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McCabeFluidSuite

Fluid mechanics · McCabe–Smith–Harriott

Reynolds number & flow regime

Chapters 3–5 · Classification of laminar, transitional or turbulent regime in internal flow.

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Entradas

Default: water at 20 °C in 2" schedule 40 commercial steel pipe (Di ≈ 52.5 mm).

Lectura

Reynolds number

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Re = ρ·u·D / μ

Laminar

Re < 2100

Transitional

2100–4000

Turbulento

Re > 4000

Pipe pressure drop — Darcy-Weisbach & Moody

Chapter 5 · Friction factor via Colebrook-White; pipe pressure drop calculator.

Entradas

Lectura

Re

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f (Darcy)

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hf

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ΔP

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Centrifugal pump sizing & available NPSH

Chapter 8 · NPSH calculator — assesses cavitation risk by comparing NPSHa against the NPSHr from the manufacturer.

Entradas

Positive = flooded suction (source above the pump). Negative = suction lift.

Lectura

NPSH disponible

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NPSHa = (Pa−Pv)/(ρg) + Za − hfs

Margen vs. NPSHr

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Rule of thumb: a margin ≥ 1 m (or ≥ 0.6 m in well-controlled systems) is considered safe; always check against the NPSHr actual value from the manufacturer.

Particle terminal velocity

Chapter 7 · Terminal velocity particle calculator — McCabe-Smith-Harriott K criterion for Stokes, intermediate regime and Newton's law.

Entradas

Default: sand settling in water at 20 °C (ρp ≈ 2650 kg/m³).

Lectura

Terminal velocity

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Criterio K

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Rep

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Stokes

K < 3.3

Intermedio

3.3–43.6

Newton

43.6–2360

Minimum fluidisation

Chapter 7 · Minimum fluidization velocity calculator — Ergun equation solved as a quadratic in Remf.

Entradas

Default: a sand bed fluidised with air.

Lectura

Minimum fluidisation velocity

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Remf (Ergun equation)

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Orifice / Venturi meters

Chapter 8 · Orifice meter calculator — flow rate from the measured pressure drop.

Entradas

Lectura

Volumetric flow rate

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Q = Co·A2·√(2ΔP / (ρ(1−β⁴)))

Diameter ratio β = D₂/D₁

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Fluid mechanics calculators for chemical engineering — free, no sign-up

McCabeFluidSuite brings together in one place the calculators a student or process engineer needs daily for fluid-flow unit operations: a reynolds number calculator to classify the flow regime in pipes, a pressure drop calculator pipe based on Darcy-Weisbach and the Moody diagram, an NPSH calculator to prevent cavitation in centrifugal pumps, an terminal velocity particle calculator and a minimum fluidization velocity calculator based on the McCabe-Smith-Harriott K criterion and the Ergun equation, and an orifice meter calculator to size orifice plates and Venturi tubes. All the pipe pressure drop calculation and the remaining routines run entirely in the browser: no backend, no accounts, and simultaneous support for SI and USCS units.

McCabe-Smith formula guide

1. Reynolds number ▾

Re = ρ·u·D / μ

The Reynolds number compares inertial forces with viscous forces inside the fluid. Below 2100 the flow is laminar and the streamlines are parallel; above 4000 turbulence dominates with chaotic mixing; between the two lies a transition zone where behaviour is unpredictable and a safety margin is advisable.

2. Darcy-Weisbach and the Colebrook-White equation ▾

hf = f·(L/D)·(u²/2g)   |   1/√f = −2log₁₀(ε/3.7D + 2.51/(Re√f))

In laminar flow the Darcy friction factor is simply 64/Re. In turbulent flow the Colebrook-White equation is implicit and must be solved iteratively; this calculator uses the Swamee-Jain approximation as its initial estimate and refines it by successive substitution until it converges — the same approach that underlies the Moody diagram.

3. NPSH disponible ▾

NPSHa = (Pa − Pv)/(ρg) ± Za − hfs

The available NPSH measures the energy above the vapour pressure present at the pump suction. If it falls below the NPSH required by the manufacturer (NPSHr), the liquid vaporises locally and collapses inside the impeller: cavitation, premature erosion and loss of hydraulic efficiency.

4. Particle terminal velocity (K criterion) ▾

K = Dp[gρ(ρp−ρ)/μ²]1/3

McCabe, Smith and Harriott propose the dimensionless parameter K to select the applicable settling law directly, without iterating: Stokes for K < 3.3, an intermediate regime for 3.3–43.6 and Newton's law for 43.6–2360, each with its own closed-form correlation for the terminal velocity ut.

5. Minimum fluidisation (Ergun equation) ▾

150(1−εmf)/(φs²εmf³)·Remf + 1.75/(φsεmf³)·Remf² = gDp³ρ(ρp−ρ)/μ²

The Ergun equation combines the viscous and inertial pressure drop across a packed bed. Setting that pressure drop equal to the apparent weight of the bed gives a quadratic in Remf, whose positive root defines the minimum superficial velocity at which the bed begins to fluidise.

6. Orifice and Venturi meters ▾

Q = Co·A2·√(2ΔP / (ρ(1−β⁴)))   |   β = D2/D1

Both meters infer the flow rate from the pressure drop generated when the fluid is forced through a restriction. The orifice plate is inexpensive but dissipative (Co ≈ 0.6); the Venturi tube recovers almost all the pressure thanks to its gradual conical profile (Co ≈ 0.98), at the cost of greater length and manufacturing cost.

Preguntas frecuentes

Aviso legal: McCabeFluidSuite is an educational and quick-check tool for chemical engineering students and practitioners. The results are based on standard correlations from the literature (McCabe, Smith & Harriott, Unit Operations of Chemical Engineering) and do not replace the judgement of a certified engineer, analysis with validated process software (Aspen Plus, Aspen HYSYS, EDR), or compliance with the applicable standards (ASME, API, ISA). Always verify critical results before using them in design, process safety or engineering decisions.