# LOGOS Engineering Workspace

> LOGOS is a SaaS platform for industrial engineering sizing. It runs 30 standards-based calculators — 17 hydraulics (Darcy-Weisbach, Colebrook-White, IEC 60534-2-1 control valves, ISO 5167-2 orifice plates, Joukowsky/Michaud water hammer, API 520/526 relief valves) and 13 electrical (IEC 60909 short circuit, IEEE 80 grounding grids, NBR 5410 ampacity, IEC 61643-11 SPD, IEC 60099-4 surge arresters, IEEE 485/1115 battery banks) — and produces a traceable calculation report in Word (.docx). Content is published in English (/en), Portuguese (/pt) and Spanish (/es) with reciprocal hreflang; the links below are the English versions.

## Plans

- Free: selected calculators, on-screen results, 2D/3D system diagrams and up to 3 saved projects.
- Pro: one discipline, unlimited projects and the Word report (.docx).
- Multidiscipline / Teams: every discipline, plus team collaboration on Teams. During the current open beta, full multidiscipline access is free for every account.

## Key pages

- [LOGOS home](https://www.logoscalc.com/en): one workspace for every industrial engineering discipline.
- [Hydraulics](https://www.logoscalc.com/en/hydraulics): pump sizing, head loss, control valves, orifice plates, water hammer.
- [Electrical](https://www.logoscalc.com/en/electrical): demand, cable sizing, short circuit, grounding, surge protection, MCC.
- [Engineering blog](https://www.logoscalc.com/en/blog): field-failure case studies linked to the calculators.
- [Create free account](https://www.logoscalc.com/en/signup): start calculating in the logged-in workspace.

## Hydraulics calculators

- [Pump sizing: system curve, operating point and NPSH](https://www.logoscalc.com/en/hydraulics/tools/pump-sizing): Size a centrifugal pump: total dynamic head TDH = static head + friction loss (Darcy-Weisbach / Swamee-Jain), operating point and available NPSH.
- [Identical pumps in parallel — combined curve, operating point and flow per pump](https://www.logoscalc.com/en/hydraulics/tools/pumps-in-parallel): Build the parallel pump curve — Q_comb = N·Q_1 at the same head — find the operating point against the system curve and get the real flow per pump.
- [Pumps in series calculation — combined curve and high-pressure discharge](https://www.logoscalc.com/en/hydraulics/tools/pumps-in-series): Pumps in series add HEAD at the same flow rate: build the combined curve H = H₁ + H₂, find the operating point and the head delivered by each pump.
- [Sizing a pumping system with a recirculation line and two control valves](https://www.logoscalc.com/en/hydraulics/tools/pump-with-recirculation): Size the minimum-flow recirculation line: the bypass flow as a share of BEP, the two valves, and the effect on the operating point of the main line.
- [Pump sizing with a control valve and Cv calculation](https://www.logoscalc.com/en/hydraulics/tools/pump-with-control-valve): Size the control valve on a pump discharge: Cv per IEC 60534-2-1, the head loss it adds and how that shifts the system curve and the operating point.
- [Orifice plate sizing in pumping systems and the ΔP at the worst-case flow](https://www.logoscalc.com/en/hydraulics/tools/pump-with-orifice-plate): Size an orifice plate on a pump discharge per ISO 5167-2: beta ratio, discharge coefficient C, the measured ΔP and the non-recoverable pressure loss.
