PE Mechanical Thermal Fluids flashcards

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

Reynolds number

Re = ρVD/μ = VD/ν. It compares inertia to viscous forces and sets whether pipe flow is laminar (below about 2300) or turbulent (above about 4000).

Darcy-Weisbach equation

h_f = f(L/D)(V²/2g) gives frictional head loss in a pipe. The friction factor f comes from 64/Re for laminar flow or the Moody chart/Colebrook equation for turbulent flow.

Bernoulli equation

P/ρ + V²/2 + gz = constant along a streamline for steady, incompressible, frictionless flow. Add pump head and subtract losses when work or friction is present.

Continuity equation

For steady flow, ṁ = ρAV = AV/v is constant between inlet and exit. For incompressible flow, A1V1 = A2V2, so velocity rises where area falls.

Dittus-Boelter correlation

Nu = 0.023 Re^0.8 Pr^n predicts turbulent, fully developed convection in a smooth pipe, with n = 0.4 for heating and 0.3 for cooling of the fluid.

Fourier conduction law

q = -kA(dT/dx). Heat rate is proportional to conductivity, area, and temperature gradient, and flows in the direction of decreasing temperature.

Thermal resistance, plane wall

R = L/(kA) for conduction through a plane wall. Resistances in series add, and q = ΔT/R_total, mirroring electrical circuits.

Log-mean temperature difference

ΔT_lm = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2) is the driving temperature difference for a heat exchanger. For multipass or crossflow arrangements, multiply by a correction factor F.

Carnot efficiency

η = 1 - T_L/T_H with absolute temperatures. It is the maximum possible efficiency for any cycle operating between those two thermal reservoirs.

Rankine cycle efficiency

η = (w_turbine - w_pump)/q_boiler. Pump work is approximated as v_f(P2 - P1); reheat and regeneration raise the mean temperature of heat addition.

Brayton cycle efficiency

For the ideal air-standard cycle, η = 1 - 1/r_p^((k-1)/k). Efficiency depends only on pressure ratio and specific heat ratio, not on turbine inlet temperature.

Otto cycle efficiency

η = 1 - 1/r^(k-1), where r is the compression ratio. Efficiency increases with compression ratio and with the specific heat ratio of the working gas.

Diesel cycle efficiency

η = 1 - (1/r^(k-1))·(r_c^k - 1)/(k(r_c - 1)), where r_c is the cutoff ratio. For a given compression ratio, Diesel efficiency is below Otto efficiency.

Vapor-compression COP

COP_R = (h1 - h4)/(h2 - h1) for a refrigeration cycle, where h1 is evaporator exit and h2 is compressor discharge. COP_HP = COP_R + 1 for the same cycle.

Humidity ratio

W = 0.622 p_v/(P - p_v) is the mass of water vapor per mass of dry air. Dew point is the temperature at which p_v equals saturation pressure.

Adiabatic flame temperature

The temperature reached when fuel burns with no heat or work transfer. It is computed from an energy balance on reactants and products and is lowered by excess air.

Lumped capacitance criterion

Use lumped capacitance when Bi = hL_c/k < 0.1, meaning internal conduction resistance is small. Then the body is treated as a single uniform temperature.

Pump affinity laws

For a constant impeller diameter, Q ∝ N, H ∝ N², and P ∝ N³ as speed N changes. Doubling speed doubles flow, quadruples head, and multiplies power by eight.

Net positive suction head

NPSH_a = (P_atm - P_v)/(ρg) + z - h_L on the suction side. Cavitation is avoided when available NPSH exceeds the pump's required NPSH with margin.

System curve

H_sys = H_static + KQ² describes head required by the piping system versus flow. The pump operating point is where the pump curve crosses the system curve.

Pump specific speed

N_s = N√Q/H^(3/4) in US units (rpm, gpm, ft). It classifies impeller geometry: low values are radial, high values are axial, and efficiency peaks near design specific speed.

Polytropic compression work

w = n/(n-1)·P1v1[(P2/P1)^((n-1)/n) - 1] per unit mass. Intercooling between stages reduces total work by approaching isothermal compression.

Hydraulic diameter

D_h = 4A/P, where A is flow area and P is wetted perimeter. It lets circular-pipe friction and Reynolds correlations apply to noncircular ducts.

Choked flow

Occurs when downstream pressure is below the critical ratio P*/P0 = (2/(k+1))^(k/(k-1)), about 0.528 for air. Further lowering downstream pressure does not increase mass flow.

Fan total pressure

Total pressure equals static pressure plus velocity pressure, ρV²/2. Fan selection must match both flow and total pressure at the system operating point.

Effectiveness-NTU method

ε = q/q_max with q_max = C_min(T_h,in - T_c,in) and NTU = UA/C_min. It is used when outlet temperatures are unknown and avoids trial-and-error with LMTD.

Overall heat transfer coefficient

1/UA sums convection, wall conduction, and fouling resistances. Fouling adds resistance, so it reduces U and heat duty over time.

Fin efficiency

η_f = tanh(mL)/(mL) for a rectangular fin with adiabatic tip, where m = √(hP/(kA_c)). Higher conductivity and thinner, shorter fins raise efficiency.

Critical insulation radius

r_cr = k/h for a cylindrical layer. Adding insulation below this radius increases heat loss; adding it above the radius reduces heat loss.

Heat exchanger energy balance

q = ṁ_h c_p,h (T_h,in - T_h,out) = ṁ_c c_p,c (T_c,out - T_c,in). Property values are evaluated at the mean bulk temperature of each stream.

Radiation heat exchange

q = εσA(T_s⁴ - T_surr⁴) for a small gray surface in a large enclosure, with σ = 5.67×10⁻⁸ W/(m²·K⁴). Radiation grows rapidly with absolute temperature.