mech 472.

Exam 2 · Thu Oct 15, 4:00 pm · MEB 128 · mostly circuits

The deep end of the widget. Every problem is modeled on a real Exam 2 question (F19 to F25) or one of your HW 5 to 9 quizzes, with fresh numbers. Work it on paper, type the number, then check.

topic

exam sim 75:00

equation sheet (build your real one from this: front and back, letter size)

	flow	potential	power	resistor	capacitor	inductor
electrical	I = dq/dt	V	VI	V = IR	I = C dV/dt	V = L dI/dt
mechanical	ẋ	F	Fẋ	F = Bẋ	spring, C ↔ 1/k	mass, F = m dẋ/dt
fluidic	Q	ΔP	ΔP·Q	W = 128μL/(πD⁴)	X = A/(ρg)	Y = 4ρL/(πD²)
thermal	q_th	ΔT	q_th itself	L/(kA), 1/(hA)	C_th = mc_p	none (2nd law)

RC step: x(t) = x∞(1 − e^(−t/τ)), τ = RC ↔ WX ↔ B/k ↔ R_th C_th. Half-way at τ ln 2, 95% at 3τ.
RL step: I = (V/R)(1 − e^(−Rt/L)), starts at 0. τ = L/R ↔ m/B ↔ Y/W.
LC: ω = 1/√(LC) ↔ √(k/m). Period 2π√(LC); +V_max to −V_max is π√(LC). ζ = B/(2√(km)), f_d = f_n√(1 − ζ²).
Re = 4ρQ/(πDμ), laminar under ~2,300. Turbulent (Blasius): ΔP = 0.241 μ^0.25 ρ^0.75 L Q^1.75 / D^4.75.
Kirchhoff: Σ flows at a node = 0; Σ potential drops around a loop = 0. Hardy Cross: add dQ to every pipe in a loop.
Lumped: Bi = h(V/A_s)/k ≪ 0.1. τ = ρcV/(hA_s). θ/θ₀ = e^(−t/τ). Cube: V/A_s = s/6.
Stokes: F = 6πμRv, v_t = 2ρgR²/(9μ). Exam 1 carry-ins: NPV, IRR, payback, P = VI and kWh.