ISRO Scientist Mechanical flashcards

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

Carnot efficiency

Maximum possible thermal efficiency between two reservoirs at absolute temperatures T_H and T_L: η = 1 − T_L/T_H. It is a reversible upper bound independent of the working fluid.

Otto cycle efficiency

For an ideal air-standard Otto cycle, η = 1 − 1/r^(γ−1), where r is the compression ratio and γ the specific heat ratio. Higher compression ratio or lower γ raises efficiency.

Diesel cycle efficiency

η = 1 − [1/r^(γ−1)]·[ρ^γ − 1]/[γ(ρ − 1)], where ρ is the cut-off ratio V_3/V_2. For equal compression ratio the Diesel cycle is less efficient than the Otto cycle.

Reynolds number

Re = ρVD/μ = VD/ν, the ratio of inertial to viscous forces. Pipe flow is laminar below about 2300, transitional to 4000, and turbulent above 4000.

Darcy–Weisbach equation

Major head loss in a pipe: h_f = f(L/D)(V²/2g), where f is the Darcy friction factor. For laminar flow f = 64/Re; for turbulent flow f comes from the Moody chart.

Bernoulli equation

P/ρg + V²/2g + z = constant along a streamline for steady, incompressible, frictionless flow. It cannot be applied across pumps, turbines, or shock waves.

Continuity equation

For steady flow, ṁ = ρ_1A_1V_1 = ρ_2A_2V_2. For incompressible flow this reduces to A_1V_1 = A_2V_2, so velocity rises where area falls.

Normal shock relations

Across a normal shock, Mach number drops below 1, static pressure and temperature rise, stagnation temperature stays constant, and stagnation pressure falls because entropy increases.

Choked flow condition

In a converging nozzle, mass flow reaches a maximum when the throat reaches Mach 1. Further lowering of downstream pressure cannot increase the mass flow rate.

First law for open system

Steady-flow energy equation per unit mass: q − w = (h_2 − h_1) + (V_2² − V_1²)/2 + g(z_2 − z_1). Throttling has q = w = 0 and constant h.

Entropy change ideal gas

Δs = c_p ln(T_2/T_1) − R ln(P_2/P_1) for constant specific heats. A process is possible only if total entropy generation is zero (reversible) or positive (irreversible).

Bending stress formula

σ = My/I, where y is distance from the neutral axis and I the second moment of area. Maximum stress occurs at the outermost fibre, y = c.

Simply supported beam deflection

Under a central point load W, maximum deflection is δ = WL³/(48EI) at midspan. Under uniform load w per unit length, δ = 5wL⁴/(384EI).

Torsion of circular shaft

Shear stress τ = Tr/J and twist angle θ = TL/(GJ). For a solid shaft J = πd⁴/32; for a hollow shaft J = π(d_o⁴ − d_i⁴)/32.

Principal stress formula

σ_1,2 = (σ_x + σ_y)/2 ± √[((σ_x − σ_y)/2)² + τ_xy²]. These are the extreme normal stresses on planes where shear stress is zero.

Maximum shear stress

In-plane maximum shear τ_max = √[((σ_x − σ_y)/2)² + τ_xy²] = (σ_1 − σ_2)/2. For 3-D stress, use (σ_max − σ_min)/2 including the zero principal stress.

Von Mises yield criterion

Yielding occurs when √(σ_1² − σ_1σ_2 + σ_2²) equals the tensile yield strength. It is based on distortion energy and matches ductile metals better than Tresca.

Tresca yield criterion

Yielding occurs when maximum shear stress reaches S_y/2, that is σ_1 − σ_3 = S_y. It is conservative relative to von Mises and is used for pressure vessels.

Euler buckling load

P_cr = π²EI/(KL)², where K depends on end conditions: 0.5 fixed-free, 0.7 pinned-fixed, 1.0 pinned-pinned, 2.0 fixed-fixed. Valid only for slenderness above the critical value.

Rankine buckling formula

For short or intermediate columns, P = σ_c A/[1 + a(L/k)²], where σ_c is crushing stress and k the radius of gyration. It applies below the critical slenderness ratio.

S-N curve and endurance limit

Stress amplitude versus cycles to failure. Below the endurance limit (about 10⁶–10⁷ cycles for steels) fatigue failure does not occur; non-ferrous metals show no true limit.

Marin modifying factors

Endurance limit of a part: S_e = k_a k_b k_c k_d k_e S_e', correcting the specimen value for surface, size, load, temperature, and reliability.

Chvorinov's rule

Solidification time t = B(V/A)², where V/A is the casting modulus. A riser must have a larger modulus than the casting so it freezes last and feeds shrinkage.

Merchant shear angle relation

2φ + β − α = 90° gives the shear angle φ for minimum cutting energy, with β the friction angle and α the rake angle. Chip ratio r = t_1/t_2 = sin φ/cos(φ − α).

Taylor tool life equation

VT^n = C, where V is cutting speed, T tool life, and n, C are empirical constants. Higher speed shortens tool life; n is about 0.1–0.15 for HSS.

Welding heat input

Heat input per unit length H = ηVI/v, where η is arc efficiency, V voltage, I current, and v travel speed. Higher travel speed lowers heat input and narrows the heat-affected zone.

Carnot COP refrigerator

COP_max = T_L/(T_H − T_L) for a refrigerator and T_H/(T_H − T_L) for a heat pump. Actual COP is always lower because of irreversibilities.

Hydraulic diameter

D_h = 4A/P, where A is flow cross-section and P the wetted perimeter. Used for Reynolds number and friction factor in non-circular ducts; for a circular pipe D_h equals D.

Stagnation temperature

T_0 = T + V²/(2c_p), the temperature reached if the flow is brought to rest adiabatically. It is constant across an adiabatic normal shock but drops across a shock with heat transfer.

Mach number regimes

M = V/c, with c = √(γRT). Subsonic M < 1, sonic M = 1, supersonic 1 < M < 5, hypersonic M > 5. Compressibility effects become significant above M ≈ 0.3.

Stress concentration factor

K_t = σ_max/σ_nom, a geometric factor for holes, fillets, and notches. For ductile materials under static load, K_t is often ignored; under fatigue it multiplies nominal stress.

Thermal stress in bar

Fully constrained bar: σ = −EαΔT. If free to expand, thermal stress is zero. Partial constraint gives σ = EαΔT multiplied by the degree of restraint.