MechanicalIntermediate
Fans and Air Systems
Fan Affinity Laws
Estimate how fan airflow, pressure, and shaft power change with rotational speed when fan geometry and air density remain similar.
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MechanicalIntermediate
Pumps and Hydronics
Pump Affinity Laws
Estimate pump flow, head, and shaft power at a different rotational speed for the same impeller and a similar system.
MechanicalBeginner
Duct Systems
Airflow, Velocity & Area
Calculate required duct cross-sectional area and an equivalent round diameter from airflow and average velocity.
MechanicalIntermediate
Duct Systems
Equivalent Round Duct
Estimate the round duct diameter with approximately the same friction rate as a rectangular duct at equal airflow.
MechanicalBeginner
Hydronic Piping
Pipe Flow & Velocity
Calculate average liquid velocity from volumetric flow and actual pipe inside diameter.
MechanicalAdvanced
Hydronic Piping
Hydronic Pressure Loss
Estimate straight-pipe and minor pressure losses with Darcy–Weisbach using actual fluid properties and a summed fitting-loss coefficient.
MechanicalIntermediate
Heat Transfer
Airside Sensible Heat
Estimate sensible airside capacity from airflow, dry-bulb temperature difference, air density, and specific heat.
MechanicalIntermediate
Heat Transfer
Water-Side Heat Transfer
Estimate hydronic heat transfer from fluid flow, temperature difference, and a user-entered fluid factor.
ElectricalBeginner
Electrical Fundamentals
Ohm’s Law
Solve the basic resistive relationship among voltage, current, resistance, and power.
ElectricalIntermediate
Electrical Fundamentals
Three-Phase Power
Calculate balanced three-phase real, apparent, and reactive power from line voltage, line current, and true power factor.
ElectricalIntermediate
Conductors and Circuits
Voltage Drop
Estimate single-phase or balanced three-phase voltage drop using a transparent conductor reference, resistance-only estimate, or project-specific AC impedance data.
ElectricalIntermediate
Motors and Drives
Motor Loading
Estimate shaft loading from measured true input power, estimated operating efficiency, and motor nameplate output rating.
PlumbingIntermediate
Domestic Water
Available Water Pressure
Estimate residual pressure after elevation, meter, backflow, piping, valve, and equipment losses.
PlumbingBeginner
Domestic Hot Water
Hot-Water Mixing
Calculate ideal hot- and cold-water flow fractions required to produce a selected mixed-water temperature.
CommissioningBeginner
Field Evaluation
Percent of Design
Compare a measured value with its scheduled or design value and evaluate the result against a user-entered tolerance.
CommissioningIntermediate
Air Systems
Fan Performance Verification
Compare measured fan airflow, pressure, and speed with scheduled values and an affinity-law speed prediction.
CommissioningIntermediate
Hydronic Systems
Pump Performance Verification
Compare measured pump flow, head, and speed with scheduled values and an affinity-law speed prediction.
CommissioningIntermediate
Heat Transfer
Coil Capacity Verification
Calculate airside sensible coil capacity and compare it with an approved design value.
CommissioningIntermediate
Central Plant
Chiller Capacity Verification
Calculate chilled-water capacity, percent of scheduled capacity, and operating kW per ton or COP-equivalent ratio.
CommissioningIntermediate
Central Plant
Boiler Efficiency Verification
Estimate boiler thermal efficiency from fuel input and measured water-side output.
CommissioningIntermediate
Central Plant
Cooling-Tower Performance
Calculate tower range, approach, effectiveness, and deviation from an entered design approach.
CommissioningIntermediate
Ventilation
Outdoor-Air Percentage
Estimate outdoor-air fraction from outdoor, return, and mixed-air temperature measurements.
CommissioningBeginner
Electrical
Electrical Phase Imbalance
Calculate line-voltage unbalance using maximum deviation from the three-reading average.
CommissioningIntermediate
Electrical
Transformer Loading
Calculate measured apparent power and percent transformer loading from voltage, current, and phase configuration.
CommissioningIntermediate
Emergency Power
Generator Load Test
Calculate generator real- and apparent-power loading, power factor, and test energy.
CommissioningBeginner
Controls
Sensor Calibration
Calculate sensor error, percent-of-span error, and corrected indicated value from a reference comparison.
CommissioningIntermediate
Measurement
Instrument Uncertainty
Combine accuracy, resolution, and an additional independent uncertainty component by root-sum-square.
CommissioningIntermediate
TAB
TAB Flow Reconciliation
Reconcile entered airflow streams and calculate the imbalance between inflow and outflow totals.
