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Complete worked lessons. Every step visible.

Choose your exam, inspect the governing method, check an application and test a changed condition. Selected examples include original narration. HVAC lessons pair equipment illustrations with calculation schematics. The PMP preview includes the full first core workshop. No account or payment is required.

PE Architectural Engineering

Narrated worked lesson: Fan affinity laws: check airflow, pressure and motor power

3 minutes 8 seconds video · Suggested 20 minutes for the complete lesson

Fan affinity laws: check airflow, pressure and motor power

Work a fan speed change using one consistent ratio, test the cubic shaft-power demand against a motor limit, and recognize when the installed system needs a new curve intersection.

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Narrated worked lesson: Parallel pumps: solve total flow at the system operating point

3 minutes 4 seconds video · Suggested 22 minutes for the complete lesson

Parallel pumps: solve total flow at the system operating point

Combine two identical pump curves at a common head, solve the actual system intersection, and distinguish total system flow from each pump's flow.

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Narrated worked lesson: Power-factor correction: upstream current and real power

3 minutes 9 seconds video · Suggested 20 minutes for the complete lesson

Power-factor correction: upstream current and real power

Convert real power to apparent power and upstream line current, calculate ideal shunt compensation, and preserve the distinction between supply current and load energy.

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Narrated worked lesson: Roof tributary width: line load, reactions and bending

3 minutes 5 seconds video · Suggested 22 minutes for the complete lesson

Roof tributary width: line load, reactions and bending

Translate roof area load into beam line load, include beam self-weight once and connect equilibrium to shear and moment diagrams.

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Narrated worked lesson: Critical-path changes: activity delay versus project delay

2 minutes 59 seconds video · Suggested 20 minutes for the complete lesson

Critical-path changes: activity delay versus project delay

Calculate each required path, respect the installation merge and distinguish an activity-duration increase from its effect on project completion.

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Written worked lesson · Suggested 20 minutes for the complete lesson

Resolve feeder capacity and equipment access together

Convert three-phase apparent power into current, then compare independent electrical and spatial constraints without trading away either one.

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PE Civil Construction

For Construction Operations and Methods, also work the earthwork and truckload example →

Narrated worked lesson: Water-table rise: total stress versus effective stress

2 minutes 34 seconds video · Suggested 20 minutes for the complete lesson

Water-table rise: total stress versus effective stress

Measure pressure head below the water table, then subtract pore pressure once.

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Narrated worked lesson: Level-loop closure: check a benchmark before using elevations

2 minutes 36 seconds video · Suggested 20 minutes for the complete lesson

Level-loop closure: check a benchmark before using elevations

Add backsights, subtract foresights, and check the independent loop closure.

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Narrated worked lesson: Moisture and density: use dry mass and total specimen volume

2 minutes 40 seconds video · Suggested 20 minutes for the complete lesson

Moisture and density: use dry mass and total specimen volume

Water content uses dry-solids mass; dry density uses the full specimen volume.

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Narrated worked lesson: Concrete takeoff: net volume, waste and purchased cost

2 minutes 42 seconds video · Suggested 22 minutes for the complete lesson

Concrete takeoff: net volume, waste and purchased cost

Keep net installed volume, waste allowance and purchased quantity separate.

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Narrated worked lesson: Procurement delay: recover time on the controlling path

2 minutes 34 seconds video · Suggested 22 minutes for the complete lesson

Procurement delay: recover time on the controlling path

Recompute the merge and controlling path before selecting a recovery action.

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Narrated worked lesson: Compaction acceptance: compare dry density and moisture separately

2 minutes 41 seconds video · Suggested 20 minutes for the complete lesson

Compaction acceptance: compare dry density and moisture separately

A wet-density reading cannot be compared directly with a dry laboratory maximum.

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Narrated worked lesson: Off-center construction load: reactions and peak bending

2 minutes 29 seconds video · Suggested 22 minutes for the complete lesson

Off-center construction load: reactions and peak bending

Solve both force and moment equilibrium; equal reactions occur when the total vertical-load resultant is at midspan.

