Mechanical Engineering StudioIPC Plumbing · NFPA 13 Sprinkler · PE Mechanical Prep · Simulators · Calculations

Applied Mechanical Engineering Professional Program

Interactive Darcy-Weisbach pipe flow simulator. Select pipe material (copper Type L/K, Schedule 40/80 steel, PVC, CPVC), nominal diameter, flow rate, and run length. The simulator calculates Reynolds number, Moody friction factor (laminar, transition, or turbulent regime), and friction head loss per 100 ft. Add fittings (elbows, tees, gate/globe/ball valves, reducers) via K-factor method to compute total minor losses. A real-time comparison table shows pressure drop and velocity across all standard pipe sizes simultaneously — so you can instantly see which size hits your target velocity (2–4 fps recommended) and stays within your pressure budget.

Step-through NFPA 13 hydraulic calculation for a branch-line sprinkler system using the density/area method. Configure hazard occupancy (Light, OH-1, OH-2, EH-1, EH-2), design area, density (gpm/sq ft), system pressure, and pipe material. The simulator walks through the most-remote-area hydraulic calc: starts at the most demanding sprinkler, applies K-factor flow at each head (Q = K√P), accumulates flow and pressure loss along the branch line and cross main using the Hazen-Williams equation, adds hose stream allowance per occupancy, and plots the final system demand point (GPM @ PSI) against a water supply curve. Pass/fail verdict against available system pressure.

Simulate a closed-loop hydronic heating system end-to-end. Configure boiler output (BTUH), supply and return water temperatures (ΔT), and terminal unit type (fin-tube baseboard, fan coil, radiant panel). The simulator calculates system flow rate (GPM = BTUH ÷ (500 × ΔT)), sizes the circulating pump (TDH from pipe losses and fittings), and sizes the expansion tank per ASME. An animated loop diagram shows water temperature dropping from supply (hot/red) to return (cool/blue) as it releases heat at each terminal unit. Real-time checks flag minimum velocity (0.5 fps), maximum velocity (4 fps), and pump operating point against a simplified system curve.

Interactive steam distribution simulator covering low-pressure (≤15 psi), medium-pressure (15–100 psi), and high-pressure (100–300 psi) systems. Configure boiler output (lb/hr or BTUH), operating pressure, and a 4-branch distribution layout. The simulator sizes supply mains and branch pipes from ASME steam tables, calculates pressure drop and velocity at each segment, and checks steam velocity limits (4,000–6,000 fpm for supply, 1,500–2,500 fpm for wet return). An animated one-line diagram shows steam flowing from the boiler header through supply mains, through steam traps at each branch takeoff, and returning as condensate via gravity return or condensate pump. Steam trap type selection (float & thermostatic, thermodynamic, inverted bucket) with load calculation per branch.

Visualize hydraulic transients (water hammer) using the Joukowsky equation: ΔP = ρ·a·ΔV, where wave speed a varies by pipe material (copper ≈ 4,400 fps, steel ≈ 4,860 fps, PVC ≈ 1,400 fps, HDPE ≈ 1,200 fps). Configure pipe material, diameter, flow velocity, pipe length, and valve closure time. An animated SVG shows the pressure wave propagating from the closed valve back to the source. The simulator calculates peak surge pressure (psi), compares it to the pipe pressure rating, determines whether closure is "instantaneous" (t_close < 2L/a — the critical threshold), calculates the wave return period (2L/a), and recommends a pressure relief valve set pressure or surge arrester pre-charge pressure to protect the system.

Simulate domestic water demand for a multi-story building using the IPC Hunter's Curve probability method. Configure building type (office, hotel, hospital, multifamily residential), number of floors (up to 20), and fixture types and counts per floor. The simulator aggregates Water Supply Fixture Units (WSFU) floor-by-floor from the top down, converts to peak design GPM using Hunter's Curve, sizes the service entrance pipe, and calculates static pressure loss due to elevation (0.433 psi/ft of height). A results panel shows whether available street pressure (configurable from 40–120 psi) is sufficient to reach the top floor with required residual pressure, or whether a booster pump is needed — and if so, calculates required pump head (ft) and minimum pressure at the pump discharge.

Interactive statics simulator covering classical mechanical engineering fundamentals — the first entrant in this studio beyond plumbing/HVAC. Select a simply-supported beam, cantilever beam, or 2D truss joint, adjust applied point loads and distributed loads via sliders, and watch a live free body diagram redraw with correctly scaled, correctly directed force and moment arrows. Reaction forces (or truss member forces) solve in real time from static equilibrium: ΣFx = 0, ΣFy = 0, ΣM = 0, with pin/roller/fixed support symbols and a tension/compression call-out for the truss joint method of joints.