CommissioningBeginner
Controls
Trend Runtime and Cycling
Calculate runtime percentage, runtime hours, and starts per hour from evenly sampled trend data.
CommissioningBeginner
Cross-Discipline Analysis
Percent Difference
Calculate symmetric percent difference between two non-reference measurements.
CommissioningBeginner
Cross-Discipline Analysis
Linear Interpolation
Interpolate a dependent value between two known points using a straight-line relationship.
CommissioningBeginner
Cross-Discipline Analysis
Data Averaging
Calculate the arithmetic mean, minimum, maximum, and range for five entered readings.
CommissioningIntermediate
Cross-Discipline Analysis
Standard Deviation
Calculate sample or population standard deviation for five entered readings.
CommissioningBeginner
Cross-Discipline Energy
Energy Cost
Estimate energy use and consumption cost from power, operating hours, load factor, and an entered energy rate.
CommissioningBeginner
Cross-Discipline Energy
Simple Payback
Calculate simple payback from net initial cost and annual net savings.
MechanicalIntermediate
Fans
Fan Air Horsepower
Calculate useful air power from fan airflow and fan pressure.
MechanicalIntermediate
Fans
Fan Brake Horsepower
Estimate required fan shaft power from airflow, fan pressure, and entered fan efficiency.
MechanicalIntermediate
Fans
Fan Efficiency
Calculate fan efficiency by dividing useful air power by measured shaft power.
MechanicalBeginner
Fans
Belt-Drive Fan RPM
Estimate driven fan speed from motor speed, sheave pitch diameters, and entered belt slip.
MechanicalIntermediate
Fans
Fan Density Correction
Correct fan pressure and shaft power between actual and reference air densities at the same flow and speed.
MechanicalIntermediate
Fans
Fan System Curve
Project a quadratic fan-system pressure at a target airflow from one known operating point.
MechanicalAdvanced
Fans
Fan Wheel-Diameter Change
Estimate flow, pressure, and power changes for geometrically similar fans at the same rotational speed.
MechanicalIntermediate
Fans
Fan Static Pressure
Calculate fan static pressure from fan total pressure and outlet velocity pressure.
MechanicalIntermediate
Fans
Fan Total Pressure
Calculate fan total-pressure rise from inlet and outlet static and velocity pressures.
MechanicalIntermediate
Fans
Fan Turndown
Calculate fan flow turndown, minimum-flow percentage, speed ratio, and ideal affinity-law power fraction.
MechanicalAdvanced
Pumps
Pump Total Dynamic Head
Calculate pump total dynamic head from pressure, elevation, and velocity-head differences between suction and discharge measurement planes.
MechanicalIntermediate
Pumps
Pump Water Horsepower
Calculate hydraulic power imparted to a liquid from flow, head, and specific gravity.
MechanicalIntermediate
Pumps
Pump Efficiency
Calculate pump efficiency by dividing hydraulic output power by measured shaft input power.
MechanicalIntermediate
Pumps
Pump System Curve
Project total system head at a target flow using an entered static head and one known operating point.
MechanicalAdvanced
Pumps
NPSH Available
Estimate source-boundary net positive suction head available from absolute liquid-surface pressure, vapor pressure, static suction head, and suction-line losses.
MechanicalIntermediate
Hydronics
Hydronic Fill Pressure
Calculate minimum cold fill pressure from elevation, fluid specific gravity, and required pressure at the system high point.
MechanicalBeginner
Hydronics
Building Static Pressure
Calculate liquid static pressure produced by a vertical fluid column.
MechanicalIntermediate
Hydronics
Valve Authority
Calculate control-valve authority from valve pressure drop and the pressure drop of the remaining controlled circuit.
MechanicalIntermediate
Pumps
Pump Power and Energy
Estimate pump electrical input power, operating energy, and energy-consumption cost from flow, head, efficiencies, and runtime.
MechanicalIntermediate
Hydronics
Differential-Pressure Flow Estimate
Estimate flow through a fixed differential-pressure device from a known reference flow and pressure drop.
MechanicalBeginner
Duct Systems
Round Duct Sizing
Calculate a preliminary round duct diameter from airflow and target average velocity.
MechanicalBeginner
Duct Systems
Rectangular Duct Sizing
Calculate preliminary rectangular duct dimensions from airflow, target velocity, and width-to-height aspect ratio.
MechanicalIntermediate
Duct Systems
Equal-Friction Duct
Estimate round duct diameter from airflow and target friction rate using a standard-air empirical relationship.
MechanicalAdvanced
Duct Systems
Duct Pressure Loss
Calculate straight-duct pressure loss with Darcy–Weisbach from hydraulic diameter, length, velocity, air density, and friction factor.