- [Fixed recirculation with an orifice plate sized for Q70](https://www.logoscalc.com/en/hydraulics/tools/recirculation-with-orifice-plate): Size the restriction orifice on a minimum-flow recirculation line: the bore for the target bypass flow, the ΔP and the non-recoverable pressure loss.
- [Gravity-Flow Rate Calculation Between Two Reservoirs](https://www.logoscalc.com/en/hydraulics/tools/gravity-flow): Gravity flow in a full pipe: the elevation head available, friction loss by Darcy-Weisbach / Colebrook — not Hazen-Williams — and the resulting flow rate.
- [Gravity flow with a control valve: flow rate, Cv and cavitation](https://www.logoscalc.com/en/hydraulics/tools/gravity-flow-with-control-valve): Size a control valve on a gravity line: Cv per IEC 60534-2-1 from the available static head, the cavitation index σ and the flashing check.
- [Sizing a multi-branch pumping network solved by Newton-Raphson](https://www.logoscalc.com/en/hydraulics/tools/multi-branch-network): Solve the flow distribution of a branched network with one pump and up to 20 branches: Newton-Raphson at the nodes, head loss by Darcy-Weisbach.
- [Multi-branch closed unification loop: supply/return headers and hydraulic balancing](https://www.logoscalc.com/en/hydraulics/tools/multi-branch-with-unification-loop): Solve a closed-loop pipe network: flow balance at the nodes and zero net head loss around the loop — the Hardy Cross problem, solved by Newton-Raphson.
- [Control valve sizing for liquids: Cv, Kv and cavitation](https://www.logoscalc.com/en/hydraulics/tools/control-valve-for-liquids): Size a liquid control valve per IEC 60534-2-1 / ISA 75.01.01: Cv = Q·√(SG/ΔP), the FL choked-flow limit, cavitation index and the Kv ↔ Cv conversion.
- [Control valve sizing for steam and gas (IEC 60534-2-1)](https://www.logoscalc.com/en/hydraulics/tools/control-valve-for-vapor): Size a steam control valve per IEC 60534-2-1 (Eq. N6): required Cv/Kv, expansion factor Y, xT, choked flow and the outlet steam velocity check.
- [Sizing a pressure relief valve (PRV) for liquids per API 520](https://www.logoscalc.com/en/hydraulics/tools/relief-valve-for-liquids): Size a liquid PSV per API 520: area A = Q/(38·Kd·Kw·Kc·Kv)·√(G/ΔP), the Kd/Kw/Kc/Kv factors and the next standard API 526 orifice letter.
- [Steam safety valve (SV) sizing per API 520](https://www.logoscalc.com/en/hydraulics/tools/safety-valve-for-steam): Size a steam PSV per API 520: required discharge area from the relieving capacity, the KN and KSH correction factors and the next API 526 orifice letter.
- [Orifice plate flow metering (ISO 5167-2)](https://www.logoscalc.com/en/hydraulics/tools/orifice-plate): Size an orifice plate per ISO 5167-2: beta ratio β = d/D, the Reader-Harris/Gallagher discharge coefficient C, the ΔP and the permanent pressure loss.
- [Water hammer — hydraulic transient, Joukowsky pressure surge and critical time 2L/a](https://www.logoscalc.com/en/hydraulics/tools/water-hammer): Joukowsky equation ΔP = ρ·a·ΔV (head: ΔH = a·ΔV/g) for water hammer, with Korteweg wave speed a, critical time Tc = 2L/a and Michaud gradual closure.

