IESL Part II Mechanical flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Otto cycle efficiency

Thermal efficiency of the ideal Otto cycle is η = 1 − 1/r^(γ−1), where r is the compression ratio and γ is the specific heat ratio. Higher compression ratio raises efficiency.

Diesel cycle cutoff ratio

The cutoff ratio ρ = V3/V2 in an ideal Diesel cycle. Setting ρ = 1 makes the Diesel efficiency formula collapse to the Otto result, since heat addition becomes isochoric.

Carnot efficiency limit

No heat engine operating between hot and cold reservoirs can exceed η = 1 − T_L/T_H, with absolute temperatures. The limit is approached only by reversible cycles.

Steady-flow energy equation

For a steady control volume, q − w = Δh + ΔKE + ΔPE per unit mass. In an adiabatic nozzle with no work, stagnation enthalpy stays constant along the flow.

Isentropic ideal-gas relation

For an ideal gas with constant specific heats undergoing an isentropic process, T2/T1 = (p2/p1)^((γ−1)/γ) and p2/p1 = (v1/v2)^γ.

Plane wall conduction resistance

Thermal resistance of a plane wall is R = L/(kA). Resistances in series add, and heat rate equals the temperature difference divided by total resistance.

Log-mean temperature difference

ΔT_lm = (ΔT1 − ΔT2)/ln(ΔT1/ΔT2), where ΔT1 and ΔT2 are terminal temperature differences in a heat exchanger. Heat transfer rate equals U·A·ΔT_lm·F.

Reynolds number regimes

Re = ρVD/μ for internal pipe flow. Flow is generally laminar below about 2300 and turbulent above about 4000, with a transition region between these values.

Dittus-Boelter correlation

Nu = 0.023·Re^0.8·Pr^n for turbulent flow in smooth tubes, with n = 0.4 when heating the fluid and n = 0.3 when cooling it.

Bernoulli equation

For steady, incompressible, frictionless flow along a streamline, p/ρg + V²/2g + z is constant. Pump head is added, while turbine and friction heads are subtracted.

Shaft power from torque

Power transmitted by a rotating shaft is P = T·ω = 2πNT, where ω is in rad/s. If speed N is given in rev/min, use P = 2πNT/60.

Compound gear train ratio

Speed ratio of a compound train equals the product of driving tooth numbers divided by the product of driven tooth numbers. Torque ratio is the inverse of speed ratio.

Endurance limit applicability

Steels exhibit an endurance limit below which fatigue life is effectively infinite, typically near 10⁶–10⁷ cycles. Aluminium alloys do not show a true endurance limit.

Von Mises equivalent stress

For plane stress, σ' = √(σx² − σxσy + σy² + 3τxy²). Ductile yielding is predicted when this equivalent stress reaches the tensile yield strength.

Torsional shear stress

Solid circular shaft: τ_max = 16T/(πd³). Hollow shaft: τ_max = 16T·d_o/(π(d_o⁴ − d_i⁴)), where d_o and d_i are outer and inner diameters.

Euler column buckling load

P_cr = π²EI/(KL)², where K depends on end conditions: K = 1 for pin-ended, 0.5 for fixed-fixed, and 2 for fixed-free columns.

Goodman fatigue criterion

The modified Goodman line gives 1/n = σa/Se + σm/Sut. It estimates the safety factor for combined alternating and mean stress against fatigue failure.

First law for closed system

Q − W = ΔU for a closed system undergoing a process. Work done by the system is positive by convention, and heat added to the system is positive.

Generalized Hooke's law

Strain in the x direction is εx = [σx − ν(σy + σz)]/E, with cyclic permutations for other axes. Shear strain relates to shear stress by γ = τ/G.

Notch sensitivity factor

Fatigue notch factor Kf = 1 + q(Kt − 1), where Kt is the geometric stress concentration factor and q is notch sensitivity, ranging from 0 to 1.

Bearing L10 life

L10 = (C/P)^p million revolutions, with p = 3 for ball bearings and 10/3 for roller bearings. C is the dynamic load rating and P the equivalent load.

Fillet weld throat stress

Throat thickness of a fillet weld equals 0.707 times the leg size. Shear stress on the throat is τ = P/(0.707·w·L) for a weld of leg w and length L.

Helical spring rate

Spring rate k = G·d⁴/(8·D³·N_a), where d is wire diameter, D mean coil diameter, G shear modulus, and N_a the number of active coils.

Carbon equivalent formula

CE = %C + %Mn/6 + (%Cr + %Mo + %V)/5 + (%Ni + %Cu)/15. Higher carbon equivalent increases hardenability and susceptibility to weld cracking.

Quenching and tempering

Quenching forms hard, brittle martensite by rapid cooling. Tempering afterward restores toughness at some cost in hardness and relieves internal residual stresses.

Cold working effects

Deformation below the recrystallization temperature causes strain hardening, raising strength and lowering ductility, while giving better surface finish and tighter dimensional tolerances.

Taylor tool life equation

V·T^n = C relates cutting speed V to tool life T. Exponent n is roughly 0.1–0.15 for high-speed steel and 0.2–0.4 for carbide tools.

Tolerance versus allowance

Tolerance is the permitted spread between upper and lower limits of a dimension. Allowance is the intentional difference between mating part sizes, giving clearance or interference.

Basic hole system fits

In the basic hole system the hole is designated H. H7/g6 gives a clearance fit, while H7/p6 gives an interference fit because the shaft lies above basic size.

Shaft equivalent torque

For combined bending moment M and torque T, the ASME equivalent torque is T_e = √(M² + T²). Equivalent bending moment is M_e = ½[M + √(M² + T²)].

Bolt preload estimate

Initial bolt preload is commonly taken as about 0.75·S_p·A_t, where S_p is proof strength and A_t the tensile stress area, for reusable bolted joints.

Riser feeding requirement

A casting riser must solidify after the casting it feeds, so the riser modulus (volume over surface area) must exceed the modulus of the casting section.