MechanicalIntermediate
Duct Systems
Duct Fitting Loss
Calculate fitting pressure loss from an entered loss coefficient and local velocity pressure.
MechanicalBeginner
Duct Systems
Total External Static Pressure
Sum entered external air-system component pressure losses on a consistent static-pressure basis.
MechanicalIntermediate
Air Measurement
Pitot-Tube Airflow
Calculate air velocity and airflow from average velocity pressure, air density, and clear duct area.
MechanicalBeginner
Ventilation
Air Changes per Hour
Calculate air changes per hour from volumetric airflow and room volume.
MechanicalBeginner
Duct Systems
Duct Leakage Percentage
Calculate measured duct leakage as a percentage of an entered reference airflow.
MechanicalIntermediate
Air Measurement
Duct Traverse Averaging
Average eight entered velocity readings and calculate airflow from clear duct area.
MechanicalAdvanced
Hydronic Piping
Darcy–Weisbach Pipe Loss
Calculate liquid velocity, Reynolds number, Darcy friction factor, and straight-pipe pressure loss from actual fluid and pipe properties.
MechanicalIntermediate
Hydronic Piping
Hazen–Williams Pipe Loss
Calculate water-pipe friction head and pressure loss using the Hazen–Williams empirical relationship.
MechanicalBeginner
Hydronic Piping
Pipe and Fitting Equivalent Length
Sum straight pipe and entered fitting equivalent lengths for preliminary pressure-loss calculations.
MechanicalBeginner
Hydronic Piping
Total Hydronic Pressure Loss
Sum entered pipe, fitting, valve, coil, strainer, heat-exchanger, and other hydronic pressure losses.
MechanicalIntermediate
Hydronic Controls
Control-Valve Cv
Calculate required liquid valve flow coefficient Cv from flow, pressure drop, and specific gravity.
MechanicalIntermediate
Hydronic Piping
Glycol Correction
Estimate required glycol-solution flow for the same heat duty and temperature difference from entered fluid density and specific heat.
MechanicalBeginner
Hydronic Piping
Hydronic System Volume
Estimate total hydronic volume from one representative pipe segment plus entered equipment and miscellaneous volume.
MechanicalAdvanced
Hydronic Piping
Expansion-Tank Preliminary Sizing
Estimate diaphragm-tank volume from system volume, entered fluid expansion, and initial and maximum absolute pressure relationships.
MechanicalAdvanced
Insulation
Pipe Insulation Surface Temperature
Estimate insulated-pipe outer-surface temperature and heat transfer per unit length with cylindrical conduction and outside convection.
MechanicalBeginner
Insulation
Pipe Condensation Risk
Compare pipe or insulation surface temperature with ambient dew point and an entered safety margin.
MechanicalIntermediate
Heat Transfer
Airside Total Heat
Calculate total airside heat transfer from airflow, air density, and moist-air enthalpy difference.
MechanicalBeginner
Heat Transfer
Chilled-Water Tonnage
Calculate chilled-water load from flow, temperature difference, and a user-entered fluid factor.
MechanicalBeginner
Heat Transfer
Heating-Water Capacity
Calculate heating-water capacity from flow, temperature difference, and an entered fluid factor.
MechanicalBeginner
Loads
Required Airflow
Calculate airflow required for a sensible load using temperature difference and a user-entered air constant.
MechanicalBeginner
Loads
Required Water Flow
Calculate required hydronic flow from load, temperature difference, and an entered fluid factor.
MechanicalIntermediate
Central Plant
Chiller Capacity
Calculate evaporator capacity from liquid flow, density, specific heat, and entering/leaving temperature.
MechanicalBeginner
Central Plant
Boiler Efficiency
Calculate direct thermal efficiency from useful heat output and fuel input on a consistent basis.
MechanicalBeginner
Heat Recovery
Heat-Recovery Effectiveness
Calculate supply-side sensible heat-recovery effectiveness from three dry-bulb temperatures.
MechanicalAdvanced
Psychrometrics
Psychrometric Properties
Calculate humidity ratio, moist-air enthalpy, dew point, and vapor pressure from dry-bulb temperature, relative humidity, and pressure.
MechanicalAdvanced
Psychrometrics
Mixed-Air Conditions
Calculate mixed-air dry-bulb temperature, humidity ratio, and enthalpy from outdoor and return moist-air states.
MechanicalBeginner
Psychrometrics
Outdoor-Air Percentage by Temperature
Estimate outdoor-air percentage from outdoor, return, and mixed dry-bulb temperatures.
MechanicalIntermediate
Psychrometrics
Dew Point
Estimate air dew-point temperature from dry-bulb temperature and relative humidity.