Apply a real tensile force to a round rod of selectable material (mild steel, structural steel, aluminum, copper, or titanium), diameter, and length. The simulator computes stress σ = F/A and strain ε from a bilinear elastic-plastic material model, animates the rod actually elongating proportionally (exaggerated for visibility), and moves an operating-point marker live along the material's σ-ε curve — flagging the moment the rod crosses from fully recoverable elastic deformation into permanent yielded set. A load-to-deformation simulator, distinct from the multi-material curve-education tool in the Civil & Structural studio.

Draws the true deflected shape of a simply-supported or cantilever beam under a point load or uniform load, computed point-by-point from the real Euler-Bernoulli beam deflection equation for each case (δmax = PL³/48EI, PL³/3EI, 5wL⁴/384EI, wL⁴/8EI) — not a simplified straight-line sketch. Select material and moment of inertia, adjust span and load with sliders, and get a live max-deflection readout plus a pass/fail check against the common L/360 serviceability limit.

Interactive ideal air-standard Otto cycle P-V diagram. Adjust compression ratio and heat input to redraw all four processes using real isentropic (Pv^γ = const) and constant-volume ideal-gas relations — isentropic compression, constant-volume heat addition, isentropic expansion, and constant-volume heat rejection — with each state point's temperature and pressure computed live. Thermal efficiency η = 1 − 1/r^(γ−1) updates instantly, alongside heat added, heat rejected, and net work per unit mass.

Animated simple or compound external gear train (1-3 meshing stages). Set driver/driven teeth counts per stage and watch the gears actually rotate at the correct relative speed via a requestAnimationFrame-driven animation, with direction reversing at each external mesh. Computes output RPM, overall gear ratio, output torque (input torque × ratio × compounded mesh efficiency), and final rotation direction relative to the input — plus a per-stage breakdown table.

Interactive venturi-style constriction simulator. Adjust inlet and throat pipe diameter, inlet velocity, inlet pressure, and elevation change, and watch continuity (A₁V₁=A₂V₂) and Bernoulli's equation (P₁+½ρV₁²+ρgh₁ = P₂+½ρV₂²+ρgh₂) compute the throat velocity and pressure live. An animated flow diagram shows particles accelerating through the constriction with a pressure-gradient overlay, plus a cavitation-risk warning if throat pressure approaches vapor pressure.

Real-time RK4 numerical integration of the single-degree-of-freedom equation m·x″+c·x′+k·x = F₀cos(ωt). Adjust mass, spring stiffness, damping coefficient, initial displacement, and forcing amplitude/frequency, and watch the mass oscillate on an animated schematic while a live displacement-vs-time chart plots the response. Computes natural frequency ωₙ=√(k/m), damping ratio ζ=c/(2√(km)), damped frequency ωd, and flags near-resonance forcing.

Tune Kp, Ki, and Kd gains for a closed-loop DC motor speed controller against a first-order motor plant (τ·ω′+ω = K·u), integrated numerically with anti-windup. A tachometer gauge and live step-response chart show the speed climbing to a setpoint step change, with rise time, overshoot, settling time, and steady-state error computed in real time — a standard controls-education exercise.

Set the ground, crank, coupler, and rocker link lengths and watch the planar four-bar mechanism animate through its range of motion, solved via vector-loop circle-circle intersection at every position. Traces the coupler-point path curve live, and automatically classifies the linkage per the Grashof criterion (s+l ≤ p+q) as a crank-rocker, double-crank, double-rocker, or non-Grashof triple-rocker.

Inspect a detailed twin-pump station, open the impeller cutaway, operate connected pump curves and diagnose faults. Run parallel capacity, standby transfer and matched-flow energy tests.

Interactive 3D V8 four-stroke engine with real slider-crank piston kinematics, cross-plane crankshaft, firing order tracking, live chamber pressure, valve lift, and a P-V indicator diagram.

Interactive 3D walkthrough of mechanical rooms, pipe runs, pump layouts, and sprinkler systems.

Real, procedural step-by-step workflows for SolidWorks — assembly design and FEA simulation setup, with exact menu names, dialog boxes, and settings.

Real, procedural step-by-step workflows for ANSYS Mechanical — structural FEA setup and thermal simulation, with exact menu names, dialog boxes, and settings.

IPC Table 604.3 pipe sizing from water supply fixture units (WSFU). Hunter's curve GPM estimate, velocity check, and recommended pipe diameter.

Tally WSFU and DFU for 12 fixture types. Running totals for sizing water supply and drainage systems per IPC.

