Practice
Worked Problems & Engineering Challenges
Solved engineering problems with every step shown, plus short challenges where you find the mistake before opening the answer. Each page lists the given data, the method, the answer and the usual errors.
See the problemsElectrical & Power
Size the Branch Circuit for a 40 hp, 460 V Motor
Conductor size, breaker, overload setting and disconnect rating for a 40 hp, 460 V, 3-phase induction motor, using NEC Article 430 tables.
Voltage Drop on a 240 V Single-Phase Feeder
Calculate percent voltage drop for a 50 A load 150 ft from the panel and choose a conductor that meets the 3% guideline.
Office Lighting Load: Connected Power and Current
A short project: total the connected lighting power for three spaces, convert to apparent power and estimate the current, then write the calculation up so another engineer can check it.
Challenge: The Current That Looks Too High
An engineer calculates a three-phase line current as 37.5 A for a 12 kW load. Find the error before opening the answer.
Size a Three-Phase Transformer for a Mixed Load
Total the connected kVA of lighting, receptacle, HVAC and miscellaneous loads, add growth, choose a standard kVA rating, and find the primary and secondary full-load currents.
Power Factor Correction: How Many kvar of Capacitors?
Find the capacitor kvar needed to raise a 500 kW load from 0.80 to 0.95 power factor, and the drop in apparent power and line current.
Short-Circuit Current at a Transformer Secondary
Estimate the available fault current on the secondary of a 500 kVA, 480 V transformer with 5.75% impedance, assuming an infinite bus.
Mechanical, HVAC & Fluids
Pump Head, Shaft Power and Motor Size
Total dynamic head, hydraulic and shaft power, and a standard motor size for water at 20 L/s through 100 m of 150 mm pipe.
Sensible Cooling Capacity from Airflow and Temperature Difference
Use Q = 1.08 × CFM × ΔT to find the sensible cooling delivered by 2,000 CFM of air at a 20 °F temperature drop, and convert it to tons.
Chilled-Water Flow Rate from Load and Delta-T
Use GPM = 24 × tons ÷ ΔT to find the chilled-water flow for a 120-ton load at a 10 °F temperature rise.
Counterflow Heat Exchanger: Log-Mean Temperature Difference
Calculate the LMTD and the heat duty of a counterflow exchanger with hot fluid cooling from 150 °C to 90 °C and cold fluid heating from 30 °C to 70 °C.
Controls & Instrumentation
4-20 mA Signal Scaling for a Pressure Transmitter
Convert a 4-20 mA reading to engineering units for a 0 to 10 bar transmitter, and work backward to the expected current for a given pressure.
Control Valve Sizing: Calculate Cv for a Water Line
Calculate the flow coefficient Cv for 100 GPM of water across a 25 psi pressure drop, and see how Cv changes with flow and pressure drop.
Fire Protection
Sprinkler Flow from K-Factor and Pressure
Use Q = K × √P to find the flow from a K-5.6 sprinkler at 7 psi and the density it delivers over a 130 ft² coverage area.
Fire Alarm Control Panel Battery Calculation
Size the standby battery for a fire alarm panel with 0.5 A standby and 2.5 A alarm current, using a 24-hour standby period and 5 minutes of alarm.
How these pages work
Read the given data
Each problem states its inputs, units and assumptions up front.
Try it first
Work the problem on paper before reading the steps.
Compare your method
Check each step, not just the final number.
Check the usual errors
Every page lists the mistakes that most often cause a wrong answer.
Questions
Are these real design calculations?
No. They use simplified inputs to teach the method. A real design needs the actual project data and the codes adopted where it is built.
Which code edition is used?
Electrical examples use NEC 2023 table values. Your jurisdiction may have adopted a different edition, so check it.
Do the pages link to calculators?
Yes. Each problem links to the calculator or lab that does the same job. Those tools are part of the All-Access Pass.
Educational material. Examples use simplified, hypothetical inputs and are not a design, a construction document or professional engineering advice. Confirm requirements with the codes and standards adopted where the work is built and with a licensed engineer.
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