MechanicalIntermediate
Psychrometrics
Surface Condensation Risk
Calculate the surface-temperature margin above air dew point from dry-bulb temperature and relative humidity.
MechanicalIntermediate
Psychrometrics
Humidification Load
Calculate required moisture addition from airflow, dry-air density, and humidity-ratio increase.
MechanicalIntermediate
Psychrometrics
Condensate Generation
Calculate airside condensate generation from dry-air mass flow and humidity-ratio decrease.
MechanicalAdvanced
Controls
Economizer Evaluation
Evaluate outdoor-air dry-bulb and enthalpy against return air and user-entered economizer limits.
MechanicalBeginner
Equipment
Cooling-Coil Sensible Heat Ratio
Calculate sensible heat ratio from sensible and total cooling capacity.
MechanicalBeginner
Equipment
Coil Approach Temperature
Calculate leaving-air approach above entering-fluid temperature for a cooling coil.
MechanicalAdvanced
Equipment
Heat-Exchanger Effectiveness
Calculate heat-exchanger effectiveness from hot- and cold-side inlet/outlet temperatures and capacity rates.
MechanicalBeginner
Equipment
Coefficient of Performance
Calculate equipment COP from useful thermal capacity and electrical input power.
MechanicalAdvanced
Equipment
AHU Performance
Calculate measured air-handler total-capacity magnitude, heat-transfer direction, and percent of entered design capacity from airflow and moist-air enthalpy difference.
MechanicalIntermediate
Equipment
VAV Box Performance
Compare measured VAV airflow with design, minimum, and maximum airflow references.
MechanicalBeginner
Central Plant
Chiller kW per Ton
Calculate chiller kW per refrigeration ton and COP from capacity and electrical input.
MechanicalIntermediate
Central Plant
Cooling-Tower Approach and Range
Calculate tower approach, range, and temperature effectiveness from hot water, cold water, and entering wet-bulb temperature.
MechanicalBeginner
Central Plant
Boiler Turndown
Calculate boiler input turndown ratio from maximum and minimum stable firing rates.
MechanicalBeginner
Air Systems
Filter Pressure-Drop Trend
Calculate the fraction of a filter pressure-drop allowance consumed between clean and final limits.
MechanicalIntermediate
Controls
Control-Valve Flow Verification
Compare measured liquid flow with a square-root flow prediction from reference and measured pressure drop.
MechanicalBeginner
Controls
Damper Position–Airflow Comparison
Compare measured airflow percentage with commanded damper position as a diagnostic screen.
MechanicalIntermediate
Controls
Sensor Offset and Span
Calculate low-point offset, high-point offset, and span error from two reference and two sensor readings.
CommissioningBeginner
Controls
Analog Signal Scaling
Linearly scale a measured analog signal into an engineering process value.
MechanicalAdvanced
Controls
PID Response Metrics
Calculate percent overshoot, peak time, settling time, and final error for a documented control response.
MechanicalBeginner
Controls
Actuator Stroke Time
Normalize a measured partial actuator movement to an equivalent full-stroke time and compare it with rated time.
MechanicalBeginner
Controls
Runtime and Cycling
Calculate runtime percentage, cycles per hour, and average on-time from an observation interval.
CommissioningBeginner
Controls
Alarm Response Time
Calculate alarm annunciation and operator/system response delays relative to an entered requirement.
MechanicalBeginner
Energy
Fan Energy Use
Calculate fan electrical energy from input power, runtime, and average load factor.
MechanicalBeginner
Energy
Pump Energy Use
Calculate pump electrical energy from input power, runtime, and average load factor.
MechanicalIntermediate
Energy
Chiller Energy Use
Calculate chiller electrical energy from cooling capacity, kW/ton, runtime, and load factor.
MechanicalIntermediate
Energy
Boiler Fuel Use
Calculate boiler fuel-energy use from useful output rate, efficiency, and runtime.
CommissioningBeginner
Energy
Operating-Cost Comparison
Compare baseline and proposed electricity cost from input power, annual hours, and energy rate.
CommissioningBeginner
Energy
Equipment Runtime Cost
Calculate electrical energy and cost from equipment input power, runtime, and energy rate.
ElectricalBeginner
Electrical Fundamentals
Single-Phase AC Power
Calculate apparent, real, and reactive-power magnitude for a measured single-phase AC load.
ElectricalIntermediate
Electrical Fundamentals
AC Power Triangle
Reconcile signed real and reactive power into apparent power, power-factor magnitude, and power angle.
ElectricalAdvanced
Power Quality
Power-Factor Correction
Estimate ideal capacitive kvar required to move a steady lagging load from an initial to a target power factor.
