Math & Numbers

Thermal stress in a fully constrained member under a uniform temperature change: σ_th = E·α·ΔT. Built-in typical Young's modulus E and expansion coefficient α for carbon/alloy steel, aluminum, copper, austenitic stainless and titanium, plus custom values. ΔT in K or °C (same magnitude), result in MPa. Heating (ΔT>0) → compressive stress in the member.

Math & Numbers

Compute the full set of moist-air (psychrometric) state properties from dry-bulb temperature plus one humidity input (relative humidity φ, wet-bulb temperature, dew-point temperature, or humidity ratio W). Returns humidity ratio W (kg/kg and g/kg), relative humidity φ (%), dew-point, wet-bulb, enthalpy h (kJ/kg dry air), specific volume v (m³/kg dry air), partial vapour pressure P_w, and saturation pressure P_ws. Uses the Magnus saturation-pressure fit; wet-bulb is solved iteratively from the thermodynamic psychrometric equation. Default standard atmosphere 101.325 kPa (adjustable). Temperature in °C/K/°F; all reported temperatures are in °C.

Math & Numbers

Compute the thermal comfort indices PMV (Predicted Mean Vote, −3 cold..+3 hot) and PPD (Predicted Percentage Dissatisfied, %) per ISO 7730 / ASHRAE 55, using the Fanger equations. Inputs: air temperature Ta, mean radiant temperature Tr, relative air velocity v_ar, relative humidity φ, metabolic rate M (met; 1 met = 58.2 W/m²), clothing insulation Icl (clo; 1 clo = 0.155 m²·K/W), and external work W (defaults to 0). The clothing surface temperature Tcl is solved iteratively. Returns a 7-level ASHRAE sensation label.

Math & Numbers

Apply the pump affinity laws to the same pump at different speeds or with a different impeller diameter. Speed mode: ratio = n2/n1; diameter mode: ratio = D2/D1. Then Q2 = Q1·ratio, H2 = H1·ratio², P2 = P1·ratio³. Q1, H1 and P1 are optional baseline-condition inputs; if all three are omitted, only the ratio is returned. Flow in m³/s/L/s/L/min/m³/h, head in m/ft, power in W/kW/hp, impeller diameter in m/cm/mm; SI equivalents (m³/s, m, W) are also reported.

Math & Numbers

Compute the total dynamic head H = (p_d - p_s)/(ρ·g) + Δz + (v_d² - v_s²)/(2g) of a centrifugal pump (m), then the fluid power P_fluid = ρ·g·Q·H and shaft power P_shaft = P_fluid/η. p_d and p_s are gauge pressures (suction may be negative for suction lift). Nozzle velocities v = 4Q/(π·D²) come from the flow rate and the discharge/suction nozzle diameters; if a nozzle diameter is left blank its velocity head is omitted. Pressure in Pa/kPa/bar/atm/psi, flow in m³/s/L/s/L/min/m³/h, density in kg/m³/g/cm³; power output in W/kW/hp.

Math & Numbers

Compute the available Net Positive Suction Head (NPSH_a) of a pump and compare it against the required NPSH (NPSH_r) from the pump curve. Head-balance form: NPSH_a = (p_surface_abs - p_vapor) / (ρ·g) + H_static - h_friction. Surface and vapor pressures are absolute; H_static is positive for flooded suction, negative for suction lift. Returns margin (NPSH_a - NPSH_r), ratio (NPSH_a/NPSH_r) and a classification: safe, marginal (margin < 0.5 m), or cavitation likely. If NPSH_r = 0, only NPSH_a is reported. Pressure in Pa/kPa/bar/atm/psi, length in m/ft, density in kg/m³/g/cm³/lb/ft³.

Math & Numbers

Compute the LC (RLC series/parallel) resonant frequency: f₀ = 1/(2π·√(L·C)). Resonant frequency is identical for series and parallel RLC; R only affects Q and bandwidth. Solves for f₀, L, or C from the other two, and returns angular resonance ω₀ and characteristic impedance √(L/C). L in H/mH/µH, C in F/µF/nF/pF, f in Hz/kHz/MHz.

Math & Numbers

Compute the Reynolds number Re = ρ·v·D/μ (dynamic viscosity) or Re = v·D/ν (kinematic viscosity, ν = μ/ρ) and classify the flow regime: Re < 2300 laminar, 2300 ≤ Re < 4000 transitional, Re ≥ 4000 turbulent. Diameter accepted in m/cm/mm. In dynamic mode the kinematic viscosity ν = μ/ρ is also returned. For internal pipe flow and general fluid-mechanics regime analysis.

Math & Numbers

Compute the operating time of an inverse-time overcurrent relay per IEC 60255-151: t = TMS·(k/((I/I_s)^α − 1)). Supports Standard Inverse (SI), Very Inverse (VI), Extremely Inverse (EI) and Long-Time Inverse (LTI) curves, and samples a T-I characteristic.

Math & Numbers

Compute transformer or feeder voltage regulation from equivalent-circuit parameters: ΔU% ≈ (I·R·cosφ ± I·X·sinφ)/U·100. Returns both the approximate (linear) and exact (phasor) values; supports lagging, unity and leading power factor.

Math & Numbers

Size the shunt capacitor needed to raise the power factor: C = P·(tanφ₁ − tanφ₂)/(2π·f·U²). Returns compensated reactive power Qc, capacitive reactance Xc, capacitor current Ic, and the required capacitance in F/μF.

Math & Numbers

Calculate the overall efficiency of a multi-stage transmission. η_total = η₁·η₂·…·ηₙ. Enter one stage efficiency per line (decimal, e.g. 0.98). Optionally add an input power to get the total loss and per-stage output power.