Brake horsepower from GPM, TDH, SG, and pump efficiency. Selects next standard NEMA motor size. Pipe velocity check included.

LMTD method for shell & tube, plate, gasketed plate, and brazed plate HX. Outputs LMTD, required area, and U-value range.

Capacity lookup table for low, medium, and high pressure steam. Selects pipe size from lb/hr demand per ASME/industry tables.

Darcy-Weisbach pressure drop for compressed air. Comparison table across pipe sizes with pass/fail velocity check.

ASME expansion tank sizing for closed hydronic systems. Expansion factor, system volume, and next standard tank size.

NFPA 13 density/area method for 6 hazard classes. Total demand GPM, hose allowance, and residual pressure requirement.

Convert between HP, kW, and torque at any RPM. Quick-select common motor speeds. Motor sizing with 10% service factor.

Reynolds number and velocity check for 6 meter types: turbine, vortex, magnetic, ultrasonic, orifice plate, and Coriolis.

Searchable, filterable reference table of standard material properties — density, Young's modulus, yield/ultimate strength, Poisson's ratio, thermal conductivity, and CTE — for steel, stainless, aluminum, cast iron, copper alloys, titanium, plastics, concrete, and wood, with a side-by-side comparison view.

ISO 281 / ABMA basic rating life for ball and roller bearings. Enter dynamic load rating C, applied load P, and speed to get L10 in millions of revolutions and hours, with illustrative presets.

Required installation torque for a target preload using T = K × D × F. Nut factor presets for dry, lubricated, and galvanized conditions, plus an optional SAE/metric bolt-grade assist.

Stress is the cause (internal force per unit area). Strain is the effect (the resulting deformation). Illustrated breakdown of what each one actually measures, and the stress-strain curve that connects them.

The idealized venturi case where pressure drops as velocity rises, side by side with a real pipe where friction alone drops pressure — no area change required. Why Bernoulli needs a head-loss term in the real world.

Why parts break well below their yield strength. The S-N curve, crack initiation at a stress concentration, and why steel/titanium show a true endurance limit while aluminum never flattens out.

Why some vibrations grow out of control. Natural frequency ωₙ = √(k/m), how resonance builds amplitude, and how the damping ratio ζ separates underdamped, critically damped, and overdamped response.

Same name, similar-looking formula, two unrelated physical quantities. I = ∫r²dm resists angular acceleration (T = Iα); I = ∫y²dA resists bending (σ = My/I) — one is dynamics, the other is pure cross-section geometry.

The deliberate gap between mating teeth that keeps gears from binding as they heat up — and the real 'dead zone' positioning error it creates every time a gear train reverses direction.

Why a small hole or fillet can locally multiply stress far above the simple F/A average — and why the same geometric notch is a minor detail in one material and a fatigue crack's origin in another.

Why the same tensile test produces two different curves — one that appears to drop after the ultimate strength, and one that keeps climbing all the way to fracture.

"Not moving" and "not accelerating" are different things. Why a stationary block and a car cruising at a constant 60 mph satisfy the exact same ΣF = 0, ΣM = 0 equilibrium equations.

Why a spinning wheel doesn't tilt where you push it. Angular momentum is a vector — τ = dL/dt means a torque perpendicular to the spin axis makes it precess sideways, not tip over.

The wrench reading isn't the thing that matters — the actual tension it creates in the bolt is. Why T = K·D·F makes torque a friction-dependent proxy for preload, with ±25-30% scatter common even with a calibrated wrench.

Why a high-torque engine and a high-power engine aren't the same thing. P = T·ω means the identical peak horsepower rating can come from huge torque at low RPM or modest torque at high RPM — and torque/power curves always cross at 5,252 RPM.

Interactive 13-section PE Mechanical exam reference covering thermodynamics, fluid mechanics, heat transfer, machine elements, dynamics, materials, HVAC, pressure vessels, and turbomachinery. First 3 free to preview.

An 8-chapter illustrated guide opening with a worked chilled-water HVAC example, then covering shaft torsion/shear stress, fillet weld design, weld distortion control, spring design, ISO 286 fits and tolerances, heat exchanger LMTD, and equal-friction duct sizing. First 3 free to preview.

Zoomable 36-sheet belt conveyor system design drawing set — layout & arrangement, drive system, belt/pulley/idler layout, structural supports, take-up & tensioning, safety/guarding, engineering calculations, and bill of materials. Sheets 1-4 free to preview.

Full HVAC load/equipment/airflow + ASHRAE 62.1 ventilation, plumbing fixture units & pipe sizing (IPC), hydronic heating, fire sprinkler density/area (NFPA 13), fuel gas (IFGC/NFPA 54), mechanical schematic, and permit-ready package.