ElectricalIntermediate
Distribution Systems
Three-Phase Demand Current
Calculate balanced three-phase line current from real demand, line voltage, and true power factor.
ElectricalIntermediate
Motors and Drives
Motor Speed and Slip
Calculate induction-motor synchronous speed, slip speed, and percent slip.
ElectricalIntermediate
Motors and Drives
Motor Operating Efficiency
Calculate motor operating efficiency from measured electrical input and independently determined shaft output.
ElectricalIntermediate
Motors and Drives
VFD Frequency and Speed
Estimate loaded motor speed at a new VFD output frequency from a documented reference point.
ElectricalIntermediate
Transformers
Transformer Efficiency
Calculate transformer operating efficiency from useful output and entered no-load and load losses.
ElectricalBeginner
Transformers
Transformer Voltage Regulation
Quantify secondary-voltage change between documented no-load and loaded conditions using loaded voltage in the denominator.
ElectricalAdvanced
Short-Circuit Screening
Transformer Fault-Current Screen
Estimate transformer-limited balanced three-phase secondary fault current from rating, voltage, and nameplate impedance.
ElectricalIntermediate
Standby Power and Batteries
UPS Battery Runtime
Estimate ideal usable runtime from nominal DC energy, usable depth, conversion efficiency, and constant AC load.
ElectricalIntermediate
Standby Power and Batteries
Battery Capacity
Calculate ideal minimum amp-hour capacity for a constant AC load and required runtime.
ElectricalBeginner
Energy and Demand
Demand and Load Factor
Calculate demand factor, average demand, and load factor over a user-defined interval.
ElectricalBeginner
Energy and Demand
Demand Charge
Estimate simple demand charges from a user-entered billing demand, rate, and number of periods.
ElectricalBeginner
Lighting
Lighting Power Density
Calculate installed lighting power per evaluated floor area and display both W/ft² and W/m².
ElectricalBeginner
Lighting and Energy
Lighting Retrofit Savings
Estimate annual lighting demand, energy, and energy-only cost reduction from existing and proposed connected power.
ElectricalAdvanced
Power Quality
Total Harmonic Distortion
Calculate voltage or current THD from the fundamental RMS component and RSS harmonic content.
ElectricalIntermediate
Power Quality
Waveform Crest Factor
Calculate crest factor from peak and RMS magnitudes and compare it mathematically with √2.
ElectricalAdvanced
Metering and Instrumentation
CT/PT Meter Scaling
Calculate CT ratio, PT ratio, combined multiplier, and primary power or energy from an unscaled secondary reading.
ElectricalIntermediate
Metering and Instrumentation
Meter Pulse Energy
Convert counted meter pulses with a Wh-per-pulse constant into interval energy and average demand.
PlumbingBeginner
Load Inventory
Fixture-Unit Summation
Sum user-entered fixture counts and fixture-unit values without embedding a code table or converting the total to probable demand.
PlumbingIntermediate
Domestic Hot Water
Water-Heater Recovery
Estimate steady water-heater recovery from input rate, thermal efficiency, and temperature rise.
PlumbingIntermediate
Domestic Hot Water
Mixed-Water Storage Yield
Estimate ideal deliverable mixed-water volume from stored hot water and selected hot, cold, and delivery temperatures.
PlumbingIntermediate
Domestic Hot Water Recirculation
Recirculation Flow
Calculate steady recirculation flow required to carry a user-entered loop heat loss at an allowable temperature drop.
PlumbingBeginner
Domestic Hot Water Recirculation
Recirculation Heat Loss
Convert a documented linear pipe heat-loss rate and effective length into steady and annual heat loss.
PlumbingBeginner
Domestic Hot Water Field Verification
Hot-Water Delivery Time
Estimate ideal pipe displacement volume and delivery time from internal diameter, developed length, and fixture flow.
PlumbingBeginner
Sanitary and Storm Drainage
Gravity Drain Slope
Calculate pipe fall and slope from upstream and downstream invert elevations and horizontal run.
PlumbingAdvanced
Sanitary and Storm Drainage
Manning Drain Capacity
Estimate full-flow circular-pipe discharge and velocity using the Manning equation.
PlumbingIntermediate
Storm Drainage
Roof Drainage Flow
Convert tributary roof area and user-entered rainfall intensity into runoff flow before code-based drain sizing.
PlumbingIntermediate
Site and Storm Drainage
Rational Runoff
Estimate peak runoff from user-entered area, rainfall intensity, and runoff coefficient.
PlumbingIntermediate
Natural and Fuel Gas
Fuel-Gas Load and Flow
Sum user-entered appliance loads and convert diversified load to ideal gas volume flow using a user-entered heating value.
