Convert magnetic permeability (μ) between absolute permeability in henry per metre (H/m, SI unit; equivalently N/A² or T·m/A) and relative permeability μ_r (dimensionless). Vacuum permeability μ₀ = 4π×10⁻⁷ H/m ≈ 1.25663706×10⁻⁶ H/m (defined pre-2019; since the 2019 SI redefinition it is a measured quantity with relative uncertainty 1.6×10⁻¹⁰, so the 4π×10⁻⁷ form is still exact for all engineering purposes). Relations used: μ = μ_r × μ₀ and μ_r = μ / μ₀ (magnetic susceptibility χ_m = μ_r − 1). Reference: vacuum μ_r = 1, copper 0.999994 (diamagnetic), aluminum 1.000022 (paramagnetic), iron ≈ 5000 (ferromagnetic).

Math & Numbers

Poisson's Ratio Calculator

Calculate Poisson's ratio ν = −ε_transverse / ε_longitudinal and solve any of the three unknowns: ratio, lateral strain, or longitudinal strain. Tensile ε_long > 0 produces lateral contraction ε_lat < 0. Typical values: steel ≈ 0.30, aluminum ≈ 0.33, rubber ≈ 0.49, cork ≈ 0. Theoretical isotropic range 0 ≤ ν ≤ 0.5.

Math & Numbers

Psychrometric Properties (Humidity Ratio / Enthalpy / RH)

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

Pump Affinity Laws Calculator (Q∝n, H∝n², P∝n³)

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

Pump Head & Shaft Power Calculator (H, P=ρgQH/η)

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

Pipe Friction Factor Calculator (Colebrook-White / Haaland)

Compute the Darcy friction factor: laminar closed-form f=64/Re for Re<2000, or iterative Colebrook-White solution for transitional/turbulent flow, with the explicit Haaland approximation always returned as a cross-check. Reports relative roughness ε/D, absolute roughness (m), diameter (m), flow regime (laminar/transitional/turbulent), effective method and iteration count. Roughness ε in m/mm/µm, diameter D in m/cm/mm.

Math & Numbers

Pipe Pressure Drop Calculator (Darcy-Weisbach)

Compute the Darcy-Weisbach major (friction) pressure drop in a straight pipe: ΔP = f·(L/D)·(ρ·v²/2) Pa and head loss h_f = f·(L/D)·v²/(2g) m. The user supplies the Darcy friction factor f (not the Fanning factor). Length in m/km/ft, diameter in m/cm/mm/inch, density in kg/m³/g/cm³/lb/ft³ — all normalised to SI internally. Returns ΔP in Pa, kPa and bar, and head loss in m and ft. Gravity defaults to 9.81 m/s² and may be overridden.

Math & Numbers

Pump NPSH (Net Positive Suction Head) Calculator & Cavitation Check

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

Power Factor Correction Calculator

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.