## Electrical calculators

- [Short-circuit current calculation per IEC 60909: Ik″, peak ip and minimum Ik″](https://www.logoscalc.com/en/electrical/tools/short-circuit): Peak factor kappa = 1.02 + 0.98 x e^(-3 x R/X) and ip = kappa x √2 x Ik″ per IEC 60909-0 (Eq. 55/56), with Ik″, minimum Ik″ and a worked example.
- [Electrical cable sizing: ampacity, correction factors and voltage drop per NBR 5410](https://www.logoscalc.com/en/electrical/tools/cable-list): Size power cables: design current Ib, ampacity with grouping and temperature correction (NBR 5410 Tab. 36/37) and the voltage drop over the run.
- [Electrical demand calculation: demand factor, diversity and reserve](https://www.logoscalc.com/en/electrical/tools/demand): Turn a connected load list into demand: P_demand = Σ(Pi × FDi), the demand and diversity factors, and the resulting transformer and feeder rating.
- [MCC sizing: drawers, incoming cubicle and busbar](https://www.logoscalc.com/en/electrical/tools/mcc-drawer-sizing): Size a motor control centre per IEC 61439: drawer per motor, columns, main busbar at 125 % of the load current and the short-circuit withstand Icw.
- [Distribution board (panelboard) sizing: nominal current, breakers, demand and busbar](https://www.logoscalc.com/en/electrical/tools/distribution-panel-sizing): Size a distribution board: busbar current rating and temperature rise, main and outgoing breakers, short-circuit withstand and the DIN module count.
- [Capacitor bank sizing: reactive power, stages and protection for power factor correction](https://www.logoscalc.com/en/electrical/tools/capacitor-bank): Size a power factor correction bank: Qc = P·(tanφ₁ − tanφ₂), the step split, the resonance check against harmonics and the IEC 60831 capacitor rating.
- [Surge arrester sizing: Uc, Ur, TOV capability and NBI protective margin](https://www.logoscalc.com/en/electrical/tools/surge-arrester): Select a metal-oxide (ZnO) arrester per IEC 60099-4: Uc/MCOV above the continuous voltage, Ur for the TOV, and the protective margin over the BIL.
- [SPD sizing: Type, Uc, Up and coordination Up ≤ Uw](https://www.logoscalc.com/en/electrical/tools/spd-surge-protection): Select a surge protective device per IEC 61643-11: Type 1/2/3 by installation point, Uc above the system voltage and Up below the equipment withstand.
- [Instrument transformer sizing: CT ratio, accuracy class, burden and thermal rating](https://www.logoscalc.com/en/electrical/tools/ct-vt): Size instrument transformers per IEC 61869-2/-3: CT ratio, metering (0.2/0.5) vs protection (5P/10P) accuracy class, burden in VA and saturation.
- [Cable trays and fill: tray width, conduit size and occupancy ratio](https://www.logoscalc.com/en/electrical/tools/trays-and-fill): Compute cable tray fill: fill % = Σ cable cross-sections / usable tray area, the 50 % limit for power cables and conduit occupancy on the same run.
- [Grounding grid sizing: earth resistance, GPR, step and touch voltage](https://www.logoscalc.com/en/electrical/tools/grounding-grid-sizing): Design an earthing grid per IEEE 80 / NBR 15751: grid resistance Rg, ground potential rise GPR, mesh voltage Em and the tolerable touch and step limits.
- [Battery bank sizing: required Ah, derating factors and series-parallel arrangement](https://www.logoscalc.com/en/electrical/tools/battery-bank-sizing): Size a stationary battery bank per IEEE 485/1115: the DC duty cycle, required Ah with aging and temperature correction, cell count and series-parallel.
- [DC cable sizing: voltage drop, ampacity and commercial cross-section](https://www.logoscalc.com/en/electrical/tools/dc-cable-sizing): Size DC cables for 24, 48 or 125 V systems: section from the voltage drop A = 2·L·I·ρ/ΔV, the ampacity check and the short-circuit thermal limit.

## Reference tables

- [Minor loss coefficients (K) for pipe fittings](https://www.logoscalc.com/en/reference/minor-loss-k-coefficients): K coefficients for minor (local) head losses: elbows, bends, tees, gate/globe/check valves, entrances and exits — with the h = K·v²/2g method explained.
- [NBR 5410 ampacity tables (current-carrying capacity)](https://www.logoscalc.com/en/reference/nbr-5410-ampacity-table): Full NBR 5410 ampacity tables (Tables 36–39): copper and aluminum, PVC 70 °C and XLPE/EPR 90 °C, methods A1–F, 2.5 to 630 mm², 3 loaded conductors.
- [NBR 5410 ampacity correction (derating) factors](https://www.logoscalc.com/en/reference/nbr-5410-derating-factors): All NBR 5410 derating factors: ambient and soil temperature (Table 40), circuit grouping (42), multilayer (43), soil resistivity (41) and burial depth.
- [Absolute pipe roughness table (ε)](https://www.logoscalc.com/en/reference/pipe-roughness): Absolute roughness ε in mm for 31 pipe materials — carbon steel, stainless, PVC, HDPE, cast iron, concrete — with min/typical/max values, new and aged.

## Blog

- [Water hammer on pump trip — the case that sets your pipeline's pressure rating](https://www.logoscalc.com/en/blog/water-hammer-pump-trip): A pump trip on power failure produces more surge than a valve closure. Korteweg, 2L/a, Joukowsky vs Michaud, and a worked 1,200 m case.

## Notes

- The physics of every calculation lives in versioned Supabase Edge Functions (single source of truth); the public pages explain the methods but do not compute — computation happens in the logged-in workspace.
- Domain terms: flow rate (Q, m³/h), total head/TDH, head loss, friction factor, NPSH, operating point, water hammer, discharge coefficient; demand factor, ampacity, fault level (Ik″), touch/step voltage, surge arrester, SPD, single-line diagram.
- Full version with abstracts and standards per tool: https://www.logoscalc.com/llms-full.txt