PlumbingBeginner
Natural and Fuel Gas
Gas-Meter Capacity Margin
Compare user-entered meter capacity with diversified design flow using a visible capacity factor.
PlumbingAdvanced
Domestic Water Pressure
Booster Pressure
Calculate preliminary booster pressure from supply pressure, required residual pressure, elevation, losses, and a visible user-entered margin.
PlumbingAdvanced
Domestic Water Pressure
PRV Setpoint
Calculate a preliminary PRV setpoint for an upper outlet and the resulting lower static-pressure screen.
PlumbingAdvanced
Domestic Hot Water
Storage and Recovery Balance
Convert a peak mixed-water draw to stored-hot-water demand and subtract recovery available during the peak interval.
PlumbingAdvanced
Sanitary Drainage Pumps
Sewage-Ejector Duty
Assemble a preliminary sewage-ejector flow and head duty point from visible user-approved inputs.
PlumbingAdvanced
Sump and Drainage Pumps
Sump-Basin Cycling
Estimate working drawdown volume, pump-on time, refill time, and starts per hour for a constant-area basin.
PlumbingAdvanced
Domestic Hot Water Field Verification
Recirculation Temperature Retention
Evaluate measured return temperature relative to supply and cold-water temperatures and calculate loop heat loss at measured flow.
PlumbingAdvanced
Domestic Hot Water Field Verification
Water-Heater Capacity Test
Calculate measured water-heating output, direct operating efficiency, and output relative to a user-entered schedule.
PlumbingAdvanced
Pump Field Verification
Plumbing-Pump Field Test
Combine measured flow, suction/discharge pressure, gauge elevation, specific gravity, and electrical input into a pump performance screen.
PlumbingAdvanced
Domestic Water Pressure
Water Loss Budget
Calculate the pressure allowance remaining for distributed pipe friction along a critical domestic-water path.
PlumbingAdvanced
Domestic Water Piping
Hazen–Williams Flow
Invert the Hazen–Williams relationship to estimate flow from diameter, length, C-factor, and available friction head.
PlumbingBeginner
Water-System Field Work
Pipe Flush Time
Calculate contained circular-pipe volume and ideal duration for a user-entered number of volume exchanges.
PlumbingIntermediate
Domestic Water Devices
Meter Loss Scaling
Scale a documented meter pressure-loss point to another flow using a visible user-entered exponent.
PlumbingBeginner
Domestic Water Devices
Backflow Loss Margin
Compare a documented backflow-device loss with the pressure allowance assigned to that device.
PlumbingIntermediate
Closed Water Systems
Thermal Expansion Volume
Calculate water-volume change from initial volume and user-entered initial and final densities.
PlumbingAdvanced
Closed Water Systems
Tank Acceptance
Estimate ideal tank acceptance between initial and maximum gauge pressures using absolute-pressure gas relationships.
PlumbingAdvanced
Pressure Transients
Water-Hammer Surge
Apply the ideal Joukowsky relationship to a user-entered density, wave speed, and signed velocity change.
PlumbingBeginner
Pressure Regulation
PRV Reduction
Calculate pressure drop, percent reduction, and inlet-to-outlet ratio for a documented PRV condition.
PlumbingBeginner
Domestic Hot Water
Draw Energy
Calculate ideal useful energy added to a documented hot-water draw volume.
PlumbingBeginner
Domestic Hot Water
First-Period Delivery
Add usable hot-water storage and recovery over a user-entered rating period.
PlumbingAdvanced
Domestic Hot Water Field Verification
Heater Standby Loss
Subtract useful delivered-water energy from measured input over a defined test boundary and duration.
PlumbingIntermediate
Domestic Hot Water
Tempering Valve Margin
Compare a design mixed-water flow with an effective user-derated tempering-valve capacity.
PlumbingIntermediate
Domestic Hot Water Recirculation
Recirculation Pump Head
Calculate signed pump head from suction/discharge pressures, gauge elevation difference, and fluid specific gravity.
PlumbingBeginner
Specialty Plumbing
Trap-Primer Demand
Calculate daily primer-water volume and water per design event from user-entered dose and schedule values.
PlumbingBeginner
Specialty Plumbing
Pure-Water Autonomy
Calculate constant-demand operating time from usable storage, reserve fraction, and average demand.
PlumbingIntermediate
Medical and Specialty Gas
Cylinder-Bank Duration
Calculate ideal constant-demand duration from cylinder count, standard gas volume, and a user-entered usable fraction.
PlumbingAdvanced
Medical and Specialty Gas
Receiver Evacuation
Estimate ideal isothermal evacuation time for a lumped receiver at constant effective pump speed.
