
- 101.3 to 101.3 kPa abs
- vapor_pressure_kpa_abs
- 2.3 to 2.3 kPa abs
- wetwell_min_level_above_pump_m
- 2.1 to 2.1 m
- suction_loss_m
- 0.42 to 0.42 m
- npsh_required_m
- 7.4 to 7.4 m
- feeder_voltage_v
- 480 to 480 V
- feeder_length_km
- 0.36 to 0.36 km
- feeder_resistance_ohm_per_km
- 0.386 to 0.386 ohm/km
- feeder_reactance_ohm_per_km
- 0.083 to 0.083 ohm/km
- motor_power_factor
- 0.86 to 0.86
- max_voltage_drop_percent
- 4 to 4 %
Executable tool: pump-station-duty-power-npsh-feeder-package_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.
{
"hazen_williams_headloss_m": <number>,
"flow_velocity_m_s": <number>,
"minor_loss_m": <number>,
"total_dynamic_head_m": <number>,
"pump_curve_head_margin_m": <number>,
"hydraulic_power_kw": <number>,
"shaft_power_kw": <number>,
"motor_input_power_kw": <number>,
"required_motor_power_kw": <number>,
"motor_size_margin_kw": <number>,
"npsh_available_m": <number>,
"npsh_margin_m": <number>,
"npsh_margin_ratio": <number>,
"load_reactive_power_kvar": <number>,
"feeder_current_a": <number>,
"feeder_voltage_drop_percent": <number>,
"voltage_drop_margin_percent": <number>,
"overall_pass_score": <number>
}- hazen_williams_headloss_m · scored within ±3%
- flow_velocity_m_s · scored within ±3%
- minor_loss_m · scored within ±3%
- total_dynamic_head_m · scored within ±3%
- pump_curve_head_margin_m · scored within ±3%
- hydraulic_power_kw · scored within ±3%
- shaft_power_kw · scored within ±3%
- motor_input_power_kw · scored within ±3%
- required_motor_power_kw · scored within ±3%
- motor_size_margin_kw · scored within ±3%
- npsh_available_m · scored within ±3%
- npsh_margin_m · scored within ±3%
- npsh_margin_ratio · scored within ±3%
- load_reactive_power_kvar · scored within ±3%
- feeder_current_a · scored within ±3%
- feeder_voltage_drop_percent · scored within ±3%
- voltage_drop_margin_percent · scored within ±3%
- overall_pass_score · scored within ±0.1%