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Narrated worked lesson: Mixed land cover: area-weighted Rational-method runoff

2 minutes 41 seconds video · Suggested 22 minutes for the complete lesson

Mixed land cover: area-weighted Rational-method runoff

Weight runoff coefficients by contributing area, then convert rainfall and area consistently.

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Narrated worked lesson: Shore tributary load: compare the full supplied axial demand

2 minutes 34 seconds video · Suggested 22 minutes for the complete lesson

Shore tributary load: compare the full supplied axial demand

Convert slab thickness to feet and multiply total area load by the interior shore tributary area.

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Narrated worked lesson: Trench egress: maximum travel and post-rain inspection

2 minutes 33 seconds video · Suggested 22 minutes for the complete lesson

Trench egress: maximum travel and post-rain inspection

Check lateral travel to safe egress, not ladder count, and reassess changing conditions.

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Written worked lesson · Suggested 18 minutes for the complete lesson

From pressure and elevation to electrical pump power

Build an SI energy balance, distinguish hydraulic output from electrical input, and test how a changed boundary affects the result.

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ARE 5.0 Project Development and Documentation (PDD)

Three narrated examples cover ceiling coordination, window-head control layers and an offset-column load path. Each includes captions, a transcript and an application check.

Narrated worked lesson: Coordinate a gravity pipe within a ceiling zone

1 minute 15 seconds video · Suggested 20 minutes for the complete lesson

Coordinate a gravity pipe within a ceiling zone

Combine slope, physical service depth and clearance into a coordinated section; select a change that preserves structural and ceiling requirements.

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Narrated worked lesson: Window-head continuity: keep water, air and thermal control separate

1 minute 18 seconds video · Suggested 20 minutes for the complete lesson

Window-head continuity: keep water, air and thermal control separate

Trace each control function through a window head and document the transition that restores the failed drainage path.

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Narrated worked lesson: Offset-column transfer: trace the load before coordinating the detail

1 minute 10 seconds video · Suggested 22 minutes for the complete lesson

Offset-column transfer: trace the load before coordinating the detail

Identify the load-path discontinuity, check a simplified reaction model and request the information needed to coordinate the transfer zone.

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PMP

Watch two narrated project-management decision scenarios: evaluate a requested change and compare schedule-recovery options using value, cost, quality, risk and the stated approval authority. The complete first core workshop is also available below.

Narrated worked lesson: Evaluate a requested change before authorizing work

3 minutes 4 seconds video · Suggested 20 minutes for the complete lesson

Evaluate a requested change before authorizing work

Evaluate a requested change using complete impact evidence, alternatives and the project's stated approval authority.

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Narrated worked lesson: Choose schedule recovery using current impacts and risk

3 minutes 15 seconds video · Suggested 20 minutes for the complete lesson

Choose schedule recovery using current impacts and risk

Compare schedule-recovery options using the current controlling branch, feasibility, cost, quality, risk and approval authority.

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Written worked lesson · Suggested 90 minutes for the complete lesson

Separate a delivered output from an achieved benefit

Explain why delivering an output and realizing a benefit are different achievements.

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PE Mechanical: HVAC and Refrigeration

Free development preview. All 24 foundation lessons include worked calculations, common errors, handbook navigation and an application check. Paid enrollment is closed.

A realistic cutaway air handler shows outdoor and return inlets joining in a mixing plenum upstream of a coil and fan.

Free foundation lesson · Equipment illustration and schematic

Air mixing and sensible processes

Two air streams combine through conservation of dry air, moisture and energy. A volume fraction is a mass fraction only under suitable density assumptions.

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A realistic closed hydronic circuit connects one low circulation pump to an elevated coil and a return riser, with an expansion vessel near suction.

Free foundation lesson · Equipment illustration and schematic

Hydronic flow, piping and system head

Thermal capacity sets hydronic flow; the pressure-loss network sets pump head. Elevation means different things in open and closed systems.

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A realistic double-pipe exchanger cutaway reveals separate inner-tube and annular flow passages and four fluid connections.

Free foundation lesson · Equipment illustration and schematic

Heat exchangers

Use flow arrangement, capacity rate and area basis to select a defensible heat-transfer method.

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Explore all 24 HVAC lessons → · Inspect HVAC technical review status

Suggested time is a study estimate. Public previews do not award training hours or certificate completion.