PlumbingIntermediate
Water Reuse
Greywater Balance
Compare treated usable daily collection with nonpotable demand using a visible treatment-recovery factor.
PlumbingIntermediate
Specialty Drainage
Interceptor Retention
Calculate ideal hydraulic retention time from operating volume, effective-volume fraction, and constant peak flow.
PlumbingAdvanced
Sanitary and Storm Drainage
Part-Full Manning Flow
Calculate part-full circular-pipe flow from depth ratio, diameter, slope, and Manning roughness.
PlumbingBeginner
Sanitary and Storm Drainage
Drain Travel Time
Calculate ideal flow travel time from path length and user-entered mean velocity.
PlumbingIntermediate
Drainage Pumps
Duplex Pump Drawdown
Compare working-volume drawdown time with the lead pump and with both pumps operating.
PlumbingIntermediate
Roof Drainage
Roof Drain Area
Invert the roof-runoff relationship to screen tributary area from documented drain flow capacity and rainfall.
PlumbingBeginner
Stormwater
Rainfall Runoff Volume
Convert tributary area, storm depth, and runoff factor into a runoff volume.
PlumbingBeginner
Stormwater
Storm Capacity Utilization
Compare design storm flow with a separately established screened capacity.
PlumbingAdvanced
Roof Drainage
Scupper Weir Flow
Apply a generic rectangular-weir form using a user-entered coefficient, clear width, and head.
PlumbingIntermediate
Stormwater
Detention Storage Balance
Calculate net storage change from average inflow, average outflow, and event duration.
PlumbingIntermediate
Stormwater Pumps
Storm Pump Drawdown
Calculate constant-flow drawdown time from stored volume, continuing inflow, and pump flow.
PlumbingBeginner
Fuel Gas
Gas Equivalent Length
Sum straight length, two fitting groups, and a visible allowance without performing gas-pipe sizing.
PlumbingIntermediate
Fuel Gas
Gas Pressure Budget
Calculate gas-piping pressure-drop allowance after required downstream pressure and fixed losses.
PlumbingIntermediate
Fuel Gas
Combustion Air
Apply a visible user-entered air rate per heat input and design factor; no code rate is embedded.
PlumbingIntermediate
Compressed Air
Air Receiver Duration
Estimate ideal receiver support time between two gauge pressures at a constant net standard demand.
PlumbingAdvanced
Compressed Air
Air Leak Rate
Estimate ideal standard-air leak rate from isolated volume, gauge-pressure decay, atmosphere, and elapsed time.
PlumbingBeginner
Compressed Air
Air Pressure Ratio
Calculate inlet-to-outlet absolute pressure ratio and percent pressure reduction.
PlumbingIntermediate
Liquid Fuels
Fuel-Oil Consumption
Calculate liquid fuel use from useful heat rate, conversion efficiency, and user-entered heating value.
PlumbingBeginner
Liquid Fuels
Day-Tank Runtime
Calculate constant-demand runtime from tank volume, usable fraction, reserve fraction, and fuel demand.
PlumbingIntermediate
Liquid Fuels
Propane Consumption
Calculate liquid-propane use from useful heat rate, conversion efficiency, and user-entered heating value.
PlumbingAdvanced
Fuel Gas Field Work
Gas-Pipe Purge Time
Calculate straight-pipe contained volume and ideal time for user-entered purge volume exchanges and flow.
PlumbingIntermediate
Medical and Specialty Gas
Gas-Pipe Velocity
Calculate mean pipe velocity from actual volumetric flow at pipe conditions and actual internal diameter.
CommissioningBeginner
Acceptance Arithmetic
Acceptance Band
Convert a target and user-entered percent tolerance into lower and upper arithmetic endpoints.
CommissioningIntermediate
Acceptance Arithmetic
Multi-Point Tolerance
Calculate three signed deviations, worst deviation, and count within a visible user-entered tolerance.
CommissioningIntermediate
Instrumentation
Sensor-Pair Agreement
Calculate signed, absolute, and relative difference between two synchronized readings.
CommissioningBeginner
Instrumentation
Sensor Drift Rate
Calculate signed change and average drift rate between two documented readings.
CommissioningIntermediate
Instrumentation
Instrument Hysteresis
Calculate upscale/downscale indication difference and percent of entered instrument span.
CommissioningIntermediate
Instrumentation
Square-Root Extraction
Convert differential-pressure signal percent to ideal flow percent and flow using the square-law relationship.
CommissioningAdvanced
Measurement Quality
Test Uncertainty Ratio
Calculate the ratio of an entered allowable tolerance magnitude to an entered expanded uncertainty magnitude.
CommissioningBeginner
Data Reduction
Median of Five
Sort five entered observations and report the middle value, minimum, and maximum.
CommissioningBeginner
Data Reduction
Weighted Average
Calculate a weighted average from three values and three nonnegative user-entered weights.
CommissioningIntermediate
Data Reduction
Coefficient of Variation
Calculate mean, sample standard deviation, and sample coefficient of variation for four values.
CommissioningBeginner
Data Reduction
Root Mean Square
Calculate RMS magnitude and arithmetic mean for four user-entered values.
CommissioningBeginner
Data Reduction
Root Sum Square
Combine four orthogonal or independent magnitude components by root-sum-square arithmetic.
CommissioningBeginner
Trend Analysis
Percent Change
Calculate signed absolute and percent change relative to the magnitude of a nonzero initial value.
CommissioningBeginner
Trend Analysis
Rate of Change
Calculate signed change per minute between two documented values.
CommissioningIntermediate
Trend Analysis
Three-Point Trend
Calculate the least-squares slope for three equally spaced values and the fitted middle value.
CommissioningIntermediate
Trend Analysis
Trapezoidal Total
Integrate three equally spaced rate samples by the trapezoidal rule.
CommissioningBeginner
Runtime and Cycling
Duty Cycle
Calculate on-time percentage and off time over a documented observation interval.
CommissioningBeginner
Runtime and Cycling
Cycle Rate
Calculate cycles per hour and mean minutes per cycle from count and observation duration.
CommissioningIntermediate
Controls Verification
Response Latency
Calculate clock-corrected latency from command and response timestamps and a signed offset correction.
CommissioningBeginner
Commissioning Management
Completion Forecast
Forecast remaining time from completed items, total items, and elapsed time at the observed average production rate.
CommissioningBeginner
Layout and Elevations
Invert from Slope
Calculate downstream invert from upstream invert, signed slope ratio, and horizontal run.
CommissioningBeginner
Layout and Elevations
Elevation Transfer
Transfer elevation from a benchmark using backsight and foresight readings.
CommissioningBeginner
Concrete and Grout
Equipment Pad Volume
Calculate rectangular equipment-pad concrete volume from plan dimensions and thickness.
CommissioningBeginner
Concrete and Grout
Concrete Quantity
Calculate net rectangular volume for repeated elements and add a visible waste allowance.
CommissioningBeginner
Concrete and Grout
Base Grout Volume
Calculate net rectangular grout volume under a base using a visible void fraction.
CommissioningBeginner
Material Quantities
Pipe Insulation Area
Calculate circular outer surface area over developed length with a visible fitting allowance.
CommissioningBeginner
Ductwork Quantities
Round-Duct Sheet Area
Calculate round-duct lateral sheet area over developed length with a visible fitting allowance.
CommissioningBeginner
Ductwork Quantities
Rectangular Duct Area
Calculate four-side rectangular-duct sheet area with a visible allowance.
CommissioningIntermediate
Ductwork Layout
Transition Corner Slant
Calculate maximum corner slant for a centered rectangular transition.
CommissioningBeginner
Pipe Layout
Pipe Offset Travel
Calculate ideal centerline travel and setback for a single-plane offset and fitting angle.
CommissioningIntermediate
Pipe Layout
Rolling Offset Travel
Calculate true offset, ideal travel, and setback from two perpendicular offsets and fitting angle.
CommissioningBeginner
Pipe Layout
Pipe Cut Length
Subtract two fitting takeouts from center-to-center length and add a visible signed cut allowance.
CommissioningBeginner
Electrical Field Quantities
Wire-Pull Length
Add horizontal and vertical route, visible slack percentage, and two termination allowances.
CommissioningIntermediate
Electrical Field Quantities
Conduit Fill
Calculate cable-area fill and compare it only with a visible user-entered criterion; no code table is embedded.
CommissioningIntermediate
Electrical Field Quantities
Tray Width Utilization
Calculate single-layer cable-width utilization from user-entered cable widths and usable tray width.
CommissioningBeginner
Supports and Layout
Hanger Count
Calculate arithmetic support count from effective run length, maximum spacing, and equal end offsets.
CommissioningBeginner
Supports and Layout
Support Spacing
Calculate equal interval spacing from supported length and a whole-number support count.
CommissioningIntermediate
Construction Progress
Weighted Completion
Calculate overall completion from three work-package percentages and visible weights.
CommissioningBeginner
Construction Progress
Punch-List Age
Calculate count-weighted average age for three punch-list age groups.
CommissioningAdvanced
Equipment Curves
Curve Interpolation
Evaluate the quadratic passing through three distinct user-entered curve points by Lagrange interpolation.